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Sample records for mean-field theory

  1. Algebraic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Dankova, T. S.; Rosensteel, G.

    1998-10-01

    Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.

  2. Embedded mean-field theory.

    PubMed

    Fornace, Mark E; Lee, Joonho; Miyamoto, Kaito; Manby, Frederick R; Miller, Thomas F

    2015-02-10

    We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarking of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory, using PBE or B3LYP/6-31G* in the high-level subsystem and LDA/STO-3G in the low-level subsystem; we also investigate different levels of density fitting in the two subsystems. Over a wide range of chemical problems, we find EMFT to perform accurately and stably, smoothly converging to the high-level of theory as the active subsystem becomes larger. In most cases, the performance is at least as good as that of ONIOM, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through aromatic systems and by examples that involve more complicated electronic structure. EMFT is simple and parameter free, and based on the tests provided here, it offers an appealing new approach to a multiscale electronic structure.

  3. Relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Meng, Jie; Ring, Peter; Zhao, Pengwei

    In this chapter, the covariant energy density functional is constructed with both the meson-exchange and the point-coupling pictures. Several widely used functionals with either nonlinear or density-dependent effective interactions are introduced. The applications of covariant density functional theory are demonstrated for infinite nuclear matter and finite nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes. Finally, a relativistic description of the nuclear landscape has been discussed, which is not only important for nuclear structure, but also important for nuclear astrophysics, where we are facing the problem of a reliable extrapolation to the very neutron-rich nuclei.

  4. The Mean-Field Flux Pinning Theory

    NASA Astrophysics Data System (ADS)

    Stejic, George

    We develop the Mean-Field Flux Pinning Theory, designed to model the flux line lattice (FLL) as it interacts with itself, the flux pinning centers and the geometry of the superconductor. Like other mean-field theories, the mean-field flux pinning theory does not attempt to model the FLL completely. Instead, it utilizes a simplified model for the FLL, termed the mean-field FLL, in which the FLL is modelled as a continuous vector field rather than as discrete fluxons as in other theories. By so doing, the interactions of the FLL are greatly simplified and more easily modelled. One application of the mean-field flux pinning theory is to predict J_{c} from microstructural data, which we use to determine the optimal Nb-Ti microstructures with (1) alpha -Ti pinning centers and (2) Nb pinning centers. The microstructure is modelled on a grid in which the local values of T_{c} and kappa reflect the spatial distribution of the pinning centers and the superconductor. Using this model, we solve the G-L equations and calculate the pinning potential defined as the vortex free energy as a function of position. We conclude that the ideal Nb-Ti microstructure with alpha-Ti pinning centers would require 40 volume percent of alpha -Ti and have 6nm thick pinning centers. In the Nb pinning center case, the ideal microstructure requires 50 volume percent of Nb and would have 6nm pinning centers. Another application for the mean-field flux pinning theory is to model the FLL as it interacts with the penetrating magnetic fields within lambda of the superconducting surface. Using this theory, we study the effects of sample geometry on the FLL and J _{c} for the thin film geometry. We find that the FLL becomes increasingly distorted as the film thickness is reduced and that J_{c } increases sharply for dimensions less that lambda. These predictions are experimentally evaluated in Nb-Ti thin films. Our results show that J_{c} values as high as 1/3 of J_{d} and a strong orientational

  5. Bosonic Dynamical Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Snoek, Michiel; Hofstetter, Walter

    2013-02-01

    We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.

  6. Beyond mean field theory: statistical field theory for neural networks

    PubMed Central

    Buice, Michael A; Chow, Carson C

    2014-01-01

    Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014

  7. Machine Learning for Dynamical Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Littlewood, P. B.; Millis, Andy

    2014-03-01

    Machine Learning (ML), an approach that infers new results from accumulated knowledge, is in use for a variety of tasks ranging from face and voice recognition to internet searching and has recently been gaining increasing importance in chemistry and physics. In this talk, we investigate the possibility of using ML to solve the equations of dynamical mean field theory which otherwise requires the (numerically very expensive) solution of a quantum impurity model. Our ML scheme requires the relation between two functions: the hybridization function describing the bare (local) electronic structure of a material and the self-energy describing the many body physics. We discuss the parameterization of the two functions for the exact diagonalization solver and present examples, beginning with the Anderson Impurity model with a fixed bath density of states, demonstrating the advantages and the pitfalls of the method. DOE contract DE-AC02-06CH11357.

  8. Nonequilibrium dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    Freericks, James

    2007-03-01

    Dynamical mean-field theory (DMFT) is establishing itself as one of the most powerful approaches to the quantum many-body problem in strongly correlated electron materials. Recently, the formalism has been generalized to study nonequilibrium problems [1,2], such as the evolution of Bloch oscillations in a material that changes from a diffusive metal to a Mott insulator [2,3]. Using a real-time formalism on the Kadanoff-Baym-Keldysh contour, the DMFT algorithm can be generalized to the case of systems that are not time-translation invariant. The computational algorithm has a parallel implementation with essentially a linear scale up when running on thousands of processors. Results on the decay of Bloch oscillations, their change of character within the Mott insulator, and movies on how electrons redistribute themselves due to their response to an external electrical field will be presented. In addition to solid-state applications, this work also applies to the behavior of mixtures of light and heavy cold atoms in optical lattices. [1] V. M. Turkowski and J. K. Freericks, Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields, Phys. Rev. B 075108 (2006); Erratum, Phys. Rev. B 73, 209902(E) (2006). [2] J. K. Freericks, V. M. Turkowski , and V. Zlati'c, Nonlinear response of strongly correlated materials to large electric fields, in Proceedings of the HPCMP Users Group Conference 2006, Denver, CO, June 26--29, 2006 edited by D. E. Post (IEEE Computer Society, Los Alamitos, CA, 2006), to appear. [3] J. K. Freericks, V. M. Turkowski, and V. Zlati'c, Nonequilibrium dynamical mean-field theory, submitted to Phys. Rev. Lett. cond-mat//0607053.

  9. Dynamics of polymers: A mean-field theory

    SciTech Connect

    Fredrickson, Glenn H.; Orland, Henri

    2014-02-28

    We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ρ and a conjugate MSR response field ϕ, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.

  10. Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models

    NASA Astrophysics Data System (ADS)

    Strand, Hugo U. R.; Eckstein, Martin; Werner, Philipp

    2015-01-01

    We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium "phase diagrams" that map out the different dynamical regimes.

  11. Dynamical mean-field theory from a quantum chemical perspective.

    PubMed

    Zgid, Dominika; Chan, Garnet Kin-Lic

    2011-03-01

    We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.

  12. Dynamical mean-field theory for flat-band ferromagnetism

    NASA Astrophysics Data System (ADS)

    Nguyen, Hong-Son; Tran, Minh-Tien

    2016-09-01

    The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.

  13. The effectiveness of mean-field theory for avalanche distributions

    NASA Astrophysics Data System (ADS)

    Lee, Edward; Raju, Archishman; Sethna, James

    We explore the mean-field theory of the pseudogap found in avalanche systems with long-range anisotropic interactions using analytical and numerical tools. The pseudogap in the density of low-stability states emerges from the competition between stabilizing interactions between spins in an avalanche and the destabilizing random movement towards the threshold caused by anisotropic couplings. Pazmandi et al. have shown that for the Sherrington-Kirkpatrick model, the pseudogap scales linearly and produces a distribution of avalanche sizes with exponent t=1 in contrast with that predicted from RFIM t=3/2. Lin et al. have argued that the scaling exponent ? of the pseudogap depends on the tail of the distribution of couplings and on non-universal values like the strain rate and the magnitude of the coupling strength. Yet others have argued that the relationship between the pseudogap scaling and the distribution of avalanche sizes is dependent on dynamical details. Despite the theoretical arguments, the class of RFIM mean-field models is surprisingly good at predicting the distribution of avalanche sizes in a variety of different magnetic systems. We investigate these differences with a combination of theory and simulation.

  14. Mean-field theory of assortative networks of phase oscillators

    NASA Astrophysics Data System (ADS)

    Restrepo, Juan G.; Ott, Edward

    2014-09-01

    Employing the Kuramoto model as an illustrative example, we show how the use of the mean-field approximation can be applied to large networks of phase oscillators with assortativity. We then use the ansatz of Ott and Antonsen (Chaos, 19 (2008) 037113) to reduce the mean-field kinetic equations to a system of ordinary differential equations. The resulting formulation is illustrated by application to a network Kuramoto problem with degree assortativity and correlation between the node degrees and the natural oscillation frequencies. Good agreement is found between the solutions of the reduced set of ordinary differential equations obtained from our theory and full simulations of the system. These results highlight the ability of our method to capture all the phase transitions (bifurcations) and system attractors. One interesting result is that degree assortativity can induce transitions from a steady macroscopic state to a temporally oscillating macroscopic state through both (presumed) Hopf and SNIPER (saddle-node, infinite period) bifurcations. Possible use of these techniques to a broad class of phase oscillator network problems is discussed.

  15. More is the Same; Phase Transitions and Mean Field Theories

    NASA Astrophysics Data System (ADS)

    Kadanoff, Leo P.

    2009-12-01

    This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related concepts derived from condensed matter and statistical physics. The key technical ideas go under the names of "singularity", "order parameter", "mean field theory", "variational method", "correlation length", "universality class", "scale changes", and "renormalization". The first four of these will be considered here. In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in some statistical variable. The discontinuous property is called the order parameter. Each phase transition has its own order parameter. The possible order parameters range over a tremendous variety of physical properties. These properties include the density of a liquid-gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when the discontinuity in the jump approaches zero. This article is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of phase transition phenomena. Much of the material in this review was first prepared for the Royal Netherlands Academy of Arts and

  16. Dynamical mean-field theory for molecules and nanostructures.

    PubMed

    Turkowski, Volodymyr; Kabir, Alamgir; Nayyar, Neha; Rahman, Talat S

    2012-03-21

    Dynamical mean-field theory (DMFT) has established itself as a reliable and well-controlled approximation to study correlation effects in bulk solids and also two-dimensional systems. In combination with standard density-functional theory (DFT), it has been successfully applied to study materials in which localized electronic states play an important role. It was recently shown that this approach can also be successfully applied to study correlation effects in nanostructures. Here, we provide some details on our recently proposed DFT+DMFT approach to study the magnetic properties of nanosystems [V. Turkowski, A. Kabir, N. Nayyar, and T. S. Rahman, J. Phys.: Condens. Matter 22, 462202 (2010)] and apply it to examine the magnetic properties of small FePt clusters. We demonstrate that DMFT produces meaningful results even for such small systems. For benchmarking and better comparison with results obtained using DFT+U, we also include the case of small Fe clusters. As in the case of bulk systems, the latter approach tends to overestimate correlation effects in nanostructures. Finally, we discuss possible ways to further improve the nano-DFT+DMFT approximation and to extend its application to molecules and nanoparticles on substrates and to nonequilibrium phenomena. PMID:22443749

  17. Real-space renormalized dynamical mean field theory

    NASA Astrophysics Data System (ADS)

    Kubota, Dai; Sakai, Shiro; Imada, Masatoshi

    2016-05-01

    We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.

  18. Mean-field theory and ɛ expansion for Anderson localization

    NASA Astrophysics Data System (ADS)

    Harris, A. B.; Lubensky, T. C.

    1981-03-01

    A general field-theoretic formulation of the Anderson model for the localization of wave functions in a random potential is given in terms of n-component replicated fields in the limit n-->0, and is analyzed primarily for spatial dimension d>=4. Lengths ξ1 and ξ2 associated with the spatial decay of correlations in the single-particle and two-particle Green's functions, respectively, are introduced. Two different regimes, the weak coupling and strong coupling, are distinguished depending on whether ξ-11 or ξ-12, respectively, vanishes as the mobility energy, Ec, is approached. The weak-coupling regime vanishes as d-->4+. Mean-field theory is developed from the uniform minimum of the Lagrangian for both the strong- and weak-coupling cases. For the strong-coupling case it gives the exponents va=14, γa=βa=12, η=0, and μ=1, where βa is the exponent associated with the density of extended states and μ is that associated with the conductivity. Simple heuristic arguments are used to verify the correctness of these unusual mean-field values. Infrared divergences in perturbation theory for the strong-coupling case occur for d<8, and an ɛ expansion (ɛ=8-d) is developed which is found to be identical to that previously analyzed for the statistics of lattice animals and which gives βa=12-ɛ12, η=-ɛ9, va=14+ɛ36, and μ=1-5ɛ36. The results are consistent with the Ward identity, which in combination with scaling arguments requires that βa+γa=1. The treatment takes account of the fact that the average of the on-site Green's function [G(x-->,x-->E)]av is nonzero and is predicated on this quantity being real, i.e., on the density of states vanishing at the mobility edge. We also show that localized states emerge naturally from local minima of finite action in the Lagrangian. These instanton solutions are analyzed on a lattice where the cutoff produced by the lattice constant leads to lattice instantons which exist for all d, in contrast to the case for the

  19. Hot and dense matter beyond relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Zhang, Xilin; Prakash, Madappa

    2016-05-01

    Properties of hot and dense matter are calculated in the framework of quantum hadrodynamics by including contributions from two-loop (TL) diagrams arising from the exchange of isoscalar and isovector mesons between nucleons. Our extension of mean field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of isospin-symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in the study of core-collapse supernovae, young and old neutron stars, and mergers of compact binary stars. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for cold and β -equilibrated neutron-star matter is substantially softer than its MFT counterpart, it is able to support a 2 M⊙ neutron star required by recent precise determinations. In addition, radii of 1.4 M⊙ stars are smaller by ˜1 km than those obtained in MFT and lie in the range indicated by analysis of astronomical data. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as Γth=1 +(Pth/ɛth) , often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of Γth at supranuclear density found in MFT is, however, suppressed in

  20. Dynamical mean-field theory for quantum chemistry.

    PubMed

    Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R

    2011-03-01

    The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.

  1. Density Functional Plus Dynamical Mean Field Theory of Correlated Oxides

    NASA Astrophysics Data System (ADS)

    Millis, Andrew

    2015-03-01

    The density functional plus dynamical mean field method is outlined and a few recent successes including applications to spin crossover molecules, oxide superlattices and metal-insulator transitions in bulk transition metals are outlined. Insights from the method into the essential role played by lattice distortions (both rotations and bond length changes) in determining the phase diagrams of correlated materials are presented. The key theoretical issue of the double counting correction is outlined, different approaches are compared, and a connection to the energy level differences between strongly and weakly correlated orbitals is presented. Charge transfer across oxide interfaces shown to depend crucially on the double counting correction, suggesting that experiments on oxide superlattices may provide insights into this important problem. Future directions are discussed. This work is performed in collaboration with Jia Chen, Hung Dang, Hyowon Park and Chris Marianetti. This research supported by the DOE Office of Science, Grant ER 046169.

  2. Zero-Temperature, Mean-Field Theory of Atomic Bose-Einstein Condensates

    PubMed Central

    Edwards, Mark; Dodd, R. J.; Clark, Charles W.; Burnett, K.

    1996-01-01

    We review the application of zero-temperature, mean-field theory to current experimental atomic Bose-Einstein condensates. We assess the validity of the approximations made by comparing the mean-field results with a variety of experimental data.

  3. Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials

    NASA Astrophysics Data System (ADS)

    Vollhardt, Dieter

    2010-11-01

    The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott-Hubbard metal-insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean-field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many-body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean-field theory for correlated fermions, the dynamical mean-field theory (DMFT), (v) derive the DMFT self-consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.

  4. Mean-field theory for Bose-Hubbard model under a magnetic field

    SciTech Connect

    Oktel, M. Oe.; Tanatar, B.; Nita, M.

    2007-01-15

    We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.

  5. Existence of a solution to an equation arising from the theory of Mean Field Games

    NASA Astrophysics Data System (ADS)

    Gangbo, Wilfrid; Święch, Andrzej

    2015-12-01

    We construct a small time strong solution to a nonlocal Hamilton-Jacobi equation (1.1) introduced in [48], the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton-Jacobi equations studied in [2,19,20] and solutions to (1.1). As a consequence we recover the existence of solutions to the First Order Mean Field Games equations (1.2), first proved in [48], and make a more rigorous connection between the master equation (1.1) and the Mean Field Games equations (1.2).

  6. Configuration Interaction as an Impurity Solver: Benchmark Dynamical Mean-Field Theory for the Hubbard Model

    NASA Astrophysics Data System (ADS)

    Go, Ara; Millis, Andrew J.

    2013-03-01

    The configuration interaction technique has been widely used in quantum chemistry to solve quantum many body systems with lower computational costs than exact diagonalization and was introduced by Dominika Zgid, Emanuel Gull, and Garnet Kin-Lic Chan [Phys. Rev. B 86, 165128 (2012)] as a solver for the impurity models of dynamical mean field theory. We extend their work, demonstrating for the one and two dimensional Hubbard model how the method reproduces the known results and allows convergence with bath size to be studied in cluster dynamical mean field theory. As an example of the power of the method, cluster dynamical mean field studies of the three band copper-oxygen model are presented. This work was supported by the CMCSN program of the US Department of Energy.

  7. Mean-field theory of spin-glasses with finite coordination number

    NASA Technical Reports Server (NTRS)

    Kanter, I.; Sompolinsky, H.

    1987-01-01

    The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.

  8. Phase transition studies of BiMnO{sub 3}: Mean field theory approximations

    SciTech Connect

    Lakshmi Priya, K. B.; Natesan, Baskaran

    2015-06-24

    We studied the phase transition and magneto-electric coupling effect of BiMnO{sub 3} by employing mean field theory approximations. To capture the ferromagnetic and ferroelectric transitions of BiMnO{sub 3}, we construct an extended Ising model in a 2D square lattice, wherein, the magnetic (electric) interactions are described in terms of the direct interactions between the localized magnetic (electric dipole) moments of Mn ions with their nearest neighbors. To evaluate our model, we obtain magnetization, magnetic susceptibility and electric polarization using mean field approximation calculations. Our results reproduce both the ferromagnetic and the ferroelectric transitions, matching very well with the experimental reports. Furthermore, consistent with experimental observations, our mean field results suggest that there is indeed a coupling between the magnetic and electric ordering in BiMnO{sub 3}.

  9. Time-odd mean fields in covariant density functional theory: Rotating systems

    SciTech Connect

    Afanasjev, A. V.; Abusara, H.

    2010-09-15

    Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration, and rotational frequency dependencies of their impact on the moments of inertia have been analyzed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean-field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid-body value. On the contrary, superdeformed and hyperdeformed nuclei have the moments of inertia which are close to rigid-body value. The structure of the currents in rotating frame, their microscopic origin, and the relations to the moments of inertia have been systematically analyzed. The phenomenon of signature separation in odd-odd nuclei, induced by time-odd mean fields, has been analyzed in detail.

  10. Mean-field theory of atomic self-organization in optical cavities

    NASA Astrophysics Data System (ADS)

    Jäger, Simon B.; Schütz, Stefan; Morigi, Giovanna

    2016-08-01

    Photons mediate long-range optomechanical forces between atoms in high-finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second-order phase transition that separates a uniform spatial density from a Bragg grating maximizing scattering into the cavity and is controlled by the laser intensity. Starting from a Fokker-Planck equation describing the semiclassical dynamics of the N -atom distribution function, we systematically develop a mean-field model and analyze its predictions for the equilibrium and out-of-equilibrium dynamics. The validity of the mean-field model is tested by comparison with the numerical simulations of the N -body Fokker-Planck equation and by means of a Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. The mean-field theory predictions well reproduce several results of the N -body Fokker-Planck equation for sufficiently short times and are in good agreement with existing theoretical approaches based on field-theoretical models. The mean field, on the other hand, predicts thermalization time scales which are at least one order of magnitude shorter than the ones predicted by the N -body dynamics. We attribute this discrepancy to the fact that the mean-field ansatz discards the effects of the long-range incoherent forces due to cavity losses.

  11. Hidden Fermi liquid, scattering rate saturation, and Nernst effect: a dynamical mean-field theory perspective.

    PubMed

    Xu, Wenhu; Haule, Kristjan; Kotliar, Gabriel

    2013-07-19

    We investigate the transport properties of a correlated metal within dynamical mean-field theory. Canonical Fermi liquid behavior emerges only below a very low temperature scale T(FL). Surprisingly the quasiparticle scattering rate follows a quadratic temperature dependence up to much higher temperatures and crosses over to saturated behavior around a temperature scale T(sat). We identify these quasiparticles as constituents of the hidden Fermi liquid. The non-Fermi-liquid transport above T(FL), in particular the linear-in-T resistivity, is shown to be a result of a strongly temperature dependent band dispersion. We derive simple expressions for the resistivity, Hall angle, thermoelectric power and Nernst coefficient in terms of a temperature dependent renormalized band structure and the quasiparticle scattering rate. We discuss possible tests of the dynamical mean-field theory picture of transport using ac measurements. PMID:23909344

  12. Hidden Fermi liquid, scattering rate saturation, and Nernst effect: a dynamical mean-field theory perspective.

    PubMed

    Xu, Wenhu; Haule, Kristjan; Kotliar, Gabriel

    2013-07-19

    We investigate the transport properties of a correlated metal within dynamical mean-field theory. Canonical Fermi liquid behavior emerges only below a very low temperature scale T(FL). Surprisingly the quasiparticle scattering rate follows a quadratic temperature dependence up to much higher temperatures and crosses over to saturated behavior around a temperature scale T(sat). We identify these quasiparticles as constituents of the hidden Fermi liquid. The non-Fermi-liquid transport above T(FL), in particular the linear-in-T resistivity, is shown to be a result of a strongly temperature dependent band dispersion. We derive simple expressions for the resistivity, Hall angle, thermoelectric power and Nernst coefficient in terms of a temperature dependent renormalized band structure and the quasiparticle scattering rate. We discuss possible tests of the dynamical mean-field theory picture of transport using ac measurements.

  13. Correlated Dirac semimetal by periodized cluster dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    Li, Qing-Xiao; He, Rong-Qiang; Lu, Zhong-Yi

    2015-10-01

    The periodized cluster dynamical mean-field theory (PCDMFT) combined with exact diagonalization as the impurity solver has been applied to the half-filled standard Hubbard model on the honeycomb lattice. A correlated Dirac semimetal is found for weak interactions and it transforms into an antiferromagnetic insulating phase for strong interactions via a first-order quantum phase transition, not intervened by a spin liquid phase in between. In this application, the PCDMFT introduces the partial translation symmetry, but cures well the problem caused by the translation symmetry breaking in the cluster dynamical mean-field theory studies for the same model, which gives rise to a spurious insulating phase in the weakly interacting region.

  14. From effective field theories to effective density functionals in and beyond the mean field

    NASA Astrophysics Data System (ADS)

    Grasso, M.; Lacroix, D.; van Kolck, U.

    2016-06-01

    Since the 1975 Nobel Prize in Physics, nuclear theory has evolved along two main directions. On the one hand, the energy-density functional (EDF) theory was established, which presently encompasses (by enlarging the EDF framework) all the mean-field and beyond-mean-field theories based on energy functionals produced by effective phenomenological interactions. Highly sophisticated structure and reaction models are currently available for the treatment of medium-mass and heavy nuclei. On the other hand, effective field theories (EFTs) have rendered possible the formulation of QCD as a low-energy hadronic theory. Ab initio methods have recently achieved remarkable success in the application of EFT or EFT-inspired potentials to structure analyses of light nuclei. Different but complementary competences have been developed during the past few decades in the EDF and EFT communities. Bridges and connections have in some cases been identified and constructed. We review here some of the developments that have been performed within the EDF theory and the EFT during recent years, with some emphasis on analogies and connections that may one day provide a unified picture of the two theories. Illustrations are given for infinite matter and finite nuclei.

  15. From effective field theories to effective density functionals in and beyond the mean field

    NASA Astrophysics Data System (ADS)

    Grasso, M.; Lacroix, D.; van Kolck, U.

    2016-06-01

    Since the 1975 Nobel Prize in Physics, nuclear theory has evolved along two main directions. On the one hand, the energy–density functional (EDF) theory was established, which presently encompasses (by enlarging the EDF framework) all the mean-field and beyond-mean-field theories based on energy functionals produced by effective phenomenological interactions. Highly sophisticated structure and reaction models are currently available for the treatment of medium-mass and heavy nuclei. On the other hand, effective field theories (EFTs) have rendered possible the formulation of QCD as a low-energy hadronic theory. Ab initio methods have recently achieved remarkable success in the application of EFT or EFT-inspired potentials to structure analyses of light nuclei. Different but complementary competences have been developed during the past few decades in the EDF and EFT communities. Bridges and connections have in some cases been identified and constructed. We review here some of the developments that have been performed within the EDF theory and the EFT during recent years, with some emphasis on analogies and connections that may one day provide a unified picture of the two theories. Illustrations are given for infinite matter and finite nuclei.

  16. Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory

    DOE PAGESBeta

    Wohlfeld, K.; Chen, Cheng-Chien; van Veenendaal, M.; Devereaux, T. P.

    2015-02-01

    Motivated by the recent success in describing the spin and orbital spectrum of a spin-orbital chain using a large-N mean-field approximation [Phys. Rev. B 91, 165102 (2015)], we apply the same formalism to the case of a spin chain in the external magnetic field. It occurs that in this case, which corresponds to N=2 in the approximation, the large-N mean-field theory cannot qualitatively reproduce the spin excitation spectra at high magnetic fields, which polarize more than 50% of the spins in the magnetic ground state. This, rather counterintuitively, shows that the physics of a spin chain can under some circumstancesmore » be regarded as more complex than the physics of a spin-orbital chain.« less

  17. Time-dependent mean field theory for quench dynamics in correlated electron systems.

    PubMed

    Schiró, Marco; Fabrizio, Michele

    2010-08-13

    A simple and very flexible variational approach to the out-of-equilibrium quantum dynamics in strongly correlated electron systems is introduced through a time-dependent Gutzwiller wave function. As an application, we study the simple case of a sudden change of the interaction in the fermionic Hubbard model and find at the mean-field level an extremely rich behavior. In particular, a dynamical transition between small and large quantum quench regimes is found to occur at half-filling, in accordance with the analysis of Eckstein, Phys. Rev. Lett. 103, 056403 (2009)10.1103/PhysRevLett.103.056403, obtained by dynamical mean-field theory, that turns into a crossover at any finite doping.

  18. Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory

    SciTech Connect

    Wohlfeld, K.; Chen, Cheng-Chien; van Veenendaal, M. ; Devereaux, T. P.

    2015-02-01

    Motivated by the recent success in describing the spin and orbital spectrum of a spin-orbital chain using a large-N mean-field approximation [Phys. Rev. B 91, 165102 (2015)], we apply the same formalism to the case of a spin chain in the external magnetic field. It occurs that in this case, which corresponds to N=2 in the approximation, the large-N mean-field theory cannot qualitatively reproduce the spin excitation spectra at high magnetic fields, which polarize more than 50% of the spins in the magnetic ground state. This, rather counterintuitively, shows that the physics of a spin chain can under some circumstances be regarded as more complex than the physics of a spin-orbital chain.

  19. Non-mean-field theory of anomalously large double layer capacitance

    NASA Astrophysics Data System (ADS)

    Loth, M. S.; Skinner, Brian; Shklovskii, B. I.

    2010-07-01

    Mean-field theories claim that the capacitance of the double layer formed at a metal/ionic conductor interface cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments the apparent width of the double layer capacitor is substantially smaller. We propose an alternate non-mean-field theory of the ionic double layer to explain such large capacitance values. Our theory allows for the binding of discrete ions to their image charges in the metal, which results in the formation of interface dipoles. We focus primarily on the case where only small cations are mobile and other ions form an oppositely charged background. In this case, at small temperature and zero applied voltage dipoles form a correlated liquid on both contacts. We show that at small voltages the capacitance of the double layer is determined by the transfer of dipoles from one electrode to the other and is therefore limited only by the weak dipole-dipole repulsion between bound ions so that the capacitance is very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the much smaller mean-field value, as seen in experimental data. We test our analytical predictions with a Monte Carlo simulation and find good agreement. We further argue that our “one-component plasma” model should work well for strongly asymmetric ion liquids. We believe that this work also suggests an improved theory of pseudocapacitance.

  20. Continuum theory of critical phenomena in polymer solutions: Formalism and mean field approximation

    NASA Astrophysics Data System (ADS)

    Goldstein, Raymond E.; Cherayil, Binny J.

    1989-06-01

    A theoretical description of the critical point of a polymer solution is formulated directly from the Edwards continuum model of polymers with two- and three-body excluded-volume interactions. A Hubbard-Stratonovich transformation analogous to that used in recent work on the liquid-vapor critical point of simple fluids is used to recast the grand partition function of the polymer solution as a functional integral over continuous fields. The resulting Landau-Ginzburg-Wilson (LGW) Hamiltonian is of the form of a generalized nonsymmetric n=1 component vector model, with operators directly related to certain connected correlation functions of a reference system. The latter is taken to be an ensemble of Gaussian chains with three-body excluded-volume repulsions, and the operators are computed in three dimensions by means of a perturbation theory that is rapidly convergent for long chains. A mean field theory of the functional integral yields a description of the critical point in which the power-law variations of the critical polymer volume fraction φc, critical temperature Tc, and critical amplitudes on polymerization index N are essentially identical to those found in the Flory-Huggins theory. In particular, we find φc ˜N-1/2, Tθ-Tc˜N-1/2 with (Tθ the theta temperature), and that the composition difference between coexisting phases varies with reduced temperature t as N-1/4t1/2. The mean field theory of the interfacial tension σ between coexisting phases near the critical point, developed by considering the LGW Hamiltonian for a weakly inhomogeneous solution, yields σ˜N-1/4t3/2, with the correlation length diverging as ξ˜N1/4t-1/2 within the same approximation, consistent with the mean field limit of de Gennes' scaling form. Generalizations to polydisperse systems are discussed.

  1. Dynamic mean field theory of the SK-spin glass. II. Order parameters and gauge invariance

    NASA Astrophysics Data System (ADS)

    Horner, H.

    1984-03-01

    The probability distribution of overlaps proposed by Parisi as order parameter for the SK-spin glass is calculated via dynamics. It is deduced from dynamic response functions and also directly obtained from a treatment with replicas and dynamics. The replica trick is not required. The comparison of the two results shows in which sense fluctuation dissipation theorems hold. Overlaps between three or more states are found to agree with those obtained by Mézard et al. using the replica trick. The origin of the ultrametric topology of spin glass states is investigated within the dynamic mean field theory and a gauge invariance is explored.

  2. Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles

    NASA Astrophysics Data System (ADS)

    Chou, Yen-Liang; Ihle, Thomas

    2015-02-01

    Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013), 10.1103/PhysRevE.88.052309] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N -particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8 , followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

  3. Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.

    PubMed

    Chou, Yen-Liang; Ihle, Thomas

    2015-02-01

    Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

  4. Implementing the density matrix embedding theory with the hierarchical mean-field approach

    NASA Astrophysics Data System (ADS)

    Qin, Jingbo; Jie, Quanlin; Fan, Zhuo

    2016-07-01

    We show an implementation of density matrix embedding theory (DMET) for the spin lattice of infinite size. It is indeed a special form of hierarchical mean-field (HMF) theory. In the method, we divide the lattice into a small part and a large part. View the small part as an impurity, embedding in the large part, which is viewed as the environment. We deal the impurity with a high accuracy method. But treat the environment with a low-level method: the states of the environment nearby the impurity are expressed by a set of multiple block product states, while the distant parts are treated by mean-field consideration. Our method allows for the computation of the ground state of the infinite two-dimensional quantum spin systems. In the text, we take the frustrated Heisenberg model as an example to test our method. The ground state energy we calculated can reach a high accuracy. We also calculate the magnetization, and the fidelity to study the quantum phase transitions.

  5. Compression induced phase transition of nematic brush: A mean-field theory study

    SciTech Connect

    Tang, Jiuzhou; Zhang, Xinghua; Yan, Dadong

    2015-11-28

    Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bending energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.

  6. Compression induced phase transition of nematic brush: A mean-field theory study

    NASA Astrophysics Data System (ADS)

    Tang, Jiuzhou; Zhang, Xinghua; Yan, Dadong

    2015-11-01

    Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bending energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.

  7. The electronic mean-field configuration interaction method. I. Theory and integral formulas

    NASA Astrophysics Data System (ADS)

    Cassam-Chenaï, Patrick

    2006-05-01

    In this article, we introduce a new method for solving the electronic Schrödinger equation. This new method follows the same idea followed by the mean-field configuration interaction method already developed for molecular vibrations; i.e., groups of electronic degrees of freedom are contracted together in the mean field of the other degrees. If the same partition of electronic degrees of freedom is iterated, a self-consistent field method is obtained. Making coarser partitions (i.e., including more degrees in the same groups) and discarding the high energy states, the full configuration interaction limit can be approached. In contrast with the usual group function theory, no strong orthogonality condition is enforced. We have made use of a generalized version of the fundamental formula defining a Hopf algebra structure to derive Hamiltonian and overlap matrix element expressions which respect the group structure of the wave function as well as its fermionic symmetry. These expressions are amenable to a recursive computation.

  8. Atomically flat superconducting nanofilms: multiband properties and mean-field theory

    NASA Astrophysics Data System (ADS)

    Shanenko, A. A.; Aguiar, J. Albino; Vagov, A.; Croitoru, M. D.; Milošević, M. V.

    2015-05-01

    Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Pérot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.

  9. Quantum correlated cluster mean-field theory applied to the transverse Ising model

    NASA Astrophysics Data System (ADS)

    Zimmer, F. M.; Schmidt, M.; Maziero, Jonas

    2016-06-01

    Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.

  10. Coagulation kinetics beyond mean field theory using an optimised Poisson representation

    NASA Astrophysics Data System (ADS)

    Burnett, James; Ford, Ian J.

    2015-05-01

    Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable "gauge" transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.

  11. Quantum correlated cluster mean-field theory applied to the transverse Ising model.

    PubMed

    Zimmer, F M; Schmidt, M; Maziero, Jonas

    2016-06-01

    Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.

  12. Quantum correlated cluster mean-field theory applied to the transverse Ising model.

    PubMed

    Zimmer, F M; Schmidt, M; Maziero, Jonas

    2016-06-01

    Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations. PMID:27415217

  13. Mean-Field Theory of the Symmetry Breaking Model for X Chromosome Inactivation

    NASA Astrophysics Data System (ADS)

    Scialdone, A.; Barbieri, M.; Pallotti, D.; Nicodemi, M.

    X Chromosome Inactivation (XCI) is the process in mammal femalecells whereby one of the X chromosomes is silenced to compensate dosage with respect to males. It is still mysterious how precisely one X chromosome is randomly chosen for inactivation. We discuss here a mean-field theory of the Symmetry Breaking (SB) model of XCI, a Statistical Mechanics model introduced to explain that process. The SB model poses that a single regulatory factor, an aggregate of molecules, is produced which acts to preserve from inactivation one of the X's. The model illustrates a physical mechanism, originating from a thermodynamic phase transition, for the self-assembling of such a single super-molecular aggregate which can spontaneously break the binding symmetry of equivalent targets. This results in a sharp, yet stochastic, regulatory mechanism of XCI. In particular, we focus here on how the model can predict the effects of genetic deletions.

  14. Mean-Field Theory of Intra-Molecular Charge Ordering in (TTM--TTP)I3

    NASA Astrophysics Data System (ADS)

    Omori, Yukiko; Tsuchiizu, Masahisa; Suzumura, Yoshikazu

    2011-02-01

    We examine an intra-molecular charge-ordered (ICO) state in the multi-orbital molecular compound (TTM--TTP)I3 on the basis of an effective two-orbital model derived from ab initio calculations. Representing the model in terms of the fragment molecular-orbital (MO) picture, the ICO state is described as the charge disproportionation on the left and right fragment MOs. By applying the mean-field theory, the phase diagram of the ground state is obtained as a function of the inter-molecular Coulomb repulsion and the intra-molecular transfer integral. The ICO state is stabilized by large inter-fragment Coulomb interactions, and the small intra-molecular transfer energy between two fragment MOs. Furthermore, we examine the finite-temperature phase diagram. The relevance to the experimental observations in the molecular compound of (TTM--TTP)I3 is also discussed.

  15. Keplerian Frequency of Uniformly Rotating Neutron Stars in Relativistic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Zhang, N. B.; Qi, B.; Wang, S. Y.; Ge, S. L.; Sun, B. Y.

    2013-11-01

    Adopting the equation of states (EOSs) from the relativistic mean field (RMF) theory, the relationships among the keplerian frequency fK, gravitational mass M and radius R for the rapidly rotating neutron stars with and without hyperons are presented and analyzed. For various RMF EOSs, the empirical formula fK(M) = 1.08 (M/M⊙)1/2(R_S/10 km)-3/2 kHz, proposed by P. Haensel et al. [Astron. Astrophys.502 (2009) 605], is found to be an approximation with the error at most 13% and such approximation is worse for the neutron stars with hyperons. It indicates that the errors should be considered when the empirical formula is used to discuss the properties of neutron stars.

  16. Stability of inhomogeneous superstructures from renormalized mean-field theory of the t-J model

    NASA Astrophysics Data System (ADS)

    Poilblanc, Didier

    2005-08-01

    Using the t-J model (which can also include Coulomb repulsion) and the “plain vanilla” renormalized mean-field theory of Zhang, [Supercond. Sci. Technol. 1, 36 (1988)], stability of inhomogeneous 4a×4a superstructures, such as those observed in cuprates superconductors around 1/8 hole doping is investigated. We find a nonuniform 4a×4a bond order wave involving simultaneously small (˜10-2t) inhomogeneous staggered plaquette currents as well as a small charge-density modulation similar to pair density wave order. On the other hand, no supersolid phase involving a decoupling in the superconducting particle-particle channel is found.

  17. Application of relativistic mean field and effective field theory densities to scattering observables for Ca isotopes

    NASA Astrophysics Data System (ADS)

    Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.

    2010-12-01

    In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for Ca40,42,44,48 with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+Ca40,42,44,48 systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.

  18. Application of relativistic mean field and effective field theory densities to scattering observables for Ca isotopes

    SciTech Connect

    Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.

    2010-12-15

    In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for {sup 40,42,44,48}Ca with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+{sup 40,42,44,48}Ca systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.

  19. Nonequilibrium dynamical mean-field theory: an auxiliary quantum master equation approach.

    PubMed

    Arrigoni, Enrico; Knap, Michael; von der Linden, Wolfgang

    2013-02-22

    We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.

  20. Mean-field density functional theory of a three-phase contact line.

    PubMed

    Lin, Chang-You; Widom, Michael; Sekerka, Robert F

    2012-01-01

    A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive overrelaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.

  1. A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes

    NASA Astrophysics Data System (ADS)

    Han, Yining; Huang, Shanghui; Yan, Tianying

    2014-07-01

    The size of ions significantly influences the electric double layer structure of room temperature ionic liquid (IL) electrolytes and their differential capacitance (Cd). In this study, we extended the mean-field theory (MFT) developed independently by Kornyshev (2007J. Phys. Chem. B 111 5545-57) and Kilic, Bazant, and Ajdari (2007 Phys. Rev. E 75 021502) (the KKBA MFT) to take into account the asymmetric 1:1 IL electrolytes by introducing an additional parameter ξ for the anion/cation volume ratio, besides the ionic compressibility γ in the KKBA MFT. The MFT of asymmetric ions becomes KKBA MFT upon ξ = 1, and further reduces to Gouy-Chapman theory in the γ → 0 limit. The result of the extended MFT demonstrates that the asymmetric ILs give rise to an asymmetric Cd, with the higher peak in Cd occurring at positive polarization for the smaller anionic size. At high potential, Cd decays asymptotically toward KKBA MFT characterized by γ for the negative polarization, and characterized by ξγ for the positive polarization, with inverse-square-root behavior. At low potential, around the potential of zero charge, the asymmetric ions cause a higher Cd, which exceeds that of Gouy-Chapman theory.

  2. Dynamic mean field theory for lattice gas models of fluid mixtures confined in mesoporous materials.

    PubMed

    Edison, J R; Monson, P A

    2013-11-12

    We present the extension of dynamic mean field theory (DMFT) for fluids in porous materials (Monson, P. A. J. Chem. Phys. 2008, 128, 084701) to the case of mixtures. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable equilibrium states for fluids in pores after a change in the bulk pressure or composition. It is especially useful for studying systems where there are capillary condensation or evaporation transitions. Nucleation processes associated with these transitions are emergent features of the theory and can be visualized via the time dependence of the density distribution and composition distribution in the system. For mixtures an important component of the dynamics is relaxation of the composition distribution in the system, especially in the neighborhood of vapor-liquid interfaces. We consider two different types of mixtures, modeling hydrocarbon adsorption in carbon-like slit pores. We first present results on bulk phase equilibria of the mixtures and then the equilibrium (stable/metastable) behavior of these mixtures in a finite slit pore and an inkbottle pore. We then use DMFT to describe the evolution of the density and composition in the pore in the approach to equilibrium after changing the state of the bulk fluid via composition or pressure changes. PMID:24102541

  3. State-of-the-art of beyond mean field theories with nuclear density functionals

    NASA Astrophysics Data System (ADS)

    Egido, J. Luis

    2016-07-01

    We present an overview of different beyond mean field theories (BMFTs) based on the generator coordinate method (GCM) and the recovery of symmetries used in many body nuclear physics with effective forces. In a first step a short reminder of the Hartree–Fock–Bogoliubov (HFB) theory is given. A general discussion of the shortcomings of any mean field approximation (MFA), stemming either from the lack of the elementary symmetries (like particle number and angular momentum) or the absence of fluctuations around the mean values, is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is also needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. A whole chapter is devoted to illustrate with examples the convenience of recovering symmetries and the differences between the projection before and after the variation. The lack of fluctuations around the average values of the MFA is a big shortcoming inherent to this approach. To build in correlations in BMFT one selects the relevant degrees of freedom of the atomic nucleus. In the low energy part of the spectrum these are the quadrupole, octupole and the pairing vibrations as well as the single particle degrees of freedom. In the GCM the operators representing these degrees of freedom are used as coordinates to generate, by the constrained (projected) HFB theory, a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill–Wheeler equation. The flexibility of the GCM Ansatz allows to describe a whole palette of physical situations by conveniently choosing the generator coordinates. We

  4. State-of-the-art of beyond mean field theories with nuclear density functionals

    NASA Astrophysics Data System (ADS)

    Egido, J. Luis

    2016-07-01

    We present an overview of different beyond mean field theories (BMFTs) based on the generator coordinate method (GCM) and the recovery of symmetries used in many body nuclear physics with effective forces. In a first step a short reminder of the Hartree-Fock-Bogoliubov (HFB) theory is given. A general discussion of the shortcomings of any mean field approximation (MFA), stemming either from the lack of the elementary symmetries (like particle number and angular momentum) or the absence of fluctuations around the mean values, is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is also needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. A whole chapter is devoted to illustrate with examples the convenience of recovering symmetries and the differences between the projection before and after the variation. The lack of fluctuations around the average values of the MFA is a big shortcoming inherent to this approach. To build in correlations in BMFT one selects the relevant degrees of freedom of the atomic nucleus. In the low energy part of the spectrum these are the quadrupole, octupole and the pairing vibrations as well as the single particle degrees of freedom. In the GCM the operators representing these degrees of freedom are used as coordinates to generate, by the constrained (projected) HFB theory, a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill-Wheeler equation. The flexibility of the GCM Ansatz allows to describe a whole palette of physical situations by conveniently choosing the generator coordinates. We discuss the

  5. Nonequilibrium Dynamical Mean-Field Theory for the Charge-Density-Wave Phase of the Falicov-Kimball Model

    SciTech Connect

    Matveev, O. P.; Shvaika, A. M.; Devereaux, T. P.; Freericks, J. K.

    2015-12-08

    Nonequilibrium dynamical mean-field theory (DMFT) is developed for the case of the charge-density-wave ordered phase. We consider the spinless Falicov-Kimball model which can be solved exactly. This strongly correlated system is then placed in an uniform external dc electric field. We present a complete derivation for nonequilibrium dynamical mean-field theory Green’s functions defined on the Keldysh-Schwinger time contour. We also discuss numerical issues involved in solving the coupled equations.

  6. Coagulation kinetics beyond mean field theory using an optimised Poisson representation

    SciTech Connect

    Burnett, James; Ford, Ian J.

    2015-05-21

    Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable “gauge” transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.

  7. Macromolecular Stabilization by Excluded Cosolutes: Mean Field Theory of Crowded Solutions.

    PubMed

    Sapir, Liel; Harries, Daniel

    2015-07-14

    We propose a mean field theory to account for the experimentally determined temperature dependence of protein stabilization that emerges in solutions crowded by preferentially excluded cosolutes. Based on regular solution theory and employing the Flory-Huggins approximation, our model describes cosolutes in terms of their size, and two temperature-dependent microscopic parameters that correspond to macromolecule-cosolute and bulk solution interactions. The theory not only predicts a "depletion force" that can account for the experimentally observed stabilization of protein folding or association in the presence of excluded cosolutes but also predicts the full range of associated entropic and enthalpic components. Remarkably, depending on cosolute identity and in accordance with experiments, the theory describes entropically as well as enthalpically dominated depletion forces, even those disfavored by entropy. This emerging depletion attraction cannot be simply linked to molecular volumes. Instead, the relevant parameter is an effective volume that represents an interplay between solvent, cosolute, and macromolecular interactions. We demonstrate that the apparent depletion free energy is often accompanied by significant yet compensating entropy and enthalpy terms that, although having a net zero contribution to stabilization, can obscure the underlying molecular mechanism. This study underscores the importance of including often-neglected free energy terms that correspond to solvent-cosolute and cosolute-macromolecule interactions, which for most typical cosolutes are expected to be temperature dependent. We propose that experiments specifically aimed at resolving the temperature-dependence of cosolute exclusion from macromolecular surfaces should help reveal the full range of the underlying molecular mechanisms of the depletion force.

  8. Macromolecular Stabilization by Excluded Cosolutes: Mean Field Theory of Crowded Solutions.

    PubMed

    Sapir, Liel; Harries, Daniel

    2015-07-14

    We propose a mean field theory to account for the experimentally determined temperature dependence of protein stabilization that emerges in solutions crowded by preferentially excluded cosolutes. Based on regular solution theory and employing the Flory-Huggins approximation, our model describes cosolutes in terms of their size, and two temperature-dependent microscopic parameters that correspond to macromolecule-cosolute and bulk solution interactions. The theory not only predicts a "depletion force" that can account for the experimentally observed stabilization of protein folding or association in the presence of excluded cosolutes but also predicts the full range of associated entropic and enthalpic components. Remarkably, depending on cosolute identity and in accordance with experiments, the theory describes entropically as well as enthalpically dominated depletion forces, even those disfavored by entropy. This emerging depletion attraction cannot be simply linked to molecular volumes. Instead, the relevant parameter is an effective volume that represents an interplay between solvent, cosolute, and macromolecular interactions. We demonstrate that the apparent depletion free energy is often accompanied by significant yet compensating entropy and enthalpy terms that, although having a net zero contribution to stabilization, can obscure the underlying molecular mechanism. This study underscores the importance of including often-neglected free energy terms that correspond to solvent-cosolute and cosolute-macromolecule interactions, which for most typical cosolutes are expected to be temperature dependent. We propose that experiments specifically aimed at resolving the temperature-dependence of cosolute exclusion from macromolecular surfaces should help reveal the full range of the underlying molecular mechanisms of the depletion force. PMID:26575781

  9. Mean field theory for biology inspired duplication-divergence network model.

    PubMed

    Cai, Shuiming; Liu, Zengrong; Lee, H C

    2015-08-01

    The duplication-divergence network model is generally thought to incorporate key ingredients underlying the growth and evolution of protein-protein interaction networks. Properties of the model have been elucidated through numerous simulation studies. However, a comprehensive theoretical study of the model is lacking. Here, we derived analytic expressions for quantities describing key characteristics of the network-the average degree, the degree distribution, the clustering coefficient, and the neighbor connectivity-in the mean-field, large-N limit of an extended version of the model, duplication-divergence complemented with heterodimerization and addition. We carried out extensive simulations and verified excellent agreement between simulation and theory except for one partial case. All four quantities obeyed power-laws even at moderate network size ( N∼10(4)), except the degree distribution, which had an additional exponential factor observed to obey power-law. It is shown that our network model can lead to the emergence of scale-free property and hierarchical modularity simultaneously, reproducing the important topological properties of real protein-protein interaction networks. PMID:26328557

  10. Higgs-Yukawa model with higher dimension operators via extended mean field theory

    NASA Astrophysics Data System (ADS)

    Akerlund, Oscar; de Forcrand, Philippe

    2016-02-01

    Using extended mean field theory (EMFT) on the lattice, we study properties of the Higgs-Yukawa model as an approximation of the standard model Higgs sector, and the effect of higher dimension operators. We remark, as has been noted before, that the discussion of vacuum stability is completely modified in the presence of a ϕ6 term, and that the Higgs mass no longer appears fine tuned. We also study the finite temperature transition. Without higher dimension operators the transition is found to be second order (crossover with gauge fields) for the experimental value of the Higgs mass Mh=125 GeV . By taking a ϕ6 interaction in the Higgs potential as a proxy for a UV completion of the standard model, the transition becomes stronger and turns first order if the scale of new physics, i.e., the mass of the lightest mediator particle, is around 1.5 TeV. This implies that electroweak baryogenesis may be viable in models which introduce new particles around that scale.

  11. Magnetic and antimagnetic rotation in 110Cd within tilted axis cranking relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Peng, J.; Zhao, P. W.

    2015-04-01

    The self-consistent tilted axis cranking relativistic mean-field (TAC-RMF) theory based on a point-coupling interaction is applied to investigate the observed magnetic and antimagnetic rotations in the nucleus 110Cd . The energy spectra, the relation between the spin and the rotational frequency, the deformation parameters, and the reduced M 1 and E 2 transition probabilities are studied with the various configurations. It is found that the configuration has to be changed to reproduce the energy spectra and the relations between the spin and the rotational frequency for both the magnetic and antimagnetic rotational bands. The shears mechanism for the magnetic rotation and the two-shears-like mechanism for the antimagnetic rotation are examined by investigating the orientation of the neutron and proton angular momenta. The calculated electromagnetic transitions B (M 1 ) and B (E 2 ) are in reasonable agreement with the data, and their tendencies are coincident with the typical characteristics of the magnetic and antimagnetic rotations.

  12. Mean-field theory of the glass transition in the one-component classical plasma

    NASA Astrophysics Data System (ADS)

    Cardenas, M.; Tosi, M. P.

    2004-08-01

    We study the supercooled-fluid region and the transition to an amorphous glassy state in the one-component classical plasma, within the replica-symmetry-breaking scenario developed by Franz and Parisi. This approach implements the slowing down of jumps of the disordered system between the minima in a rugged free-energy landscape by examining its correlations with a quenched replica as a function of their coupling expressed through a suitable short-range attractive potential. We carry out these calculations within a mean-field theory for the structure of a quenched-annealed mixture, using both the hypernetted chain approximation and a refinement to include an account of the bridge function. In both formulations our theoretical results demonstrate the existence of a glassy state for the plasma and yield an estimate of the phase-transition line, which has the form T∝ Z2n1/3 where n is the particle number density, T the temperature and Z the valence, with a numerical coefficient which is about one eighth of that for equilibrium freezing. The consequences for various types of ionic fluids (simple molten salts, colloidal dispersions, and astrophysical plasmas) are illustrated.

  13. Analytic models of regularly branched polymer brushes using the self-consistent mean field theory

    NASA Astrophysics Data System (ADS)

    LeSher, Daniel

    2015-10-01

    Polymer brushes consist of multiple monomers connected together with one of the polymer chain's ends attached to a surface. Polymer brushes have shown great promise for a wide variety of applications including drug delivery dendrimer systems and as tunable brushes that can change their shape and physical properties in response to changes in their environment. Regularly branched polymer brushes which are structured as a function of their chemical indices are investigated here using the self-consistent mean field theory for electrically neutral polymers. The brushes were described using weighting functions, f(n), were n was the fewest number of monomers from a specified location to a free end. Brushes with weighting functions of the form f(n)=nb, f(n)=ebn, as well as f(n)=dan when d 2 and alpha > 2 were found to match the parabolic free chain end profile expected, while it was determined that polymer brushes described using f(n)=n b must be very small in order to remain in equilibrium. However, brushes described by f(n)=2G(N-n) N and f(n)2n were found to be unstable for real, positive values of the potential of the system.

  14. Diffuse phase transition in ferroelectrics with mesoscopic heterogeneity: Mean-field theory

    SciTech Connect

    Li, S.; Eastman, J.A.; Newnham, R.E.; Cross, L.E.

    1997-05-01

    The diffuse phase transition in ferroelectrics with mesoscopic heterogeneity has been discussed within the context of a superparaelectric model by using the Ginzburg-Landau formalism. In the Curie region ferroelectrics with mesoscopic heterogeneity are treated as {open_quotes}superparaelectrics{close_quotes} consisting of a mass of polar clusters, each of which has Ising character. Based on the mean-field theory, the influence of the finite-size effects of polar clusters on their structural instability has been discussed by considering a coherent lattice coupling between two structurally different regions. In particular, we have analytically derived the explicit solutions of the distribution of local polarizations. In turn, the processes of polar nanophase precipitation and coarsening have been also discussed in conjunction with the local chemical or structural inhomogeneity. Moreover, we have also analyzed the relationship between the local polarization distribution and the static dielectric susceptibility in ferroelectrics with the nanometric scale heterogeneity. The width of the Curie region is dependent upon the distribution of the sum of localized correlation length, which reflects the size distribution of heterogeneity. The presented analysis reveals that the diffuse phase transition is closely associated with the existence of nanometric polar clusters and their physical size distribution. Intriguingly, our theoretical results bear a very close resemblance to most experimental observations. {copyright} {ital 1997} {ital The American Physical Society}

  15. Embedding dynamical mean-field theory for superconductivity in layered materials and heterostructures

    NASA Astrophysics Data System (ADS)

    Petocchi, Francesco; Capone, Massimo

    2016-06-01

    We study layered systems and heterostructures of s -wave superconductors by means of a suitable generalization of dynamical mean-field theory. In order to reduce the computational effort, we consider an embedding scheme in which a relatively small number of active layers is embedded in an effective potential accounting for the effect of the rest of the system. We introduce a feedback of the active layers on the embedding potential that improves on previous approaches and essentially eliminates the effects of the finiteness of the active slab allowing for cheap computation of very large systems. We extend the method to the superconducting state, and we benchmark the approach by means of simple paradigmatic examples showing some examples on how an interface affects the superconducting properties. As examples, we show that superconductivity can penetrate from an intermediate coupling superconductor into a weaker coupling one for around ten layers, and that the first two layers of a system with repulsive interaction can turn superconducting by proximity effects even when charge redistribution is inhibited.

  16. General model of phospholipid bilayers in fluid phase within the single chain mean field theory.

    PubMed

    Guo, Yachong; Pogodin, Sergey; Baulin, Vladimir A

    2014-05-01

    Coarse-grained model for saturated phospholipids: 1,2-didecanoyl-sn-glycero-3-phosphocholine (DCPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and unsaturated phospholipids: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2- dioleoyl-sn-glycero-3-phosphocholine (DOPC) is introduced within the single chain mean field theory. A single set of parameters adjusted for DMPC bilayers gives an adequate description of equilibrium and mechanical properties of a range of saturated lipid molecules that differ only in length of their hydrophobic tails and unsaturated (POPC, DOPC) phospholipids which have double bonds in the tails. A double bond is modeled with a fixed angle of 120°, while the rest of the parameters are kept the same as saturated lipids. The thickness of the bilayer and its hydrophobic core, the compressibility, and the equilibrium area per lipid correspond to experimentally measured values for each lipid, changing linearly with the length of the tail. The model for unsaturated phospholipids also fetches main thermodynamical properties of the bilayers. This model is used for an accurate estimation of the free energies of the compressed or stretched bilayers in stacks or multilayers and gives reasonable estimates for free energies. The proposed model may further be used for studies of mixtures of lipids, small molecule inclusions, interactions of bilayers with embedded proteins.

  17. Cluster radioactive decay within the preformed cluster model using relativistic mean-field theory densities

    SciTech Connect

    Singh, BirBikram; Patra, S. K.; Gupta, Raj K.

    2010-07-15

    We have studied the (ground-state) cluster radioactive decays within the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta, in Proceedings of the 5th International Conference on Nuclear Reaction Mechanisms, Varenna, edited by E. Gadioli (Ricerca Scientifica ed Educazione Permanente, Milano, 1988), p. 416; S. S. Malik and R. K. Gupta, Phys. Rev. C 39, 1992 (1989)]. The relativistic mean-field (RMF) theory is used to obtain the nuclear matter densities for the double folding procedure used to construct the cluster-daughter potential with M3Y nucleon-nucleon interaction including exchange effects. Following the PCM approach, we have deduced empirically the preformation probability P{sub 0}{sup emp} from the experimental data on both the alpha- and exotic cluster-decays, specifically of parents in the trans-lead region having doubly magic {sup 208}Pb or its neighboring nuclei as daughters. Interestingly, the RMF-densities-based nuclear potential supports the concept of preformation for both the alpha and heavier clusters in radioactive nuclei. P{sub 0}{sup a}lpha{sup (emp)} for alpha decays is almost constant (approx10{sup -2}-10{sup -3}) for all the parent nuclei considered here, and P{sub 0}{sup c(emp)} for cluster decays of the same parents decrease with the size of clusters emitted from different parents. The results obtained for P{sub 0}{sup c(emp)} are reasonable and are within two to three orders of magnitude of the well-accepted phenomenological model of Blendowske-Walliser for light clusters.

  18. Revival of oscillation from mean-field-induced death: Theory and experiment

    NASA Astrophysics Data System (ADS)

    Ghosh, Debarati; Banerjee, Tanmoy; Kurths, Jürgen

    2015-11-01

    The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning in many physical, biological, and physiological systems. Recently a general technique of restoration of rhythmicity in diffusively coupled networks of nonlinear oscillators has been proposed in Zou et al. [Nat. Commun. 6, 7709 (2015), 10.1038/ncomms8709], where it is shown that a proper feedback parameter that controls the rate of diffusion can effectively revive oscillation from an oscillation suppressed state. In this paper we show that the mean-field diffusive coupling, which can suppress oscillation even in a network of identical oscillators, can be modified in order to revoke the cessation of oscillation induced by it. Using a rigorous bifurcation analysis we show that, unlike other diffusive coupling schemes, here one has two control parameters, namely the density of the mean-field and the feedback parameter that can be controlled to revive oscillation from a death state. We demonstrate that an appropriate choice of density of the mean field is capable of inducing rhythmicity even in the presence of complete diffusion, which is a unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the experimental observation of revival of oscillation from the mean-field-induced oscillation suppression state that supports our theoretical results.

  19. Revival of oscillation from mean-field-induced death: Theory and experiment.

    PubMed

    Ghosh, Debarati; Banerjee, Tanmoy; Kurths, Jürgen

    2015-11-01

    The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning in many physical, biological, and physiological systems. Recently a general technique of restoration of rhythmicity in diffusively coupled networks of nonlinear oscillators has been proposed in Zou et al. [Nat. Commun. 6, 7709 (2015)], where it is shown that a proper feedback parameter that controls the rate of diffusion can effectively revive oscillation from an oscillation suppressed state. In this paper we show that the mean-field diffusive coupling, which can suppress oscillation even in a network of identical oscillators, can be modified in order to revoke the cessation of oscillation induced by it. Using a rigorous bifurcation analysis we show that, unlike other diffusive coupling schemes, here one has two control parameters, namely the density of the mean-field and the feedback parameter that can be controlled to revive oscillation from a death state. We demonstrate that an appropriate choice of density of the mean field is capable of inducing rhythmicity even in the presence of complete diffusion, which is a unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the experimental observation of revival of oscillation from the mean-field-induced oscillation suppression state that supports our theoretical results. PMID:26651763

  20. Mean-field theory for the inverse Ising problem at low temperatures.

    PubMed

    Nguyen, H Chau; Berg, Johannes

    2012-08-01

    The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of spin configurations sampled from the Boltzmann measure. To invert the relationship between model parameters and observables (magnetizations and correlations), mean-field approximations are often used, allowing the determination of model parameters from data. However, all known mean-field methods fail at low temperatures with the emergence of multiple thermodynamic states. Here, we show how clustering spin configurations can approximate these thermodynamic states and how mean-field methods applied to thermodynamic states allow an efficient reconstruction of Ising models also at low temperatures.

  1. Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses.

    PubMed

    Bressloff, P C

    1999-08-01

    We analyze the effects of synaptic depression or facilitation on the existence and stability of the splay or asynchronous state in a population of all-to-all, pulse-coupled neural oscillators. We use mean-field techniques to derive conditions for the local stability of the splay state and determine how stability depends on the degree of synaptic depression or facilitation. We also consider the effects of noise. Extensions of the mean-field results to finite networks are developed in terms of the nonlinear firing time map.

  2. Band mixing effects in mean field theories. I. E 2 transitions in the interacting boson model 1

    SciTech Connect

    Kuyucak, S.; Morrison, I. )

    1990-04-01

    The 1/{ital N} expansion method, which is an angular momentum projected mean field theory, is used to investigate the nature of electromagnetic transitions in the interacting boson model. Conversely, comparison with the exact interacting boson model results sheds light on the range of validity of the mean field theory. It is shown that the projected mean field results for the {ital E}2 transitions among the ground, {beta}, and {gamma} bands are incomplete for the spin-dependent terms, and it is essential to include band mixing effects for a correct (Mikhailov) analysis of {ital E}2 data. The algebraic expressions derived are general and will be useful in the analysis of experimental data in terms of both the {ital sd} and {ital sdg} boson models.

  3. Nuclear matter properties in the relativistic mean-field theory at finite temperature with interaction between sigma-omega mesons

    SciTech Connect

    Costa, R. S.; Duarte, S. B.; Oliveira, J. C. T.; Chiapparini, M.

    2010-05-21

    We study the nuclear matter properties in the regime of high temperatures using a relativistic mean-field theory. Contrasting with the usual linear Walecka model, we include the sigma-omega meson coupling in order to investigate the role of this interaction in the nucleon effective mass behavior. Some numerical results are presented and discussed.

  4. Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

    SciTech Connect

    Kelly, Aaron; Markland, Thomas E.; Brackbill, Nora

    2015-03-07

    In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

  5. Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations.

    PubMed

    Kelly, Aaron; Brackbill, Nora; Markland, Thomas E

    2015-03-01

    In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

  6. Temperature Dependence of the Nuclear Energy in Relativistic Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Nerlo-Pomorska, B.; Pomorski, K.; Sykut, J.; Bartel, J.

    Self-consistent relativistic mean-field (RMF) calculations with the NL3 parameter set were performed for 171 spherical even-even nuclei with 16≤A≤224 at temperatures in the range 0≤T≤4 MeV. For this sample of nuclei single-particle level densities are determined by analyzing the data obtained for various temperatures. A new shell-correction method is used to evaluate shell effects at all temperatures. The single-particle level density is expressed as function of mass number A and relative isospin I and compared with previous estimates.

  7. LETTER TO THE EDITOR: Car-oriented mean-field theory for traffic flow models

    NASA Astrophysics Data System (ADS)

    Schadschneider, Andreas; Schreckenberg, Michael

    1997-02-01

    We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between consecutive cars. Therefore certain longer-ranged correlations are taken into account and even a mean-field approach yields non-trivial results. In fact for the model with 0305-4470/30/4/005/img5 the exact solution is reproduced. For 0305-4470/30/4/005/img6 the fundamental diagram shows a good agreement with results from simulations.

  8. Landau-like theory for universality of critical exponents in quasistationary states of isolated mean-field systems

    NASA Astrophysics Data System (ADS)

    Ogawa, Shun; Yamaguchi, Yoshiyuki Y.

    2015-06-01

    An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two nonclassical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends the universality class of the nonclassical exponents to spatially periodic one-dimensional systems and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.

  9. Hyperdeformation in the cranked relativistic mean field theory: The Z=40-58 region of the nuclear chart

    SciTech Connect

    Afanasjev, A. V.; Abusara, H.

    2008-07-15

    The systematic investigation of hyperdeformation (HD) at high spin in the Z=40-58 region of the nuclear chart was performed in the framework of the cranked relativistic mean-field theory. The properties of the moments of inertia of the HD bands, the role of the single-particle and necking degrees of freedom at HD, the spins at which the HD bands become yrast, the possibility to observe discrete HD bands, and so on are discussed in detail.

  10. MEAN-FIELD THEORY AND COMPUTATION OF ELECTROSTATICS WITH IONIC CONCENTRATION DEPENDENT DIELECTRICS *

    PubMed Central

    LI, BO; WEN, JIAYI; ZHOU, SHENGGAO

    2015-01-01

    We construct a mean-field variational model to study how the dependence of dielectric coefficient (i.e., relative permittivity) on local ionic concentrations affects the electrostatic interaction in an ionic solution near a charged surface. The electrostatic free-energy functional of ionic concentrations, which is the key object in our model, consists mainly of the electrostatic potential energy and the ionic ideal-gas entropy. The electrostatic potential is determined by Poisson’s equation in which the dielectric coefficient depends on the sum of concentrations of individual ionic species. This dependence is assumed to be qualitatively the same as that on the salt concentration for which experimental data are available and analytical forms can be obtained by the data fitting. We derive the first and second variations of the free-energy functional, obtain the generalized Boltzmann distributions, and show that the free-energy functional is in general nonconvex. To validate our mathematical analysis, we numerically minimize our electrostatic free-energy functional for a radially symmetric charged system. Our extensive computations reveal several features that are significantly different from a system modeled with a dielectric coefficient independent of ionic concentration. These include the non-monotonicity of ionic concentrations, the ionic depletion near a charged surface that has been previously predicted by a one-dimensional model, and the enhancement of such depletion due to the increase of surface charges or bulk ionic concentrations. PMID:26877718

  11. Systematic study of low-lying E1 strength using the time-dependent mean field theory

    SciTech Connect

    Ebata, S.; Nakatsukasa, T.; Inakura, T.

    2012-11-12

    We carry out systematic investigation of electric dipole (E1) mode from light to heavy nuclei, using a new time-dependent mean field theory: the Canonical-basis Time-Dependent Hartree-Fock-Bogoliubov (Cb-TDHFB) theory. The Cb-TDHFB in the three-dimensional coordinate space representation can deal with pairing correlation and any kind of deformation in the timedependent framework. We report the neutron-number dependence of the low-energy E1 mode for light (A > 40) and heavy isotopes (A < 100) around N= 82.

  12. Mott Multiferroics and Ferroelectric Metals from Dynamical Mean-Field Theory combined with Density-Functional Theory

    NASA Astrophysics Data System (ADS)

    Capone, Massimo

    2015-03-01

    Multiferroic materials, in which ferroelectricity and long-range magnetic ordering coexist, are natural candidates for applications. In this perspective, the most promising compounds are those in which the two phenomena do not simply coexist, but they influence each other through a magnetoelectric coupling. We present different applications of Density Functional Theory combined with Dynamical Mean-Field Theory in which electron-electron correlation effects are crucial in the stabilization of multiferroic behavior and in the magnetoelectric coupling. Within this wide family we can distinguish different cases. In Sr0.5Ba0.5MnO3 the multiferroic behavior is associated with a Mott insulating state in which the Mn half-filled t2g orbitals are responsible of the magnetic properties and the value of the polarization is strongly affected by the magnetic state. LiOsO3 shares the same electronic configuration with half-filled Os t2g orbitals. Despite this configuration enhances the effect of electron-electron interactions, the material remains metallic and represents a peculiar ferroelectric metal. We propose however how to turn this non-magnetic polar metal into a multiferroic through the design of a superlattice, which increases the degree of correlation, leading to Mott localization of the Os orbitals. In completely different systems, such as organic crystals like (TMTTF)2-X, strong correlations can lead to multiferroicity in organic crystals such as (TMTTF)2-X, where charge ordering promotes a polarization which is favored by an antiferromagnetic ordering. We finally discuss how strong correlations can play a major role away from half-filling when the Hund's coupling is sizable in compounds with a nominal valence of, e.g., two electrons in the three t2g orbitals. Such ``Hund's metals'' are correlated despite being far from Mott localization. This physical regime can be a fertile ground to obtain other ferroelectric metals. This work is supported by ERC/FP7 through the

  13. Screened exchange dynamical mean-field theory and its relation to density functional theory: SrVO3 and SrTiO3

    NASA Astrophysics Data System (ADS)

    van Roekeghem, Ambroise; Biermann, Silke

    2014-12-01

    We present the first application of a recently proposed electronic-structure scheme to transition metal oxides: screened exchange dynamical mean-field theory includes non-local exchange beyond the local density approximation and dynamical correlations beyond standard dynamical mean-field theory. Our results for the spectral function of SrVO3 are in agreement with the available experimental data, including photoemission spectroscopy and thermodynamics. Finally, the 3d0 compound SrTiO3 serves as a test case to illustrate how the theory reduces to the band structure of standard electronic-structure techniques for weakly correlated compounds.

  14. Current-voltage profile of a strongly correlated materials heterostructure using non-equilibrium dynamical mean field theory

    NASA Astrophysics Data System (ADS)

    Najafi, Khadijeh; Freericks, James

    We investigate the nonlinear electronic transport across a multilayered heterostructure which consists of Mott insulator layers connected to ballistic metal leads on both sides. To create current flow, we turn on an electric field in the leads for a finite period of time and then turn it off and let the system reach the steady state by adding an electric field over the correlated region. We use nonequilibrium dynamical mean-field theory to obtain the current-voltage relation. To do so, we current bias the device, and adjust the voltage profile to ensure current conservation and charge conservation throughout. The calculation ultimately works directly in the steady-state limit.

  15. Generalized gradient expansion for inhomogeneous dynamical mean-field theory: Application to ultracold atoms in a harmonic trap

    NASA Astrophysics Data System (ADS)

    Freericks, J. K.; Han, Shuyang; Mikelsons, Karlis; Krishnamurthy, H. R.

    2016-08-01

    We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher temperatures, in the normal phase, it shows why the local density approximation works so well, since the local density and generalized gradient approximations are essentially indistinguishable from each other (and from the exact solution within full inhomogeneous dynamical mean-field theory). But because the generalized gradient expansion only involves nearest-neighbor corrections, it does not work as well at low temperatures, when the systems enter into ordered phases. This is primarily due to the problem that ordered phases often satisfy some global constraints, which determine the spatial ordering pattern, and the local density and generalized gradient approximations are not able to impose those kinds of constraints; they also overestimate the tendency to order. The theory is applied to phase separation of different mass fermionic mixtures represented by the Falicov-Kimball model and to determining the entropy per particle of a fermionic system represented by the Hubbard model. The generalized gradient approximation is a useful diagnostic for the accuracy of the local density approximation—when both methods agree, they are likely accurate, when they disagree, neither is likely to be correct.

  16. Hartree-Fock mean-field theory for trapped dirty bosons

    NASA Astrophysics Data System (ADS)

    Khellil, Tama; Pelster, Axel

    2016-06-01

    Here we work out in detail a non-perturbative approach to the dirty boson problem, which relies on the Hartree-Fock theory and the replica method. For a weakly interacting Bose gas within a trapped confinement and a delta-correlated disorder potential at finite temperature, we determine the underlying free energy. From it we determine via extremization self-consistency equations for the three components of the particle density, namely the condensate density, the thermal density, and the density of fragmented local Bose-Einstein condensates within the respective minima of the random potential landscape. Solving these self-consistency equations in one and three dimensions in two other publications has revealed how these three densities change for increasing disorder strength.

  17. Studies of 44Ti and 48Cr Nuclei Within Variational Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Roy, Prianka; Dhiman, Shashi K.

    We have studied the nuclear structure properties of high angular momentum states in N = Z, 44Ti, and 48Cr nuclei by using Hartree-Fock-Bogoliubov (HFB) method with variation after angular momentum projection (VAP-HFB) technique. Effect of Kuo-Brown "KB" and its modified effective interactions has been studied using four sets of single-particle energies (SPEs) on rotational bands of these nuclei. It is seen that the HFB theory with projected wave functions by employing the VAP method describes well the overall trends of the experimental yrast level spectrum and the transition probabilities in these nuclei. The backbending of the 48Cr nucleus has been well reproduced by the present VAP-HFB calculations with the original "KB" effective interaction at J = 12ℏ. The modified effective interaction also gives backbending for 48Cr but at J = 10ℏ. The shape change associated with backbending effect in 48Cr is due to the large decrease in B(E2↓) values beyond J = 12ℏ state.

  18. Mean Field Theory of a Coupled Heisenberg Model and Its Application to an Organic Antiferromagnet with Magnetic Anions

    NASA Astrophysics Data System (ADS)

    Ito, Kazuhiro; Shimahara, Hiroshi

    2016-02-01

    We examine the mean field theory of a uniaxial coupled Heisenberg antiferromagnet with two subsystems, one of which consists of strongly interacting small spins and the other consists of weakly interacting large spins. We reanalyze the experimental data of specific heat and magnetic susceptibility obtained by previous authors for the organic compound λ-(BETS)2FeCl4 at low temperatures, where BETS stands for bis(ethylenedithio)tetraselenafulvalene. The model parameters for this compound are evaluated, where the applicability of the theory is checked. As a result, it is found that J1 ≫ J12 ≫ J2, where J1, J2, and J12 denote the exchange coupling constant between π spins, that between 3d spins, and that between π and 3d spins, respectively. At the low-temperature limit, both sublattice magnetizations of the 3d and π spins are saturated, and the present model is reduced to the Schottky model, which successfully explains experimental observations in previous studies. As temperature increases, fluctuations of 3d spins increase, while π spins remain almost saturated. Near the critical temperature, both spins fluctuate significantly, and thus the mean field approximation breaks down. It is revealed that the magnetic anisotropy, which may be crucial to the antiferromagnetic long-range order, originates from J12 rather than from J2 and that the angle between the magnetic easy-axis and the crystal c-axis is approximately 26-27° in the present effective model.

  19. Superheavy nuclei with the vector self-coupling of the ω-meson in relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Saldanha, A. A.; Farhan, A. R.; Sharma, M. M.

    2009-11-01

    We have studied properties and the shell structure of the superheavy elements from Z = 102 to Z = 120 within the framework of relativistic mean field (RMF) theory. The region of study spans nuclides with neutron numbers N = 150-190. The Lagrangian model NL-SV1 with the inclusion of the vector self-coupling of the ω-meson has been employed in this work. We have performed RMF + BCS calculations for an axially deformed configuration of nuclei. The ground-state binding energies, single-particle properties and quadrupole deformation of nuclei have been obtained from the mean-field minimizations. Two-neutron separation energies, Qα values and α-decay half-life have been evaluated. It is shown that a large number of nuclides exhibit the phenomenon of shape coexistence over a significant region of the superheavy elements. Shape coexistence of a prolate and an oblate shape is prevalent in nuclides far below N = 184, whilst nuclei in the vicinity of N = 184 tend to show a shape coexistence between a spherical and an oblate shape. The shell structure and two-neutron separation energies obtained with RMF theory reinforce the neutron number N = 184 as a major magic number. It is shown that the neutron number N = 172 acts akin to a magic number in the deformed region. It is suggested that the combination of Z = 120 and N = 172 has the potential of being a doubly magic number in the superheavy region.

  20. Analysis of surface segregation in polymer mixtures: A combination of mean field and statistical associated fluid theories

    NASA Astrophysics Data System (ADS)

    Krawczyk, Jaroslaw; Croce, Salvatore; Chakrabarti, Buddhapriya; Tasche, Jos

    The surface segregation in polymer mixtures remains a challenging problem for both academic exploration as well as industrial applications. Despite its ubiquity and several theoretical attempts a good agreement between computed and experimentally observed profiles has not yet been achieved. A simple theoretical model proposed in this context by Schmidt and Binder combines Flory-Huggins free energy of mixing with the square gradient theory of wetting of a wall by fluid. While the theory gives us a qualitative understanding of the surface induced segregation and the surface enrichment it lacks the quantitative comparison with the experiment. The statistical associating fluid theory (SAFT) allows us to calculate accurate free energy for a real polymeric materials. In an earlier work we had shown that increasing the bulk modulus of a polymer matrix through which small molecules migrate to the free surface causes reduction in the surface migrant fraction using Schmidt-Binder and self-consistent field theories. In this work we validate this idea by combining mean field theories and SAFT to identify parameter ranges where such an effect should be observable. Department of Molecular Physics, Łódź University of Technology, Żeromskiego 116, 90-924 Łódź, Poland.

  1. The spectrum of random magnetic fields in the mean field dynamo theory of the Galactic magnetic field

    NASA Technical Reports Server (NTRS)

    Kulsrud, Russell M.; Anderson, Stephen W.

    1992-01-01

    The fluctuation spectrum that must arise in a mean field dynamo generation of galactic fields if the initial field is weak is considered. A kinetic equation for its evolution is derived and solved. The spectrum evolves by transfer of energy from one magnetic mode to another by interaction with turbulent velocity modes. This kinetic equation is valid in the limit that the rate of evolution of the magnetic modes is slower than the reciprocal decorrelation time of the turbulent modes. This turns out to be the case by a factor greater than 3. Most of the fluctuation energy concentrates on small scales, shorter than the hydrodynamic turbulent scales. The fluctuation energy builds up to equipartition with the turbulent energy in times that are short compared to the e-folding time of the mean field. The turbulence becomes strongly modified before the dynamo amplification starts. Thus, the kinematic assumption of the mean dynamo theory is invalid. Thus, the galactic field must have a primordial origin, although it may subsequently be modified by dynamo action.

  2. Dynamical Mean-Field Theory Study of Correlated Electronic Structures and the Phase Diagram of Hydrocarbon Superconductors

    NASA Astrophysics Data System (ADS)

    Kim, Minjae; Choi, Hong Chul; Shim, Ji Hoon; Min, B. I.

    2014-03-01

    We have studied correlated electronic structures and the phase diagram of electron-doped hydrocarbon molecular solids, based on the dynamical mean-field theory. We have determined the phase diagram of hydrocarbon molecular solids as functions of doping and energy parameters including the Coulomb correlation, the Hund coupling, and the molecular-orbital (MO) energy level splitting. We have found that the hydrocarbon superconductors (electron-doped picene and coronene) belong to the multi-band Fermi liquid state, while non-superconducting electron-doped pentacene belongs to the single-band state in the proximity of the metal-insulator transition. The size of the MO energy level splitting plays an important role in deriving the superconductivity of electron-doped hydrocarbon solids. The multi-band nature of hydrocarbon solids from the small MO energy level splitting boosts the superconductivity through the enhanced density of states at the Fermi level.

  3. Incommensurate phase of a triangular frustrated Heisenberg model studied via Schwinger-boson mean-field theory

    NASA Astrophysics Data System (ADS)

    Li, Peng; Su, Haibin; Dong, Hui-Ning; Shen, Shun-Qing

    2009-08-01

    We study a triangular frustrated antiferromagnetic Heisenberg model with nearest-neighbor interactions J1 and third-nearest-neighbor interactions J3 by means of Schwinger-boson mean-field theory. By setting an antiferromagnetic J3 and varying J1 from positive to negative values, we disclose the low-temperature features of its interesting incommensurate phase. The gapless dispersion of quasiparticles leads to the intrinsic T2 law of specific heat. The magnetic susceptibility is linear in temperature. The local magnetization is significantly reduced by quantum fluctuations. We address possible relevance of these results to the low-temperature properties of NiGa2S4. From a careful analysis of the incommensurate spin wavevector, the interaction parameters are estimated as J1≈-3.8755 K and J3≈14.0628 K, in order to account for the experimental data.

  4. Single-proton resonant states and the isospin dependence investigated by Green’s function relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Sun, T. T.; Niu, Z. M.; Zhang, S. Q.

    2016-08-01

    The relativistic mean field theory formulated with Green’s function method (RMF-GF) is applied to investigate single-proton resonant states and isospin dependence. The calculated energies and widths for the single-proton resonant states in {}120{{Sn}} are in good agreement with previous investigations. The single-proton resonant states of the Sn isotopes and the N = 82 isotones are systematically studied and it is shown that the calculated energies and widths decrease monotonically with the increase of neutron number while increase monotonically with the increase of proton number. To further examine the evolutions of the single-proton resonant states, their dependence on the depth, radius and diffuseness of nuclear potential is investigated with the help of an analytic Woods-Saxon potential, and it is found that the increase of radius plays the most important role in the cross phenomenon appearing in the single-proton resonant states of the Sn isotopes.

  5. Mean-field theory of strongly nonlinear random composites: Strong power-law nonlinearity and scaling behavior

    NASA Astrophysics Data System (ADS)

    Wan, W. M. V.; Lee, H. C.; Hui, P. M.; Yu, K. W.

    1996-08-01

    The effective response of random media consisting of two different kinds of strongly nonlinear materials with strong power-law nonlinearity is studied. Each component satisfies current density and electric-field relation of the form J=χ\\|E\\|βE. A simple self-consistent mean-field theory, which leads to a simple way in determining the average local electric field in each constituent, is introduced. Each component is assumed to have a conductivity depending on the averaged local electric field. The averaged local electric field is then determined self-consistently. Numerical simulations of the system are carried out on random nonlinear resistor networks. Theoretical results are compared with simulation data, and excellent agreements are found. Results are also compared with the Hashin-Shtrikman lower bound proposed by Ponte Castaneda et al. [Phys. Rev. B 46, 4387 (1992)]. It is found that the present theory, at small contrasts of χ between the two components, gives a result identical to that of Ponte Castaneda et al. up to second order of the contrast. The crossover and scaling behavior of the effective response near the percolation threshold as suggested by the present theory are discussed and demonstrated.

  6. Mean-field theory for the Mott-insulator-paired-superfluid phase transition in the two-species Bose-Hubbard model

    SciTech Connect

    Iskin, M.

    2010-11-15

    The standard mean-field theory for the Mott-insulator-superfluid phase transition is not sufficient to describe the Mott-insulator-paired-superfluid phase transition. Therefore, by restricting the two-species Bose-Hubbard Hamiltonian to the subspace of paired particles, and using perturbation theory, here we derive an analytic mean-field expression for the Mott-insulator-paired-superfluid transition boundary.

  7. Combined local-density and dynamical mean field theory calculations for the compressed lanthanides Ce, Pr, and Nd

    SciTech Connect

    McMahan, A K

    2005-03-30

    This paper reports calculations for compressed Ce (4f{sup 1}), Pr (4f{sup 2}), and Nd (4f{sup 3}) using a combination of the local-density approximation (LDA) and dynamical mean field theory (DMFT), or LDA+DMFT. The 4f moment, spectra, and the total energy among other properties are examined as functions of volume and atomic number for an assumed face-centered cubic (fcc) structure. These materials are seen to be strongly localized at ambient pressure and for compressions up through the experimentally observed fcc phases ({gamma} phase for Ce), in the sense of having fully formed Hund's rules moments and little 4f spectral weight at the Fermi level. Subsequent compression for all three lanthanides brings about significant deviation of the moments from their Hund's rules values, a growing Kondo resonance at the fermi level, an associated softening in the total energy, and quenching of the spin orbit since the Kondo resonance is of mixed spin-orbit character while the lower Hubbard band is predominantly j = 5/2. while the most dramatic changes for Ce occur within the two-phase region of the {gamma}-{alpha} volume collapse transition, as found in earlier work, those for Pr and Nd occur within the volume range of the experimentally observed distorted fcc (dfcc) phase, which is therefore seen here as transitional and not part of the localized trivalent lanthanide sequence. The experimentally observed collapse to the {alpha}-U structure in Pr occurs only on further compression, and no such collapse is found in Nd. These lanthanides start closer to the localized limit for increasing atomic number, and so the theoretical signatures noted above are also offset to smaller volume as well, which is possibly related to the measured systematics of the size of the volume collapse being 15%, 9%, and none for Ce, Pr, and Nd, respectively.

  8. Doping-driven evolution of the superconducting state from a doped Mott insulator: Cluster dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    Civelli, M.

    2009-05-01

    In this paper we investigate the zero-temperature doping-driven evolution of a superconductor toward the Mott insulator in a two-dimensional electron model, relevant for high-temperature superconductivity. To this purpose we use a cluster extension of dynamical mean-field theory. Our results show that a standard d -wave superconductor, realized at high doping, is driven into the Mott insulator via an intermediate superconducting state displaying unconventional physical properties. By restoring the translational invariance of the lattice, we give an interpretation of these findings in momentum space. In particular, we show that at a finite doping a strong momentum-space differentiation takes place: non-Fermi liquid and insulatinglike (pseudogap) characters rise in some regions (antinodes), while Fermi liquid quasiparticles survive in other regions (nodes) of momentum space. We describe the consequence of these happenings on the spectral properties, stressing in particular the behavior of the superconducting gap, which reveals two distinct nodal and antinodal energy scales as a function of doping, detected in photoemission and Raman spectroscopy experiments. We study and compare with experimental results the doping-dependent behavior of other physical quantities, such as for instance, the nodal quasiparticle velocity (extracted in angle-resolved photoemission) and the low-energy slopes of the local density of states and of the Raman scattering response. We then propose a description of the evolution of the electronic structure while approaching the Mott transition. We show that, within our formalism, a strong asymmetry naturally arises in the local density of states, measured in scanning tunneling spectroscopy. We investigate in detail the doping evolution of the electronic bands, focusing on the kinklike quasiparticle dispersion observed with angle-resolved photoemission in specific cuts of the momentum-energy space. We finally show the consequences of the

  9. Tetragonal and collapsed-tetragonal phases of CaFe2As2 : A view from angle-resolved photoemission and dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    van Roekeghem, Ambroise; Richard, Pierre; Shi, Xun; Wu, Shangfei; Zeng, Lingkun; Saparov, Bayrammurad; Ohtsubo, Yoshiyuki; Qian, Tian; Sefat, Athena S.; Biermann, Silke; Ding, Hong

    2016-06-01

    We present a study of the tetragonal to collapsed-tetragonal transition of CaFe2As2 using angle-resolved photoemission spectroscopy and dynamical mean field theory-based electronic structure calculations. We observe that the collapsed-tetragonal phase exhibits reduced correlations and a higher coherence temperature due to the stronger Fe-As hybridization. Furthermore, a comparison of measured photoemission spectra and theoretical spectral functions shows that momentum-dependent corrections to the density functional band structure are essential for the description of low-energy quasiparticle dispersions. We introduce those using the recently proposed combined "screened exchange + dynamical mean field theory" scheme.

  10. α -decay chains of 288 173 115 and 287 172 1 15 in the relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Geng, L. S.; Toki, H.; Meng, J.

    2003-12-01

    In the recent experiments designed to synthesize the element 115 in the 243 Am+ 48 Ca reaction at Dubna in Russia, three similar decay chains consisting of five consecutive α decays and another different decay chain of four consecutive α decays are detected, and the decay properties of these synthesized nuclei are claimed to be consistent with consecutive α decays originating from the parent isotopes of the new element 115, 288 115 and 287 115 , respectively. Here in the present work, the recently developed deformed relativistic mean field + BCS method with a density-independent δ function interaction in the pairing channel is applied to the analysis of these newly synthesized superheavy nuclei. The calculated α -decay energies and half-lives agree well with the experimental values and with those of the macroscopic-microscopic finite-range droplet model with folded-Yukawa single-particle potentials and Yukawa-plus-exponential model with Woods-Saxon single-particle potentials. In the mean field Lagrangian, the TMA parameter set is used. Particular emphasis is laid on the influence to both the ground-state properties and energy surfaces introduced by different treatments of pairing. Two different effective interactions in the particle-particle channel, i.e., the constant pairing and the density-independent δ -function interaction, together with the blocking effect are discussed in detail.

  11. Mean-Field Theories for Terrace-Width Distributions of Vicinal Surfaces: Beyond the Generalized Wigner Distribution

    NASA Astrophysics Data System (ADS)

    Richards, Howard L.; Einstein, T. L.

    2000-03-01

    The so-called generalized Wigner distribution (GWD) has been shown to provide an excellent description of terrace width distributions (TWDs) on vicinal surfaces for which there are repulsive interactions between steps that are proportional to the inverse square of the step separation.(T. L. Einstein and O. Pierre-Louis, Surface Sci. 424), L299 (1999). (S. D. Cohen, H. L. Richards, and T. L. Einstein, preprint.) Until recently, however, there was no plausible physical explanation for the excellent agreement between the GWD and the TWDs observed in Monte Carlo simulations^3 or derived from a few integrable models.^2 Here we show that the GWD can be derived from a mean-field approximation similar in spirit to the Gruber-Mullins approximation.(E. E. Gruber and W. W. Mullins, J. Phys. Chem. Solids 28), 875 (1967) This mean-field treatment can be generalized to other forms of step-step repulsions; the resulting predictions are in good agreement with Monte Carlo simulations. Finally, the process can be inverted to allow nontrivial step-step interactions to be extracted from experimental TWDs.

  12. What is a particle-conserving Topological Superfluid? The fate of Majorana modes beyond mean-field theory

    NASA Astrophysics Data System (ADS)

    Ortiz, Gerardo; Cobanera, Emilio

    2016-09-01

    We investigate Majorana modes of number-conserving fermionic superfluids from both basic physics principles, and concrete models perspectives. After reviewing a criterion for establishing topological superfluidity in interacting systems, based on many-body fermionic parity switches, we reveal the emergence of zero-energy modes anticommuting with fermionic parity. Those many-body Majorana modes are constructed as coherent superpositions of states with different number of fermions. While realization of Majorana modes beyond mean field is plausible, we show that the challenge to quantum-control them is compounded by particle-conservation, and more realistic protocols will have to balance engineering needs with astringent constraints coming from superselection rules. Majorana modes in number-conserving systems are the result of a peculiar interplay between quantum statistics, fermionic parity, and an unusual form of spontaneous symmetry breaking. We test these ideas on the Richardson-Gaudin-Kitaev chain, a number-conserving model solvable by way of the algebraic Bethe ansatz, and equivalent in mean field to a long-range Kitaev chain.

  13. Global study of beyond-mean-field correlation energies in covariant energy density functional theory using a collective Hamiltonian method

    NASA Astrophysics Data System (ADS)

    Lu, K. Q.; Li, Z. X.; Li, Z. P.; Yao, J. M.; Meng, J.

    2015-02-01

    We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from Z =8 to Z =108 by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD -ME δ (2.29 MeV), and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by ˜34 % in comparison with the cranking prescription.

  14. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles.

    PubMed

    Speck, Thomas; Menzel, Andreas M; Bialké, Julian; Löwen, Hartmut

    2015-06-14

    Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.

  15. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

    SciTech Connect

    Speck, Thomas; Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut

    2015-06-14

    Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.

  16. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles.

    PubMed

    Speck, Thomas; Menzel, Andreas M; Bialké, Julian; Löwen, Hartmut

    2015-06-14

    Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results. PMID:26071703

  17. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

    NASA Astrophysics Data System (ADS)

    Speck, Thomas; Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut

    2015-06-01

    Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.

  18. Dynamic mean field theory for lattice gas models of fluids confined in porous materials: Higher order theory based on the Bethe-Peierls and path probability method approximations

    SciTech Connect

    Edison, John R.; Monson, Peter A.

    2014-07-14

    Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.

  19. Screening and nonlocal correlations in the extended Hubbard model from self-consistent combined GW and dynamical mean field theory

    NASA Astrophysics Data System (ADS)

    Ayral, Thomas; Biermann, Silke; Werner, Philipp

    2013-03-01

    We describe a recent implementation of the combined GW and dynamical mean field method (GW+DMFT) for the two-dimensional Hubbard model with onsite and nearest-neighbor repulsion. We clarify the relation of the GW+DMFT scheme to alternative approaches in the literature, and discuss the corresponding approximations to the free-energy functional of the model. Furthermore, we describe a numerically exact technique for the solution of the GW+DMFT equations, namely, the hybridization expansion continuous-time algorithm for impurity models with retarded interactions. We compute the low-temperature phase diagram of the half-filled extended Hubbard model, addressing the metal-insulator transition at small intersite interactions and the transition to a charge-ordered state for stronger intersite repulsions. GW+DMFT introduces a nontrivial momentum dependence into the many-body self-energy and polarization. We find that the charge fluctuations included in the present approach have a larger impact on the latter than on the former. Finally, within the GW+DMFT framework, as in extended DMFT, the intersite repulsion translates into a frequency dependence of the local effective interaction. We analyze this dependence and show how it affects the local spectral function.

  20. Optical potential obtained from relativistic-mean-field theory-based microscopic nucleon-nucleon interaction: applied to cluster radioactive decays

    NASA Astrophysics Data System (ADS)

    Singh, BirBikram; Bhuyan, M.; Patra, S. K.; Gupta, Raj K.

    2012-02-01

    A microscopic nucleon-nucleon (NN) interaction is derived from the popular relativistic-mean-field (RMF) theory Lagrangian and used to obtain the optical potential by folding it with the RMF densities of cluster and daughter nuclei. The NN-interaction is remarkably related to the inbuilt fundamental parameters of RMF theory, and the results of the application of the so obtained optical potential, made to exotic cluster radioactive decays and α+α scattering, are found comparable to that for the well-known, phenomenological M3Y effective NN-interaction. The RMF-based NN-interaction can also be used to calculate a number of other nuclear observables.

  1. Spin-orbit and orbit-orbit strengths for the radioactive neutron-rich doubly magic nucleus {sup 132}Sn in relativistic mean-field theory

    SciTech Connect

    Liang Haozhao; Zhao Pengwei; Li Lulu; Meng Jie

    2011-01-15

    Relativistic mean-field (RMF) theory is applied to investigate the properties of the radioactive neutron-rich doubly magic nucleus {sup 132}Sn and the corresponding isotopes and isotones. The two-neutron and two-proton separation energies are well reproduced by the RMF theory. In particular, the RMF results agree with the experimental single-particle spectrum in {sup 132}Sn as well as the Nilsson spin-orbit parameter C and orbit-orbit parameter D thus extracted, but remarkably differ from the traditional Nilsson parameters. Furthermore, the present results provide a guideline for the isospin dependence of the Nilsson parameters.

  2. Equivalence between fractional exclusion statistics and self-consistent mean-field theory in interacting-particle systems in any number of dimensions

    NASA Astrophysics Data System (ADS)

    Anghel, D. V.; Nemnes, G. A.; Gulminelli, F.

    2013-10-01

    We describe a mean field interacting particle system in any number of dimensions and in a generic external potential as an ideal gas with fractional exclusion statistics (FES). We define the FES quasiparticle energies, we calculate the FES parameters of the system and we deduce the equations for the equilibrium particle populations. The FES gas is “ideal,” in the sense that the quasiparticle energies do not depend on the other quasiparticle levels’ populations and the sum of the quasiparticle energies is equal to the total energy of the system. We prove that the FES formalism is equivalent to the semiclassical or Thomas Fermi limit of the self-consistent mean-field theory and the FES quasiparticle populations may be calculated from the Landau quasiparticle populations by making the correspondence between the FES and the Landau quasiparticle energies. The FES provides a natural semiclassical ideal gas description of the interacting particle gas.

  3. Comparison of the order of magnetic phase transitions in several magnetocaloric materials using the rescaled universal curve, Banerjee and mean field theory criteria

    SciTech Connect

    Burrola-Gándara, L. A. Santillan-Rodriguez, C. R.; Rivera-Gomez, F. J.; Saenz-Hernandez, R. J.; Botello-Zubiate, M. E.; Matutes-Aquino, J. A.

    2015-05-07

    Magnetocaloric materials with second order phase transition near the Curie temperature can be described by critical phenomena theory. In this theory, scaling, universality, and renormalization are key concepts from which several phase transition order criteria are derived. In this work, the rescaled universal curve, Banerjee and mean field theory criteria were used to make a comparison for several magnetocaloric materials including pure Gd, SmCo{sub 1.8}Fe{sub 0.2}, MnFeP{sub 0.46}As{sub 0.54}, and La{sub 0.7}Ca{sub 0.15}Sr{sub 0.15}MnO{sub 3}. Pure Gd, SmCo{sub 1.8}Fe{sub 0.2}, and La{sub 0.7}Ca{sub 0.15}Sr{sub 0.15}MnO{sub 3} present a collapse of the rescaled magnetic entropy change curves into a universal curve, which indicates a second order phase transition; applying Banerjee criterion to H/σ vs σ{sup 2} Arrot plots and the mean field theory relation |ΔS{sub M}| ∝ (μ{sub 0}H/T{sub c}){sup 2/3} for the same materials also determines a second order phase transition. However, in the MnFeP{sub 0.46}As{sub 0.54} sample, the Banerjee criterion applied to the H/σ vs σ{sup 2} Arrot plot indicates a first order magnetic phase transition, while the mean field theory prediction for a second order phase transition, |ΔS{sub M}| ∝ (μ{sub 0}H/T{sub c}){sup 2/3}, describes a second order behavior. Also, a mixture of first and second order behavior was indicated by the rescaled universal curve criterion. The diverse results obtained for each criterion in MnFeP{sub 0.46}As{sub 0.54} are apparently related to the magnetoelastic effect and to the simultaneous presence of weak and strong magnetism in Fe (3f) and Mn (3g) alternate atomic layers, respectively. The simultaneous application of the universal curve, the Banerjee and the mean field theory criteria has allowed a better understanding about the nature of the order of the phase transitions in different magnetocaloric materials.

  4. An effective mean field theory for the coexistence of anti-ferromagnetism and superconductivity: Applications to iron-based superconductors and cold Bose-Fermi atomic mixtures

    NASA Astrophysics Data System (ADS)

    Brackett, Jeremy; Newman, Joseph; De Silva, Theja N.

    2016-10-01

    We study an effective fermion model on a square lattice to investigate the cooperation and competition of superconductivity and anti-ferromagnetism. In addition to particle tunneling and on-site interaction, a bosonic excitation mediated attractive interaction is also included in the model. We assume that the attractive interaction is mediated by spin fluctuations and excitations of Bose-Einstein condensation (BEC) in electronic systems and Bose-Fermi mixtures on optical lattices, respectively. Using an effective mean-field theory to treat both superconductivity and anti-ferromagnetism at equal footing, we study a single effective model relevant for both systems within the Landau energy functional approach and a linearized theory. Within our approaches, we find possible co-existence of superconductivity and anti-ferromagnetism for both electronic and cold-atomic models. Our linearized theory shows while spin fluctuations favor d-wave superconductivity and BEC excitations favor s-wave superconductivity.

  5. Impurity-induced magnetic moments on the graphene-lattice Hubbard model: An inhomogeneous cluster dynamical mean-field theory study

    NASA Astrophysics Data System (ADS)

    Charlebois, M.; Sénéchal, D.; Gagnon, A.-M.; Tremblay, A.-M. S.

    2015-01-01

    Defect-induced magnetic moments are at the center of the research effort on spintronic applications of graphene. Here, we study the problem of a nonmagnetic impurity in graphene with a new theoretical method, inhomogeneous cluster dynamical mean-field theory (I-CDMFT), which takes into account interaction-induced short-range correlations while allowing long-range inhomogeneities. The system is described by a Hubbard model on the honeycomb lattice. The impurity is modeled by a local potential. For a large enough potential, interactions induce local antiferromagnetic correlations around the impurity and a net total spin 1/2 appears, in agreement with Lieb's theorem. Bound states caused by the impurity are visible in the local density of states (LDOS) and have their energies shifted by interactions in a spin-dependent way, leading to the antiferromagnetic correlations. Our results take into account dynamical correlations; nevertheless they qualitatively agree with previous mean-field and density functional theory (DFT) studies. Moreover, they provide a relation between impurity potential and on-site repulsion U that could in principle be used to determine experimentally the value of U .

  6. Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring.

    PubMed

    Cattes, Stefanie M; Gubbins, Keith E; Schoen, Martin

    2016-05-21

    In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases. PMID:27208962

  7. Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring.

    PubMed

    Cattes, Stefanie M; Gubbins, Keith E; Schoen, Martin

    2016-05-21

    In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.

  8. Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring

    NASA Astrophysics Data System (ADS)

    Cattes, Stefanie M.; Gubbins, Keith E.; Schoen, Martin

    2016-05-01

    In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.

  9. Dynamical screening effects in correlated electron materials-a progress report on combined many-body perturbation and dynamical mean field theory: 'GW + DMFT'.

    PubMed

    Biermann, Silke

    2014-04-30

    We give a summary of recent progress in the field of electronic structure calculations for materials with strong electronic Coulomb correlations. The discussion focuses on developments beyond the by now well established combination of density functional and dynamical mean field theory dubbed 'LDA + DMFT'. It is organized around the description of dynamical screening effects in the solid. Indeed, screening in the solid gives rise to dynamical local Coulomb interactions U(ω) (Aryasetiawan et al 2004 Phys. Rev. B 70 195104), and this frequency dependence leads to effects that cannot be neglected in a truly first principles description. We review the recently introduced extension of LDA + DMFT to dynamical local Coulomb interactions 'LDA + U(ω) + DMFT' (Casula et al 2012 Phys. Rev. B 85 035115, Werner et al 2012 Nature Phys. 1745-2481). A reliable description of dynamical screening effects is also a central ingredient of the 'GW + DMFT' scheme (Biermann et al 2003 Phys. Rev. Lett. 90 086402), a combination of many-body perturbation theory in Hedin's GW approximation and dynamical mean field theory. Recently, the first GW + DMFT calculations including dynamical screening effects for real materials have been achieved, with applications to SrV O3 (Tomczak et al 2012 Europhys. Lett. 100 67001, Tomczak et al Phys. Rev. B submitted (available electronically as arXiv:1312.7546)) and adatom systems on surfaces (Hansmann et al 2013 Phys. Rev. Lett. 110 166401). We review these and comment on further perspectives in the field. This review is an attempt to put elements of the original works into the broad perspective of the development of truly first principles techniques for correlated electron materials.

  10. Dynamical screening effects in correlated electron materials-a progress report on combined many-body perturbation and dynamical mean field theory: 'GW + DMFT'.

    PubMed

    Biermann, Silke

    2014-04-30

    We give a summary of recent progress in the field of electronic structure calculations for materials with strong electronic Coulomb correlations. The discussion focuses on developments beyond the by now well established combination of density functional and dynamical mean field theory dubbed 'LDA + DMFT'. It is organized around the description of dynamical screening effects in the solid. Indeed, screening in the solid gives rise to dynamical local Coulomb interactions U(ω) (Aryasetiawan et al 2004 Phys. Rev. B 70 195104), and this frequency dependence leads to effects that cannot be neglected in a truly first principles description. We review the recently introduced extension of LDA + DMFT to dynamical local Coulomb interactions 'LDA + U(ω) + DMFT' (Casula et al 2012 Phys. Rev. B 85 035115, Werner et al 2012 Nature Phys. 1745-2481). A reliable description of dynamical screening effects is also a central ingredient of the 'GW + DMFT' scheme (Biermann et al 2003 Phys. Rev. Lett. 90 086402), a combination of many-body perturbation theory in Hedin's GW approximation and dynamical mean field theory. Recently, the first GW + DMFT calculations including dynamical screening effects for real materials have been achieved, with applications to SrV O3 (Tomczak et al 2012 Europhys. Lett. 100 67001, Tomczak et al Phys. Rev. B submitted (available electronically as arXiv:1312.7546)) and adatom systems on surfaces (Hansmann et al 2013 Phys. Rev. Lett. 110 166401). We review these and comment on further perspectives in the field. This review is an attempt to put elements of the original works into the broad perspective of the development of truly first principles techniques for correlated electron materials. PMID:24722486

  11. Successively thresholded domain boundary roughening driven by pinning centers and missing bonds: Hard-spin mean-field theory applied to d=3 Ising magnets.

    PubMed

    Çağlar, Tolga; Berker, A Nihat

    2015-12-01

    Hard-spin mean-field theory has recently been applied to Ising magnets, correctly yielding the absence and presence of an interface roughening transition respectively in d=2 and d=3 dimensions and producing the ordering-roughening phase diagram for isotropic and anisotropic systems. The approach has now been extended to the effects of quenched random pinning centers and missing bonds on the interface of isotropic and anisotropic Ising models in d=3. We find that these frozen impurities cause domain boundary roughening that exhibits consecutive thresholding transitions as a function of interaction anisotropy. For both missing-bond and pinning-center impurities, for moderately large values of the anisotropy, the systems saturate to the "solid-on-solid" limit, exhibiting a single universal curve for the domain boundary width as a function of impurity concentration. PMID:26764656

  12. Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point

    SciTech Connect

    Katanin, A. A.

    2015-06-15

    We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.

  13. Radius studies of 8Li and 8B using the optical-limit Glauber model in conjunction with relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Fan, Guang-Wei; Xu, Wang; Fukuda, M.; Pan, Qiang-Yan; Cai, Xiao-Lu; Fan, Gong-Tao; Li, Yong-Jiang; Luo, Wen; Xu, Ben-Ji; Yan, Zhe; Yang, Li-Feng

    2010-10-01

    We study the reaction cross sections (σR) and root-mean-square (RMS) radii of 8Li and 8B, the halo-like nuclei, with stable target 12C, 27Al and 9Be within the standard optical-limit Glauber model, using densities obtained from relativistic mean-field (RMF) formalisms and other types of distributions. It is found that the experimental σR can be reproduced well at high energy. The RMS radius and Δr extracted by RMF-theory and harmonic oscillator distribution are compared. We find that the RMS radius and Δr of 8B are larger than those of 8Li. In addition, we analyze in detail the relationship between σR and density distribution.

  14. {alpha}-decay and fusion phenomena in heavy ion collisions using nucleon-nucleon interactions derived from relativistic mean-field theory

    SciTech Connect

    Singh, BirBikram; Sahu, B. B.; Patra, S. K.

    2011-06-15

    Nucleus-nucleus potentials are determined in the framework of the double-folding model for a new microscopic nucleon-nucleon (NN) interaction relativistic mean field-3-Yukawa (R3Y) derived from the popular relativistic mean-field theory Lagrangian, and the results are compared for the use of Michigan-3-Yukawa (M3Y) effective NN interactions. The double-folding potentials so obtained are further taken up in the context of the preformed cluster model (PCM) of Gupta and collaborators and the barrier penetration model to study respectively the ground-state (g.s.) {alpha}-decay and low-energy fusion reactions. In this paper, using PCM, we deduce empirically the {alpha} preformation probability P{sub 0}{sup {alpha}(emp)} from experimental data on a few g.s. {alpha} decays in the trans-lead region. For fusion reactions, two projectile-target systems {sup 12}C+{sup 208}Pb and {sup 16}O+{sup 208}Pb are selected for calculating the barrier energies as well positions, fusion cross sections ({sigma}{sub fus}), and fusion barrier distribution [D(E{sub c.m.})]. The barrier energies and positions change for the R3Y NN interactions in comparison with those of the M3Y NN interactions. We find that in the {alpha}-decay studies the values of P{sub 0}{sup {alpha}(emp)}(R3Y) are similar to those of P{sub 0}{sup {alpha}(emp)}(M3Y). Further, both NN interactions give similar {sigma}{sub fus} values using the Wong formula specifically when the R3Y NN interaction calculated {sigma}{sub fus} values are reduced by 1.5 times, and the results are in agreement with the experimental data for both the systems, especially for the higher energies. Results for D(E{sub c.m.}) are also quite similar for both choices of NN interaction.

  15. Composition and temperature dependent electronic structures of NiS2 -xSex alloys: First-principles dynamical mean-field theory approach

    NASA Astrophysics Data System (ADS)

    Moon, Chang-Youn; Kang, Hanhim; Jang, Bo Gyu; Shim, Ji Hoon

    2015-12-01

    We investigate the evolution of the electronic structure of NiS2 -xSex alloys with varying temperature and composition x by using the combined approach of density-functional theory and dynamical mean-field theory. Adopting realistic alloy structures containing S and Se dimers, we map their electronic correlation strength on the phase diagram and observe the metal-insulator transition (MIT) at the composition x =0.5 , which is consistent with the experimental measurements. The temperature dependence of the local magnetic susceptibility is found to show a typical Curie-Weiss-like behavior in the insulating phase while it shows a constant Pauli-like behavior in the metallic phase. A comparison of the electronic structures for NiS2 and NiSe2 in different lattice structures suggests that the MIT in this alloy system can be classified as of bandwidth-control type, where the change in the hybridization strength between Ni d and chalcogen p orbitals is the most important parameter.

  16. Cluster dynamical mean field theory study of antiferromagnetic transition in the square-lattice Hubbard model: Optical conductivity and electronic structure

    NASA Astrophysics Data System (ADS)

    Sato, Toshihiro; Tsunetsugu, Hirokazu

    2016-08-01

    We numerically study optical conductivity σ (ω ) near the "antiferromagnetic" phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections and, to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature and ω dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the ω dependence, and sharpen the Drude peak and a high-ω incoherent peak in the paramagnetic phase. They also enhance the dip in σ (ω ) at ω =0 in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but σ (ω ) retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.

  17. The elimination of deviations of the mean-field Landau-type theory from the fancy size effect experiment in nanoscale ferroelectric BaTiO 3 capacitors

    NASA Astrophysics Data System (ADS)

    Wang, Ying-Long; Wang, Xing-Yuan; Liu, Yang; Liu, Bao-Ting; Fu, Guang-Sheng

    2010-11-01

    A time-dependent mean-field Landau-type model is established based on the dipole energies in epitaxial film in order to investigate thickness dependence of the remanent polarization. It is found that the deviations of the mean-field Landau-type theoretical prediction from the experimental data for size effect can be eliminated in SrRuO 3/BaTiO 3/SrRuO 3 capacitor.

  18. Spins and parities of the odd-A P isotopes within a relativistic mean-field model and elastic magnetic electron-scattering theory

    NASA Astrophysics Data System (ADS)

    Wang, Zaijun; Ren, Zhongzhou; Dong, Tiekuang; Xu, Chang

    2014-08-01

    The ground-state spins and parities of the odd-A phosphorus isotopes 25-47P are studied with the relativistic mean-field (RMF) model and relativistic elastic magnetic electron-scattering theory (REMES). Results of the RMF model with the NL-SH, TM2, and NL3 parameters show that the 2s1/2 and 1d3/2 proton level inversion may occur for the neutron-rich isotopes 37-47P, and, consequently, the possible spin-parity values of 37-47P may be 3/2+, which, except for P47, differs from those given by the NUBASE2012 nuclear data table by Audi et al. Calculations of the elastic magnetic electron scattering of 37-47P with the single valence proton in the 2s1/2 and 1d3/2 state show that the form factors have significant differences. The results imply that elastic magnetic electron scattering can be a possible way to study the 2s1/2 and 1d3/2 level inversion and the spin-parity values of 37-47P. The results can also provide new tests as to what extent the RMF model, along with its various parameter sets, is valid for describing the nuclear structures. In addition, the contributions of the upper and lower components of the Dirac four-spinors to the form factors and the isotopic shifts of the magnetic form factors are discussed.

  19. Sensitivity of neutron radii in a {sup 208}Pb nucleus and a neutron star to nucleon-{sigma}-{rho} coupling corrections in relativistic mean field theory

    SciTech Connect

    Shen, G.; Li, J.; Hillhouse, G.C.; Meng, J.

    2005-01-01

    We study the sensitivity of the neutron skin thickness S in a {sup 208}Pb nucleus to the addition of nucleon-{sigma}-{rho} coupling corrections to a selection (PK1, NL3, S271, and Z271) of interactions in a relativistic mean field model. The PK1 and NL3 effective interactions lead to a minimum value of S= 0.16 fm in comparison with the original value of S= 0.28 fm. The S271 and Z271 effective interactions yield even smaller values of S= 0.11 fm, which are similar to those for nonrelativistic mean field models. A precise measurement of the neutron radius, and therefore S, in {sup 208}Pb will place an important constraint on both relativistic and nonrelativistic mean field models. We also study the correlation between the radius of a 1.4-solar-mass neutron star and S.

  20. A mean field approach to watershed hydrology

    NASA Astrophysics Data System (ADS)

    Bartlett, Mark; Porporato, Amilcare

    2016-04-01

    Mean field theory (also known as self-consistent field theory) is commonly used in statistical physics when modeling the space-time behavior of complex systems. The mean field theory approximates a complex multi-component system by considering a lumped (or average) effect for all individual components acting on a single component. Thus, the many body problem is reduced to a one body problem. For watershed hydrology, a mean field theory reduces the numerous point component effects to more tractable watershed averages, resulting in a consistent method for linking the average watershed fluxes to the local fluxes at each point. We apply this approach to the spatial distribution of soil moisture, and as a result, the numerous local interactions related to lateral fluxes of soil water are parameterized in terms of the average soil moisture. The mean field approach provides a basis for unifying and extending common event-based models (e.g. Soil Conservation Service curve number (SCS-CN) method) with more modern semi-distributed models (e.g. Variable Infiltration Capacity (VIC) model, the Probability Distributed (PDM) model, and TOPMODEL). We obtain simple equations for the fractions of the different source areas of runoff, the spatial variability of runoff, and the average runoff value (i.e., the so-called runoff curve). The resulting space time distribution of soil moisture offers a concise description of the variability of watershed fluxes.

  1. Sensitivity of de-excitation energies of superdeformed secondary minima to the density dependence of symmetry energy with the relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Jiang, W. Z.; Ren, Z. Z.; Sheng, Z. Q.; Zhu, Z. Y.

    2010-06-01

    The relationship between de-excitation energies of superdeformed secondary minima relative to ground states and the density dependence of the symmetry energy is investigated for heavy nuclei using the relativistic mean-field (RMF) model. It is shown that the de-excitation energies of superdeformed secondary minima are sensitive to differences in the symmetry energy that are mimicked by the isoscalar-isovector coupling included in the model. With deliberate investigations on a few Hg isotopes that have data of de-excitation energies, we find that the description for the de-excitation energies can be improved due to the softening of the symmetry energy. Further, we have investigated de-excitation energies of odd-odd heavy nuclei that are nearly independent of pairing correlations, and have discussed the possible extraction of the constraint on the density dependence of the symmetry energy with the measurement of de-excitation energies of these nuclei.

  2. The Brownian mean field model

    NASA Astrophysics Data System (ADS)

    Chavanis, Pierre-Henri

    2014-05-01

    We discuss the dynamics and thermodynamics of the Brownian mean field (BMF) model which is a system of N Brownian particles moving on a circle and interacting via a cosine potential. It can be viewed as the canonical version of the Hamiltonian mean field (HMF) model. The BMF model displays a second order phase transition from a homogeneous phase to an inhomogeneous phase below a critical temperature T c = 1 / 2. We first complete the description of this model in the mean field approximation valid for N → +∞. In the strong friction limit, the evolution of the density towards the mean field Boltzmann distribution is governed by the mean field Smoluchowski equation. For T < T c , this equation describes a process of self-organization from a non-magnetized (homogeneous) phase to a magnetized (inhomogeneous) phase. We obtain an analytical expression for the temporal evolution of the magnetization close to T c . Then, we take fluctuations (finite N effects) into account. The evolution of the density is governed by the stochastic Smoluchowski equation. From this equation, we derive a stochastic equation for the magnetization and study its properties both in the homogenous and inhomogeneous phase. We show that the fluctuations diverge at the critical point so that the mean field approximation ceases to be valid. Actually, the limits N → +∞ and T → T c do not commute. The validity of the mean field approximation requires N( T - T c ) → +∞ so that N must be larger and larger as T approaches T c . We show that the direction of the magnetization changes rapidly close to T c while its amplitude takes a long time to relax. We also indicate that, for systems with long-range interactions, the lifetime of metastable states scales as e N except close to a critical point. The BMF model shares many analogies with other systems of Brownian particles with long-range interactions such as self-gravitating Brownian particles, the Keller-Segel model describing the chemotaxis

  3. Co-non-solvency: Mean-field polymer theory does not describe polymer collapse transition in a mixture of two competing good solvents

    NASA Astrophysics Data System (ADS)

    Mukherji, Debashish; Marques, Carlos M.; Stuehn, Torsten; Kremer, Kurt

    2015-03-01

    Smart polymers are a modern class of polymeric materials that often exhibit unpredictable behavior in mixtures of solvents. One such phenomenon is co-non-solvency. Co-non-solvency occurs when two (perfectly) miscible and competing good solvents, for a given polymer, are mixed together. As a result, the same polymer collapses into a compact globule within intermediate mixing ratios. More interestingly, polymer collapses when the solvent quality remains good and even gets increasingly better by the addition of the better cosolvent. This is a puzzling phenomenon that is driven by strong local concentration fluctuations. Because of the discrete particle based nature of the interactions, Flory-Huggins type mean field arguments become unsuitable. In this work, we extend the analysis of the co-non-solvency effect presented earlier [D. Mukherji et al., Nat. Commun. 5, 4882 (2014)]. We explain why co-non-solvency is a generic phenomenon, which can only be understood by the thermodynamic treatment of the competitive displacement of (co)solvent components. This competition can result in a polymer collapse upon improvement of the solvent quality. Specific chemical details are not required to understand these complex conformational transitions. Therefore, a broad range of polymers are expected to exhibit similar reentrant coil-globule-coil transitions in competing good solvents.

  4. Co-non-solvency: Mean-field polymer theory does not describe polymer collapse transition in a mixture of two competing good solvents

    SciTech Connect

    Mukherji, Debashish; Stuehn, Torsten; Kremer, Kurt; Marques, Carlos M.

    2015-03-21

    Smart polymers are a modern class of polymeric materials that often exhibit unpredictable behavior in mixtures of solvents. One such phenomenon is co-non-solvency. Co-non-solvency occurs when two (perfectly) miscible and competing good solvents, for a given polymer, are mixed together. As a result, the same polymer collapses into a compact globule within intermediate mixing ratios. More interestingly, polymer collapses when the solvent quality remains good and even gets increasingly better by the addition of the better cosolvent. This is a puzzling phenomenon that is driven by strong local concentration fluctuations. Because of the discrete particle based nature of the interactions, Flory-Huggins type mean field arguments become unsuitable. In this work, we extend the analysis of the co-non-solvency effect presented earlier [D. Mukherji et al., Nat. Commun. 5, 4882 (2014)]. We explain why co-non-solvency is a generic phenomenon, which can only be understood by the thermodynamic treatment of the competitive displacement of (co)solvent components. This competition can result in a polymer collapse upon improvement of the solvent quality. Specific chemical details are not required to understand these complex conformational transitions. Therefore, a broad range of polymers are expected to exhibit similar reentrant coil-globule-coil transitions in competing good solvents.

  5. Spatial Correlations and the Insulating Phase of the High-Tc Cuprates: Insights from a Configuration-Interaction-Based Solver for Dynamical Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Go, Ara; Millis, Andrew J.

    2015-01-01

    A recently proposed configuration-interaction-based impurity solver is used in combination with the single-site and four-site cluster dynamical mean field approximations to investigate the three-band copper oxide model believed to describe the electronic structure of high transition temperature copper-oxide superconductors. Use of the configuration interaction solver enables verification of the convergence of results with respect to the number of bath orbitals. The spatial correlations included in the cluster approximation substantially shift the metal-insulator phase boundary relative to the prediction of the single-site approximation and increase the predicted energy gap of the insulating phase by about 1 eV above the single-site result. Vertex corrections occurring in the four-site approximation act to dramatically increase the value of the optical conductivity near the gap edge, resulting in better agreement with the data. The calculations reveal two distinct correlated insulating states: the "magnetically correlated insulator," in which nontrivial intersite correlations play an essential role in stabilizing the insulating state, and the strongly correlated insulator, in which local physics suffices. Comparison of the calculations to the data places the cuprates in the magnetically correlated Mott insulator regime.

  6. Stochastic kinetic mean field model

    NASA Astrophysics Data System (ADS)

    Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, Volodymyr; Tomán, János J.; Gajdics, Bence; Gusak, Andriy M.

    2016-07-01

    This paper introduces a new model for calculating the change in time of three-dimensional atomic configurations. The model is based on the kinetic mean field (KMF) approach, however we have transformed that model into a stochastic approach by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which produces results similar to the lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to implement the algorithm (open source program code is provided on http://skmf.eu website). We will show that the result of one SKMF run may correspond to the average of several KMC runs. The number of KMC runs is inversely proportional to the amplitude square of the noise in SKMF. This makes SKMF an ideal tool also for statistical purposes.

  7. Non-mean-field critical exponent in a mean-field model: dynamics versus statistical mechanics.

    PubMed

    Ogawa, Shun; Patelli, Aurelio; Yamaguchi, Yoshiyuki Y

    2014-03-01

    Mean-field theory tells us that the classical critical exponent of susceptibility is twice that of magnetization. However, linear response theory based on the Vlasov equation, which is naturally introduced by the mean-field nature, makes the former exponent half of the latter for families of quasistationary states having second order phase transitions in the Hamiltonian mean-field model and its variances, in the low-energy phase. We clarify that this strange exponent is due to the existence of Casimir invariants which trap the system in a quasistationary state for a time scale diverging with the system size. The theoretical prediction is numerically confirmed by N-body simulations for the equilibrium states and a family of quasistationary states. PMID:24730814

  8. Mean-field sparse optimal control

    PubMed Central

    Fornasier, Massimo; Piccoli, Benedetto; Rossi, Francesco

    2014-01-01

    We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modelling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dynamics of the probability distribution of the followers. In the classical mean-field theory, one studies the behaviour of a large number of small individuals freely interacting with each other, by simplifying the effect of all the other individuals on any given individual by a single averaged effect. In this paper, we address instead the situation where the leaders are actually influenced also by an external policy maker, and we propagate its effect for the number N of followers going to infinity. The technical derivation of the sparse mean-field optimal control is realized by the simultaneous development of the mean-field limit of the equations governing the followers dynamics together with the Γ-limit of the finite dimensional sparse optimal control problems. PMID:25288818

  9. Optical weights and waterfalls in doped charge-transfer insulators: A local density approximation and dynamical mean-field theory study of La2-xSrxCuO4

    NASA Astrophysics Data System (ADS)

    Weber, Cédric; Haule, Kristjan; Kotliar, Gabriel

    2008-10-01

    We use the local density approximation in combination with the dynamical mean-field theory to investigate intermediate energy properties of the copper oxides. We identify coherent and incoherent spectral features that result from doping a charge-transfer insulator, namely quasiparticles, Zhang-Rice singlet band, and the upper and lower Hubbard bands. Angle resolving these features, we identify a waterfall-like feature between the quasiparticle part and the incoherent part of the Zhang-Rice band. We investigate the asymmetry between particle and hole doping. On the hole-doped side, there is a very rapid transfer of spectral weight upon doping in the one particle spectra. The optical spectral weight increases superlinearly on the hole-doped side in agreement with experiments.

  10. Continuous Time Finite State Mean Field Games

    SciTech Connect

    Gomes, Diogo A.; Mohr, Joana Souza, Rafael Rigao

    2013-08-01

    In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.

  11. Nuclear fission with mean-field instantons

    SciTech Connect

    Skalski, Janusz

    2008-06-15

    We present a description of nuclear spontaneous fission, and generally of quantum tunneling, in terms of instantons, that is, periodic imaginary-time solutions to time-dependent mean-field equations. This description allows comparisons to be made with the more familiar generator coordinate (GCM) and adiabatic time-dependent Hartree-Fock (ATDHF) methods. It is shown that the action functional whose value for the instanton is the quasiclassical estimate of the decay exponent fulfills the minimum principle when additional constraints are imposed on trial fission paths. In analogy with mechanics, these are conditions of energy conservation and the velocity-momentum relations. In the adiabatic limit, the instanton method reduces to the time-odd ATDHF equation, with collective mass including the time-odd Thouless-Valatin term, while the GCM mass completely ignores velocity-momentum relations. This implies that GCM inertia generally overestimates the instanton-related decay rate. The very existence of the minimum principle offers hope for a variational search for instantons. After the inclusion of pairing, the instanton equations and the variational principle can be expressed in terms of the imaginary-time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The adiabatic limit of this theory reproduces ATDHFB inertia.

  12. Deterministic Mean-Field Ensemble Kalman Filtering

    DOE PAGESBeta

    Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

    2016-05-03

    The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d theory.« less

  13. Mean-Field Games for Marriage

    PubMed Central

    Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul

    2014-01-01

    This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple’s network on their feeling states and their well-being. PMID:24804835

  14. Mean field approach to nuclear structure

    SciTech Connect

    Nazarewicz, W. |

    1993-12-01

    Several examples of mean-field calculations, relevant to the recent and planned low-spin experimental works, are presented. The perspectives for future studies (mainly related to spectroscopy of exotic nuclei) are reviewd.

  15. Microscopically constrained mean-field models from chiral nuclear thermodynamics

    NASA Astrophysics Data System (ADS)

    Rrapaj, Ermal; Roggero, Alessandro; Holt, Jeremy W.

    2016-06-01

    We explore the use of mean-field models to approximate microscopic nuclear equations of state derived from chiral effective field theory across the densities and temperatures relevant for simulating astrophysical phenomena such as core-collapse supernovae and binary neutron star mergers. We consider both relativistic mean-field theory with scalar and vector meson exchange as well as energy density functionals based on Skyrme phenomenology and compare to thermodynamic equations of state derived from chiral two- and three-nucleon forces in many-body perturbation theory. Quantum Monte Carlo simulations of symmetric nuclear matter and pure neutron matter are used to determine the density regimes in which perturbation theory with chiral nuclear forces is valid. Within the theoretical uncertainties associated with the many-body methods, we find that select mean-field models describe well microscopic nuclear thermodynamics. As an additional consistency requirement, we study as well the single-particle properties of nucleons in a hot/dense environment, which affect e.g., charged-current weak reactions in neutron-rich matter. The identified mean-field models can be used across a larger range of densities and temperatures in astrophysical simulations than more computationally expensive microscopic models.

  16. Parametrization of light clusters within relativistic mean field models

    SciTech Connect

    Ferreira, Marcio; Providencia, Constanca

    2013-06-10

    Light clusters are included in the equation of state of nuclearmatter within the relativistic mean field theory. The effect of the cluster-meson coupling constants on the dissolution density is discussed. Theoretical and experimental constraints are used to fix the cluster-meson couplings at T Almost-Equal-To 5 MeV.

  17. "Phase diagram" of a mean field game

    NASA Astrophysics Data System (ADS)

    Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis

    2016-01-01

    Mean field games were introduced by J-M. Lasry and P-L. Lions in the mathematical community, and independently by M. Huang and co-workers in the engineering community, to deal with optimization problems when the number of agents becomes very large. In this article we study in detail a particular example called the "seminar problem" introduced by O. Guéant, J-M. Lasry, and P-L. Lions in 2010. This model contains the main ingredients of any mean field game but has the particular feature that all agents are coupled only through a simple random event (the seminar starting time) that they all contribute to form. In the mean field limit, this event becomes deterministic and its value can be fixed through a self consistent procedure. This allows for a rather thorough understanding of the solutions of the problem, through both exact results and a detailed analysis of various limiting regimes. For a sensible class of initial configurations, distinct behaviors can be associated to different domains in the parameter space. For this reason, the "seminar problem" appears to be an interesting toy model on which both intuition and technical approaches can be tested as a preliminary study toward more complex mean field game models.

  18. Instabilities in the Mean Field Limit

    NASA Astrophysics Data System (ADS)

    Han-Kwan, Daniel; Nguyen, Toan T.

    2016-03-01

    Consider a system of N particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a {C}^2 smooth potential in any dimension. We prove that in the mean field limit N → + ∞, the N particles system displays instabilities in times of order log N, for some configurations approximately distributed according to unstable homogeneous equilibria.

  19. Analytic Beyond-Mean-Field BEC Wave Functions

    NASA Astrophysics Data System (ADS)

    Dunn, Martin; Laing, W. Blake; Watson, Deborah K.; Loeser, John G.

    2006-05-01

    We present analytic N-body beyond-mean-field wave functions for Bose-Einstein condensates. This extends our previous beyond-mean-field energy calculations to the substantially more difficult problem of determining correlated N-body wave functions for a confined system. The tools used to achieve this have been carefully chosen to maximize the use of symmetry and minimize the dependence on numerical computation. We handle the huge number of interactions when N is large (˜N^2/2 two-body interactions) by bringing together three theoretical methods. These are dimensional perturbation theory, the FG method of Wilson et al, and the group theory of the symmetric group. The wave function is then used to derive the density profile of a condensate in a cylindrical trap.This method makes no assumptions regarding the form or strength of the interactions and is applicable to both small-N and large-N systems.

  20. Robust mean field games for coupled Markov jump linear systems

    NASA Astrophysics Data System (ADS)

    Moon, Jun; Başar, Tamer

    2016-07-01

    We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents' individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.

  1. On Mean Field Limits for Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Boers, Niklas; Pickl, Peter

    2016-07-01

    We present a purely probabilistic proof of propagation of molecular chaos for N-particle systems in dimension 3 with interaction forces scaling like 1/\\vert q\\vert ^{3λ - 1} with λ smaller but close to one and cut-off at q = N^{-1/3}. The proof yields a Gronwall estimate for the maximal distance between exact microscopic and approximate mean-field dynamics. This can be used to show weak convergence of the one-particle marginals to solutions of the respective mean-field equation without cut-off in a quantitative way. Our results thus lead to a derivation of the Vlasov equation from the microscopic N-particle dynamics with force term arbitrarily close to the physically relevant Coulomb- and gravitational forces.

  2. Relativistic mean field description of exotic nuclei

    NASA Astrophysics Data System (ADS)

    Meng, Jie; Ring, Peter; Zhao, Pengwei; Zhou, Shan-Gui

    In this chapter, we will present relativistic mean field (RMF) models with pairing treated by the Bardeen-Cooper-Schrieffer (BCS) and the relativistic Hartree-Bogoliubov (RHB) approaches and applications for exotic nuclear phenomena including nuclear halos, the position of the proton drip line and proton radioactivity, the surface diffuseness and its relation to nuclear exotic phenomena, and the effects of pairing correlations on the nuclear size.

  3. A minimax approach to mean field games

    NASA Astrophysics Data System (ADS)

    Averboukh, Yu V.

    2015-07-01

    An initial boundary value problem for the system of equations of a determined mean field game is considered. The proposed definition of a generalized solution is based on the minimax approach to the Hamilton-Jacobi equation. We prove the existence of the generalized (minimax) solution using the Nash equilibrium in the auxiliary differential game with infinitely many identical players. We show that the minimax solution of the original system provides the \\varepsilon-Nash equilibrium in the differential game with a finite number of players. Bibliography: 34 titles.

  4. The breakdown of de Gennes Scaling in TbxEr1-xNi2B2C and its mean field theory explanation

    SciTech Connect

    Gao, Chunwang

    2004-01-01

    The Neel temperatures, TN, of TbxEr1-xNi2B2C samples have been determined from the temperature dependence of magnetization measurements. A breakdown of the de Gennes scaling of TN with a clear turning point around x = 0.45 has been observed. The TN values of TbxEr1-xNi2B2C do not change much within the range of O < x < 0.45 and then, for larger x they increase almost linearly with concentration until TN = 14.9K is reached for x = 1, TbNi2B2C. The clear change in the x-dependence of TN around x = 0.45 can be linked to a change in the local moment ordering direction from transverse to longitudinal, a change which is consistent with recent resonant X-ray scattering data. These features in TN(x) can be explained using a mean field model.

  5. Invisible dynamo in mean-field models

    NASA Astrophysics Data System (ADS)

    Reshetnyak, M. Yu.

    2016-07-01

    The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.

  6. Relativistic mean field for nuclear periphery

    NASA Astrophysics Data System (ADS)

    Gambhir, Y. K.; Bhagwat, A. A.

    2002-09-01

    The antiproton annihilation experiments help to extract so-called peripheral factors representing the ratio of neutron to proton densities at the annihilation site that is about 2.5 fm away from the half-density radius of the nucleus. The relativistic mean field (RMF) approach is used to calculate the peripheral factors. The RMF equations (with frozen gap) and relativistic Hartree-Bogoliubov (RHB) equations (with finite range Gogny interaction-D1S for pairing) are solved employing the basis expansion method. The RHB equations are also solved in the coordinate space using a large box (30 fm); with an effective zero range density dependent interaction (consistent with Gogny D1S interaction) for pairing. The results are analyzed to ascertain quantitatively the effect of using these different techniques for solving the RMF/RHB equations. The calculated peripheral factors obtained by solving RHB equations in the coordinate space are relatively closer to the corresponding experimental values.

  7. Coulomb Glass: a Mean Field Study

    NASA Astrophysics Data System (ADS)

    Mandra, Salvatore; Palassini, Matteo

    2012-02-01

    We study the Coulomb glass model of disordered localized electrons with long-range Coulomb interaction, which describes systems such as disordered insulators, granular metals, amorphous semiconductors, or doped crystalline semiconductors. Long ago Efros and Shklovskii showed that the long-range repulsion induces a soft Coulomb gap in the single particle density of states at low temperatures. Recent works suggested that this gap is associated to a transition to a glass phase, similar to the Almeida-Thouless transition in spin glasses. In this work, we use a mean field approach to characterize several physical properties of the Coulomb glass. In particular, following a seminal work of Bray and Moore, we show that the Edward-Anderson parameter qEA and the spin glass susceptibility χSG are directly related to spectrum distribution of the Hessian matrix around free energy minima. Using this result, we show that no glass transition is associated to the gap formation.

  8. Mean Field Analysis of Quantum Annealing Correction.

    PubMed

    Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A

    2016-06-01

    Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.

  9. Mean Field Analysis of Quantum Annealing Correction.

    PubMed

    Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A

    2016-06-01

    Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder. PMID:27314705

  10. Mean Field Analysis of Quantum Annealing Correction

    NASA Astrophysics Data System (ADS)

    Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A.

    2016-06-01

    Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p -body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p =2 , where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p ≥3 , where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.

  11. Benchmarking mean-field approximations to level densities

    NASA Astrophysics Data System (ADS)

    Alhassid, Y.; Bertsch, G. F.; Gilbreth, C. N.; Nakada, H.

    2016-04-01

    We assess the accuracy of finite-temperature mean-field theory using as a standard the Hamiltonian and model space of the shell model Monte Carlo calculations. Two examples are considered: the nucleus 162Dy, representing a heavy deformed nucleus, and 148Sm, representing a nearby heavy spherical nucleus with strong pairing correlations. The errors inherent in the finite-temperature Hartree-Fock and Hartree-Fock-Bogoliubov approximations are analyzed by comparing the entropies of the grand canonical and canonical ensembles, as well as the level density at the neutron resonance threshold, with shell model Monte Carlo calculations, which are accurate up to well-controlled statistical errors. The main weak points in the mean-field treatments are found to be: (i) the extraction of number-projected densities from the grand canonical ensembles, and (ii) the symmetry breaking by deformation or by the pairing condensate. In the absence of a pairing condensate, we confirm that the usual saddle-point approximation to extract the number-projected densities is not a significant source of error compared to other errors inherent to the mean-field theory. We also present an alternative formulation of the saddle-point approximation that makes direct use of an approximate particle-number projection and avoids computing the usual three-dimensional Jacobian of the saddle-point integration. We find that the pairing condensate is less amenable to approximate particle-number projection methods because of the explicit violation of particle-number conservation in the pairing condensate. Nevertheless, the Hartree-Fock-Bogoliubov theory is accurate to less than one unit of entropy for 148Sm at the neutron threshold energy, which is above the pairing phase transition. This result provides support for the commonly used "back-shift" approximation, treating pairing as only affecting the excitation energy scale. When the ground state is strongly deformed, the Hartree-Fock entropy is significantly

  12. Dispersion-Corrected Mean-Field Electronic Structure Methods.

    PubMed

    Grimme, Stefan; Hansen, Andreas; Brandenburg, Jan Gerit; Bannwarth, Christoph

    2016-05-11

    Mean-field electronic structure methods like Hartree-Fock, semilocal density functional approximations, or semiempirical molecular orbital (MO) theories do not account for long-range electron correlation (London dispersion interaction). Inclusion of these effects is mandatory for realistic calculations on large or condensed chemical systems and for various intramolecular phenomena (thermochemistry). This Review describes the recent developments (including some historical aspects) of dispersion corrections with an emphasis on methods that can be employed routinely with reasonable accuracy in large-scale applications. The most prominent correction schemes are classified into three groups: (i) nonlocal, density-based functionals, (ii) semiclassical C6-based, and (iii) one-electron effective potentials. The properties as well as pros and cons of these methods are critically discussed, and typical examples and benchmarks on molecular complexes and crystals are provided. Although there are some areas for further improvement (robustness, many-body and short-range effects), the situation regarding the overall accuracy is clear. Various approaches yield long-range dispersion energies with a typical relative error of 5%. For many chemical problems, this accuracy is higher compared to that of the underlying mean-field method (i.e., a typical semilocal (hybrid) functional like B3LYP). PMID:27077966

  13. Mean field approach to fluctuations of surface line defects

    NASA Astrophysics Data System (ADS)

    Margetis, Dionisios

    2011-03-01

    Below the roughening transition temperature, the dynamics of crystal surfaces are driven by the motion of line defects (steps) of atomic size. According to the celebrated Burton Cabrera-Frank (BCF) model, the steps move by mass conservation, as adsorbed atoms (adatoms) diffuse on terraces and attach/detach at step edges. The resulting deterministic equations of motion incorporate nonlinear couplings due to entropic and elastic-dipole step-step interactions. In this talk, I will discuss a formal theory for stochastic aspects of step motion by adding noise to the BCF model in 1+1 dimensions. I will define systematically a ``mean field'' that enables the conversion of the coupled, nonlinear stochastic equations for the distance between neighboring steps (terrace widths) to a single Langevin-type equation for an effective terrace width. In the course of my study, I invoke the Bogoliubov-Born-Green Kirkwood-Yvon (BBGKY) hierarchy for joint terrace-width probability densities and a decorrelation ansatz for terrace widths. By using an example drawn from epitaxial growth (with material deposition from above), I will compare the mean field approach to an exact result from a linearized growth model. [D. Margetis, J. Phys A: Math. Theor. 43, 065003 (2010).] This work was supported by NSF under Grant DMS-0847587.

  14. Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria

    NASA Astrophysics Data System (ADS)

    Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian

    2014-02-01

    We introduce a new mean field kinetic model for systems of rational agents interacting in a game-theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. An application of the presented theory to a social model (herding behavior) is discussed.

  15. Phase transitions of nuclear matter beyond mean field theory

    SciTech Connect

    Tran Huu Phat; Nguyen Tuan Anh; Nguyen Van Long; Le Viet Hoa

    2007-10-15

    The Cornwall-Jackiw-Tomboulis (CJT) effective action approach is applied to study the phase transition of nuclear matter modeled by the four-nucleon interaction. It is shown that in the Hartree-Fock approximation (HFA) a first-order phase transition takes place at low temperature, whereas the phase transition is of second order at higher temperature.

  16. Hall Current Effects in Mean-Field Dynamo Theory

    NASA Astrophysics Data System (ADS)

    Lingam, Manasvi; Bhattacharjee, Amitava

    2016-09-01

    The role of the Hall term on large-scale dynamo action is investigated by means of the first-order smoothing approximation. It is shown that the standard α coefficient is altered, and is zero when a specific double Beltrami state is attained, in contrast to the Alfvénic state for magnetohydrodynamical dynamos. The β coefficient is no longer positive definite, and thereby enables dynamo action even if α-quenching were to operate. The similarities and differences with the (magnetic) shear-current effect are pointed out, and a mechanism that may be potentially responsible for β \\lt 0 is advanced. The results are compared against previous studies, and their astrophysical relevance is also highlighted.

  17. A new method to optimize the satellite broadcasting schedules using the mean field annealing of a Hopfield neural network.

    PubMed

    Ansari, N; Hou, E H; Yu, Y

    1995-01-01

    Reports a new method for optimizing satellite broadcasting schedules based on the Hopfield neural model in combination with the mean field annealing theory. A clamping technique is used with an associative matrix, thus reducing the dimensions of the solution space. A formula for estimating the critical temperature for the mean field annealing procedure is derived, hence enabling the updating of the mean field theory equations to be more economical. Several factors on the numerical implementation of the mean field equations using a straightforward iteration method that may cause divergence are discussed; methods to avoid this kind of divergence are also proposed. Excellent results are consistently found for problems of various sizes.

  18. Dynamic scaling in entangled mean-field gelation polymers.

    PubMed

    Das, Chinmay; Read, Daniel J; Kelmanson, Mark A; McLeish, Tom C B

    2006-07-01

    We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al. [Phys. Rev. E 60, 5657 (1999)] to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed in the experiments are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the "rheologically relevant" linear segment length is smaller than that estimated from the experimental results. We use a numerical method based on a tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of mean-field behavior--which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, the contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches a Rouse-like value. PMID:16907093

  19. Quark mean field model with pion and gluon corrections

    NASA Astrophysics Data System (ADS)

    Xing, Xueyong; Hu, Jinniu; Shen, Hong

    2016-10-01

    The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pions and gluons on the nucleon structure are treated in second-order perturbation theory. In a nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, mq, we determine three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1, QMF-NK2, and QMF-NK3, by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give a satisfactory description of properties of nuclear matter and finite nuclei, moreover they also predict a larger neutron star mass around 2.3 M⊙ without hyperon degrees of freedom.

  20. Relativistic mean field models for finite nuclei and neutron stars

    NASA Astrophysics Data System (ADS)

    Chen, Wei-Chia

    In this dissertation we have created theoretical models for finite nuclei, nuclear matter, and neutron stars within the framework of relativistic mean field (RMF) theory, and we have used these models to investigate the elusive isovector sector and related physics, in particular, the neutron-skin thickness of heavy nuclei, the nuclear symmetry energy, and the properties of neutron stars. To build RMF models that incorporate collective excitations in finite nuclei in addition to their ground-state properties, we have extended the non-relativistic sum rule approach to the relativistic domain. This allows an efficient estimate of giant monopole energies. Moreover, we have combined an exact shell-model-like approach with the mean-field calculation to describe pairing correlations in open-shell nuclei. All the ingredients were then put together to establish the calibration scheme. We have also extended the transformation between model parameters and pseudo data of nuclear matter within the RMF context. Performing calibration in this pseudo data space can not only facilitate the searching algorithm but also make the pseudo data genuine model predictions. This calibration scheme is also supplemented by a covariance analysis enabling us to extract the information content of a model, including theoretical uncertainties and correlation coefficients. A series of RMF models subject to the same isoscalar constraints but one differing isovector assumption were then created using this calibration scheme. By comparing their predictions of the nuclear matter equation of state to both experimental and theoretical constraints, we found that a small neutron skin of about 0.16 fm in Pb208 is favored, indicating that the symmetry energy should be soft. To obtain stronger evidence, we proceeded to examine the evolution of the isotopic chains in both oxygen and calcium. Again, it was found that the model with such small neutron skin and soft symmetry energy can best describe both isotopic

  1. Activated processes and Inherent Structure dynamics of finite-size mean-field models for glasses

    NASA Astrophysics Data System (ADS)

    Crisanti, A.; Ritort, F.

    2000-12-01

    We investigate the Inherent Structure (IS) dynamics of mean-field finite-size spin-glass models whose high-temperature dynamics is described in the thermodynamic limit by the schematic Mode Coupling Theory for supercooled liquids. Near the threshold energy the dynamics is ruled by activated processes which induce a logarithmic slow relaxation. We show the presence of aging in both the IS correlation and integrated response functions and check the validity of the one-step replica symmetry breaking scenario in the presence of activated processes. Our work shows: 1) the violation of the fluctuation-dissipation theorem can be computed from the configurational entropy obtained in the Stillinger and Weber approach, 2) the intermediate time regime (log (t) ~ N) in mean-field theory automatically includes activated processes opening the way to analytically investigate activated processes by computing corrections beyond mean field.

  2. Mean-field dynamos: The old concept and some recent developments. Karl Schwarzschild Award Lecture 2013

    NASA Astrophysics Data System (ADS)

    Rädler, K.-H.

    This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α2 and α Ω type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.

  3. Mean field limit for bosons and propagation of Wigner measures

    NASA Astrophysics Data System (ADS)

    Ammari, Z.; Nier, F.

    2009-04-01

    We consider the N-body Schrödinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [Ammari, Z. and Nier, F., "Mean field limit for bosons and infinite dimensional phase-space analysis," Ann. Henri Poincare 9, 1503 (2008)], the mean field limit is translated into a semiclassical problem with a small parameter ɛ →0, after introducing an ɛ-dependent bosonic quantization. The limits of quantum correlation functions are expressed as a push forward by a nonlinear flow (e.g., Hartree) of the associated Wigner measures. These object and their basic properties were introduced by Ammari and Nier in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for a rather general class of quantum states in their mean field limit.

  4. Mean field limit for bosons and propagation of Wigner measures

    SciTech Connect

    Ammari, Z.; Nier, F.

    2009-04-15

    We consider the N-body Schroedinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [Ammari, Z. and Nier, F., 'Mean field limit for bosons and infinite dimensional phase-space analysis', Ann. Henri Poincare 9, 1503 (2008)], the mean field limit is translated into a semiclassical problem with a small parameter {epsilon}{yields}0, after introducing an {epsilon}-dependent bosonic quantization. The limits of quantum correlation functions are expressed as a push forward by a nonlinear flow (e.g., Hartree) of the associated Wigner measures. These object and their basic properties were introduced by Ammari and Nier in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for a rather general class of quantum states in their mean field limit.

  5. Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows

    SciTech Connect

    Raedler, Karl-Heinz; Brandenburg, Axel; Del Sordo, Fabio; Rheinhardt, Matthias

    2011-10-15

    Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Peclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to nonlocal and noninstantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.

  6. Mean-field Ohm's law and coaxial helicity injection in force-free plasmas

    SciTech Connect

    Weening, R. H.

    2011-12-15

    A theoretical analysis of steady-state coaxial helicity injection (CHI) in force-free plasmas is presented using a parallel mean-field Ohm's law that includes resistivity {eta} and hyper-resistivity {Lambda} terms. Using Boozer coordinates, a partial differential equation is derived for the time evolution of the mean-field poloidal magnetic flux, or magnetic Hamiltonian function, from the parallel mean-field Ohm's law. A general expression is obtained from the mean-field theory for the efficiency of CHI current drive in force-free plasmas. Inductances of internal energy, magnetic helicity, and poloidal magnetic flux are used to characterize axisymmetric plasma equilibria that have a model current profile. Using the model current profile, a method is suggested to determine the level of magnetohydrodynamic activity at the magnetic axis and the consequent deviation from the completely relaxed Taylor state. The mean-field Ohm's law model suggests that steady-state CHI can be viewed most simply as a boundary layer problem.

  7. MEAN FIELD AND MONTE CARLO MODELING OF MULTIBLOCK COPOLYMERS

    SciTech Connect

    K. RASMUSSEN; ET AL

    2001-01-01

    The authors discuss and apply extensions needed to treat multiblock copolymers within the mean field theoretical framework for microphase separation in diblock copolymer metals, originally due to Leibler. The mean field calculations are complemented by lattice Monte Carlo realizations using the bond fluctuation model. They find that the microphase separation transition occurs at larger {sub {chi}}N as the number of blocks in increased beyond two (i.e., beyond diblock), and that the characteristic length scale of the emerging morphology decreases as the number of blocks increases. The latter prediction is in qualitative agreement with published experimental results due to Sontak and co-workers for model multiblock poly(styrene-isoprene) systems and recent results due to Hjelm and co-workers for a segmented poly(ester-urethane) relevant to Los Alamos interests. Additionally, the mean field predictions and bond fluctuation realizations yield consistent results.

  8. Mean-field fluid behavior of the Gaussian core model

    NASA Astrophysics Data System (ADS)

    Louis, A. A.; Bolhuis, P. G.; Hansen, J. P.

    2000-12-01

    We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated ``mean-field fluid'' over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.

  9. Density-Dependent Properties of Hadronic Matter in the self-consistent Chiral ({sigma},{pi},{omega}) Mean-Field Model

    SciTech Connect

    Uechi, Schun T.; Uechi, Hiroshi

    2011-05-06

    Density-dependent relations among saturation properties of symmetric nuclear matter and properties of hadronic stars are discussed by applying the conserving chiral nonlinear ({sigma},{pi},{omega}) hadronic mean-field theory. The chiral nonlinear ({sigma},{pi},{omega}) mean-field theory is an extension of the conserving nonlinear (nonchiral) {sigma}-{omega} hadronic mean-field theory which is thermodynamically consistent, relativistic and is a Lorentz-covariant mean-field theory of hadrons. In the extended chiral ({sigma},{pi},{omega}) mean-field model, all the masses of hadrons are produced by the breaking of chiral symmetry, which is different from other conventional chiral partner models. By comparing both nonchiral and chiral mean-field approximations, the effects of the chiral symmetry breaking mechanism on the mass of {sigma}-meson, coefficients of nonlinear interactions and Fermi-liquid properties are investigated in nuclear matter and neutron stars.

  10. {sup 208}Pb neutron density: A mean field problem?

    SciTech Connect

    Gmuca, Stefan

    1998-12-21

    The ground-state nuclear densities and radii of {sup 208}Pb doubly-magic nucleus have been evaluated within the framework of the relativistic mean-field approach. It is pointed out that the neutron density and the neutron radius in the RMF approach are quite different from both, the empirical data and the predictions of the Skyrme-Hartree-Fock model.

  11. Mean Field Approach to the Giant Wormhole Problem

    NASA Astrophysics Data System (ADS)

    Gamba, A.; Kolokolov, I.; Martellini, M.

    We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.

  12. On the Mean Field and Classical Limits of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Golse, François; Mouhot, Clément; Paul, Thierry

    2016-04-01

    The main result in this paper is a new inequality bearing on solutions of the N-body linear Schrödinger equation and of the mean field Hartree equation. This inequality implies that the mean field limit of the quantum mechanics of N identical particles is uniform in the classical limit and provides a quantitative estimate of the quality of the approximation. This result applies to the case of C 1,1 interaction potentials. The quantity measuring the approximation of the N-body quantum dynamics by its mean field limit is analogous to the Monge-Kantorovich (or Wasserstein) distance with exponent 2. The inequality satisfied by this quantity is reminiscent of the work of Dobrushin on the mean field limit in classical mechanics [Func. Anal. Appl. 13, 115-123, (1979)]. Our approach to this problem is based on a direct analysis of the N-particle Liouville equation, and avoids using techniques based on the BBGKY hierarchy or on second quantization.

  13. Spectral properties of the one-dimensional Hubbard model: cluster dynamical mean-field approaches

    NASA Astrophysics Data System (ADS)

    Go, Ara; Jeon, Gun Sang

    2011-03-01

    We investigate static and dynamic properties of the one-dimensional Hubbard model using cluster extensions of the dynamical mean-field theory. It is shown that the two different extensions, the cellular dynamical mean-field theory and the dynamic cluster approximation, yield the ground-state properties which are qualitatively in good agreement with each other. We compare the results with the Bethe ansatz results to check the accuracy of the calculation with finite sizes of clusters. We also analyze the spectral properties of the model with the focus on the spin-charge separation and discuss the dependency on the cluster size in the two approaches. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2010-0010937).

  14. Deviations from the mean-field predictions for the phase behaviour of random copolymers melts

    NASA Astrophysics Data System (ADS)

    Houdayer, J.; Müller, M.

    2002-06-01

    We investigate the phase behaviour of random copolymers melts via large-scale Monte Carlo simulations. We observe macrophase separation into A- and B-rich phases as predicted by the mean-field theory only for systems with a very large correlation λ of blocks along the polymer chains, far away from the Lifshitz point. For smaller values of λ, we find that a locally segregated, disordered microemulsion-like structure gradually forms as the temperature decreases. As we increase the number of blocks in the polymers, the region of macrophase separation further shrinks. The results of our Monte Carlo simulation are in agreement with a Ginzburg criterium, which suggests that the mean-field theory becomes worse as the number of blocks in polymers increases.

  15. Schrödinger Approach to Mean Field Games

    NASA Astrophysics Data System (ADS)

    Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis

    2016-03-01

    Mean field games (MFG) provide a theoretical frame to model socioeconomic systems. In this Letter, we study a particular class of MFG that shows strong analogies with the nonlinear Schrödinger and Gross-Pitaevskii equations introduced in physics to describe a variety of physical phenomena. Using this bridge, many results and techniques developed along the years in the latter context can be transferred to the former, which provides both a new domain of application for the nonlinear Schrödinger equation and a new and fruitful approach in the study of mean field games. Utilizing this approach, we analyze in detail a population dynamics model in which the "players" are under a strong incentive to coordinate themselves.

  16. Nilsson parameters κ and μ in relativistic mean field models

    NASA Astrophysics Data System (ADS)

    Sulaksono, A.; Mart, T.; Bahri, C.

    2005-03-01

    Nilsson parameters κ and μ have been studied in the framework of relativistic mean field (RMF) models. They are used to investigate the reason why RMF models give a relatively good prediction of the spin-orbit splitting but fail to reproduce the placement of the states with different orbital angular momenta. Instead of the relatively small effective mass M*, the independence of M* from the angular momentum l is found to be the reason.

  17. Stochastic Mean-Field Dynamics For Nuclear Collisions

    SciTech Connect

    Ayik, Sakir

    2008-11-11

    We discuss a stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. For small amplitude fluctuations, this approach gives a result for the dispersion of a one-body observable that is identical to the result obtained previously through a variational approach. Furthermore, it incorporates one-body dissipation and fluctuation mechanisms in accordance with quantal fluctuation-dissipation relation.

  18. Mean-Field Description of Plastic Flow in Amorphous Solids

    NASA Astrophysics Data System (ADS)

    Lin, Jie; Wyart, Matthieu

    2016-01-01

    Failure and flow of amorphous materials are central to various phenomena including earthquakes and landslides. There is accumulating evidence that the yielding transition between a flowing and an arrested phase is a critical phenomenon, but the associated exponents are not understood, even at a mean-field level where the validity of popular models is debated. Here, we solve a mean-field model that captures the broad distribution of the mechanical noise generated by plasticity, whose behavior is related to biased Lévy flights near an absorbing boundary. We compute the exponent θ characterizing the density of shear transformation P (x )˜xθ, where x is the stress increment beyond which they yield. We find that after an isotropic thermal quench, θ =1 /2 . However, θ depends continuously on the applied shear stress; this dependence is not monotonic, and its value at the yield stress is not universal. The model rationalizes previously unexplained observations and captures reasonably well the value of exponents in three dimensions. Values of exponents in four dimensions are accurately predicted. These results support the fact that it is the true mean-field model that applies in large dimensions, and they raise fundamental questions about the nature of the yielding transition.

  19. A mean field Ohm's law for collisionless plasmas

    SciTech Connect

    Biglari, H. ); Diamond, P.H. )

    1993-11-01

    A mean field Ohm's law valid for collisionless plasmas is derived kinetically. It is shown that contrary to conventional thinking, the resulting hyperresistivity is significantly smaller than its fluid counterpart due to the fact that the turbulent decorrelation rate is linked to the rapid electron ballistic motion rather than the slower nonlinear mixing time. Moreover, the off-diagonal contributions to the parallel electron momentum flux are shown to result in Ohm's law renormalizations that dwarf the current diffusivity and break radial parity symmetry.

  20. MAP segmentation of magnetic resonance images using mean field annealing

    NASA Astrophysics Data System (ADS)

    Logenthiran, Ambalavaner; Snyder, Wesley E.; Santago, Peter, II; Link, Kerry M.

    1991-06-01

    An algorithm is described which segments magnetic resonance images while removing the noise from the images without blurring or other distortion of edges. The problem of segmentation and noise removal is posed as a restoration of an uncorrupted image, given additive white Gaussian noise and a segmentation cost. The problem is solved using a strategy called Mean Field Annealing. An a priori statistical model of the image, which includes the region classification, is chosen which drives the minimization toward solutions which are locally homogeneous and globally classified. Application of the algorithm to brain and knee images is presented.

  1. Relativistic mean field calculations in neutron-rich nuclei

    SciTech Connect

    Gangopadhyay, G.; Bhattacharya, Madhubrata; Roy, Subinit

    2014-08-14

    Relativistic mean field calculations have been employed to study neutron rich nuclei. The Lagrange's equations have been solved in the co-ordinate space. The effect of the continuum has been effectively taken into account through the method of resonant continuum. It is found that BCS approximation performs as well as a more involved Relativistic Continuum Hartree Bogoliubov approach. Calculations reveal the possibility of modification of magic numbers in neutron rich nuclei. Calculation for low energy proton scattering cross sections shows that the present approach reproduces the density in very light neutron rich nuclei.

  2. Thermal entanglement of spins in mean-field clusters

    SciTech Connect

    Asoudeh, M.; Karimipour, V.

    2006-06-15

    We determine thermal entanglement in mean-field clusters of N spin one-half particles interacting via the anisotropic Heisenberg interaction, with and without external magnetic field. For the xxx cluster in the absence of magnetic field we prove that only the N=2 ferromagnetic cluster shows entanglement. An external magnetic field B can only entangle xxx antiferromagnetic clusters in certain regions of the B-T plane. On the other hand, the xxz clusters of size N>2 are entangled only when the interaction is ferromagnetic. Detailed dependence of the entanglement on various parameters is investigated in each case.

  3. Many-Body Mobility Edge in a Mean-Field Quantum Spin Glass

    NASA Astrophysics Data System (ADS)

    Laumann, C. R.; Pal, A.; Scardicchio, A.

    2014-11-01

    The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body localization-delocalization (MBLD) transition when viewed as a closed quantum system. The mean-field structure of the model allows an analytically tractable description of the MBLD transition using the forward-scattering approximation and replica techniques. The predictions are in good agreement with the numerics. The MBLD transition lies at energy density significantly above the equilibrium spin glass transition, indicating that the closed system dynamics freezes well outside of the traditional glass phase. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.

  4. An assessment of mean-field mixed semiclassical approaches: Equilibrium populations and algorithm stability

    NASA Astrophysics Data System (ADS)

    Bellonzi, Nicole; Jain, Amber; Subotnik, Joseph E.

    2016-04-01

    We study several recent mean-field semiclassical dynamics methods, focusing on the ability to recover detailed balance for long time (equilibrium) populations. We focus especially on Miller and Cotton's [J. Phys. Chem. A 117, 7190 (2013)] suggestion to include both zero point electronic energy and windowing on top of Ehrenfest dynamics. We investigate three regimes: harmonic surfaces with weak electronic coupling, harmonic surfaces with strong electronic coupling, and anharmonic surfaces with weak electronic coupling. In most cases, recent additions to Ehrenfest dynamics are a strong improvement upon mean-field theory. However, for methods that include zero point electronic energy, we show that anharmonic potential energy surfaces often lead to numerical instabilities, as caused by negative populations and forces. We also show that, though the effect of negative forces can appear hidden in harmonic systems, the resulting equilibrium limits do remain dependent on any windowing and zero point energy parameters.

  5. Kinetic and mean field description of Gibrat's law

    NASA Astrophysics Data System (ADS)

    Toscani, Giuseppe

    2016-11-01

    I introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat (1930, 1931). Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that can be studied analytically, by virtue of a transformation of variables recently utilized in Iagar and Sánchez (2013) to study the heat equation in a nonhomogeneous medium with critical density. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate.

  6. Simulated Tempering and Swapping on Mean-Field Models

    NASA Astrophysics Data System (ADS)

    Bhatnagar, Nayantara; Randall, Dana

    2016-08-01

    Simulated and parallel tempering are families of Markov Chain Monte Carlo algorithms where a temperature parameter is varied during the simulation to overcome bottlenecks to convergence due to multimodality. In this work we introduce and analyze the convergence for a set of new tempering distributions which we call entropy dampening. For asymmetric exponential distributions and the mean field Ising model with an external field simulated tempering is known to converge slowly. We show that tempering with entropy dampening distributions mixes in polynomial time for these models. Examining slow mixing times of tempering more closely, we show that for the mean-field 3-state ferromagnetic Potts model, tempering converges slowly regardless of the temperature schedule chosen. On the other hand, tempering with entropy dampening distributions converges in polynomial time to stationarity. Finally we show that the slow mixing can be very expensive practically. In particular, the mixing time of simulated tempering is an exponential factor longer than the mixing time at the fixed temperature.

  7. Mean-field limit of systems with multiplicative noise.

    PubMed

    Muñoz, Miguel A; Colaiori, Francesca; Castellano, Claudio

    2005-11-01

    A detailed study of the mean-field solution of Langevin equations with multiplicative noise is presented. Three different regimes depending on noise intensity (weak, intermediate, and strong noise) are identified by performing a self-consistent calculation on a fully connected lattice. The most interesting, strong-noise, regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations, as a Ginzburg criterion shows. On the other hand, the self-consistent approach is shown to be valid only in the thermodynamic limit, while for finite systems the critical behavior is found to be different. In this last case, the self-consistent field itself is broadly distributed rather than taking a well defined mean value; its fluctuations, described by an effective zero-dimensional multiplicative noise equation, govern the critical properties. These findings are obtained analytically for a fully connected graph, and verified numerically both on fully connected graphs and on random regular networks. The results presented here shed some doubt on what is the validity and meaning of a standard mean-field approach in systems with multiplicative noise in finite dimensions, where each site does not see an infinite number of neighbors, but a finite one. The implications of all this on the existence of a finite upper critical dimension for multiplicative noise and Kardar-Parisi-Zhang problems are briefly discussed.

  8. Mean field game theoretic approach for security in mobile ad-hoc networks

    NASA Astrophysics Data System (ADS)

    Wang, Yanwei; Tang, Helen; Yu, F. Richard; Huang, Minyi

    2013-05-01

    Game theory can provide a useful tool to study the security problem in mobile ad hoc networks (MANETs). Most existing work on applying game theories to security only considers two players in the security game model: an attacker and a defender. While this assumption is valid for a network with centralized administration, it may not be realistic in MANETs, where centralized administration is not available. Consequently, each individual node in a MANET should be treated separately in the security game model. In this paper, using recent advances in mean field game theory, we propose a novel game theoretic approach for security in MANETs. Mean field game theory provides a powerful mathematical tool for problems with a large number of players. Since security defence mechanisms consume precious system resources (e.g., energy), the proposed scheme considers not only the security requirement of MANETs but also the system resources. In addition, each node only needs to know its own state information and the aggregate effect of the other nodes in the MANET. Therefore, the proposed scheme is a fully distributed scheme. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

  9. Fractional flux lattice and the anyon mean-field approximation

    SciTech Connect

    Pryor, C. )

    1991-12-01

    The anyon mean-field approximation (MFA) is tested by computing the band structure of a charged particle in an infinite two-dimensional square lattice of infinitesimal flux tubes. The band structure and density of states are compared with the MFA and found to be in agreement for {Phi}=1/{ital n}, with {ital n}{gt}3. For {Phi}=1/2 and 1/3, there is no gap, unlike the MFA which predicts a gap. For {Phi}={ital m}/{ital n} (with {ital m}{gt}1), there is a gap, opening up the possibility that a superfluid may form for any rational value of the statistical parameter. A physical realization of the {Phi}=1/2 flux lattice is proposed and a connection between the {Phi}={ital m}/{ital n} lattice and the fractional quantum Hall effect is discussed.

  10. Lifting mean field degeneracies in anisotropic spin systems

    NASA Astrophysics Data System (ADS)

    Sizyuk, Yuriy; Perkins, Natalia; Wolfle, Peter

    We propose a method for calculating the fluctuation contribution to the free energy of anisotropic spin systems with generic bilinear superexchange magnetic Hamiltonian based on the Hubbard-Stratonovich transformation. We show that this contribution splits the set of mean field degenerate states with rotational symmetry, and chooses states with the order parameter directed along lattice symmetric directions as the true ground states. We consider the simple example of Heisenberg-compass model on cubic lattice to show that depending on the relative strength of the compass and Heisenberg interactions the spontaneous magnetization is pinned to either one of the cubic directions or one of the cubic body diagonals with a intermediate phase in between where the minima and maxima of the free energy interchange. DMR-1005932, DMR-1511768, and NSF PHY11-25915.

  11. Double binding energy differences: Mean-field or pairing effect?

    NASA Astrophysics Data System (ADS)

    Qi, Chong

    2012-10-01

    In this Letter we present a systematic analysis on the average interaction between the last protons and neutrons in atomic nuclei, which can be extracted from the double differences of nuclear binding energies. The empirical average proton-neutron interaction Vpn thus derived from experimental data can be described in a very simple form as the interplay of the nuclear mean field and the pairing interaction. It is found that the smooth behavior as well as the local fluctuations of the Vpn in even-even nuclei with N ≠ Z are dominated by the contribution from the proton-neutron monopole interactions. A strong additional contribution from the isoscalar monopole interaction and isovector proton-neutron pairing interaction is seen in the Vpn for even-even N = Z nuclei and for the adjacent odd-A nuclei with one neutron or proton being subtracted.

  12. Relativistic mean-field models and nuclear matter constraints

    NASA Astrophysics Data System (ADS)

    Dutra, M.; Lourenço, O.; Carlson, B. V.; Delfino, A.; Menezes, D. P.; Avancini, S. S.; Stone, J. R.; Providência, C.; Typel, S.

    2013-05-01

    This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear σ3 + σ4 models, (iii) σ3 + σ4 + ω4 models, (iv) models containing mixing terms in the fields σ and ω, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the σ (ω) field. The isospin dependence of the interaction is modeled by the ρ meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.

  13. Temperature dependent relativistic mean field for highly excited hot nuclei

    NASA Astrophysics Data System (ADS)

    Gambhir, Y. K.; Maharana, J. P.; Lalazissis, G. A.; Panos, C. P.; Ring, P.

    2000-11-01

    The temperature dependent relativistic mean field (RMF-T) results obtained by using nonlinear Lagrangian parameter set NL3 are presented for a few selected representative spherical and deformed nuclei. The calculated total binding energy (entropy) decrease (increase) as temperature (T) increases. The depths of the potentials and the single particle (sp) energies change very little with temperature. The density slightly spreads out; as a result the radius increases as temperature rises. For well deformed nuclei the shell effects disappear at around T~3 MeV. This value of T is relatively higher as compared to the corresponding value of T (~1.8 MeV) obtained in the Strutinsky-type calculations. This difference in the value of T is shown to be due to the use of the effective nucleon mass (< the bare mass) appearing in the Skyrme III interaction or emerging from the RMF Lagrangian.

  14. Variation after projection with a triaxially deformed nuclear mean field

    NASA Astrophysics Data System (ADS)

    Gao, Zao-Chun; Horoi, Mihai; Chen, Y. S.

    2015-12-01

    We implemented a variation after projection (VAP) algorithm based on a triaxially deformed Hartree-Fock-Bogoliubov vacuum state. This is the first projected mean field study that includes all the quantum numbers (except parity), i.e., spin (J ), isospin (T ), and mass number (A ). Systematic VAP calculations with JTA projection have been performed for the even-even s d -shell nuclei with the USDB Hamiltonian. All the VAP ground state energies are within 500 keV above the exact shell model values. Our VAP calculations show that the spin projection has two important effects: (1) the spin projection is crucial in achieving good approximation of the full shell model calculation; (2) the intrinsic shapes of the VAP wave functions with spin projection are always triaxial, while the Hartree-Fock-Bogoliubov methods likely provide axial intrinsic shapes. Finally, our analysis suggests that one may not be possible to associate an intrinsic shape to an exact shell model wave function.

  15. Helicity Inferences Stemming from a Mean-Field Solar Dynamo

    NASA Astrophysics Data System (ADS)

    Pipin, Valery

    The global magnetic field of the Sun is generated by dynamo instability that stems from interactions of magnetic field with the large and small-scale flows. Theoretically, it is expected that such interactions produce a helical magnetic field which evolves following to magnetic helicity conservation law. We discuss some consequences of magnetic helicity conservation for the mean-field solar dynamo. We also discuss the observational aspect of the problem including the recent results about observations of the current helicity of solar active regions, the magnetic helicity of the global magnetic field as revealed by SOHO/MDI observations, and the problem of magnetic helicity transport from the solar convection zone to the outer atmosphere.

  16. Finite- to zero-range relativistic mean-field interactions

    SciTech Connect

    Niksic, T.; Vretenar, D.; Lalazissis, G. A.; Ring, P.

    2008-03-15

    We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the {sigma}-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.

  17. Two stochastic mean-field polycrystal plasticity methods

    SciTech Connect

    Tonks, Michael

    2008-01-01

    In this work, we develop two mean-field polycrystal plasticity models in which the L{sup c} are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the L{sup c} tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the STM and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates D{sup c} are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the FCM, and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.

  18. Antimagnetic rotation in 108,110In with tilted axis cranking relativistic mean-field approach

    NASA Astrophysics Data System (ADS)

    Sun, Wu-Ji; Xu, Hai-Dan; Li, Jian; Liu, Yong-Hao; Ma, Ke-Yan; Yang, Dong; Lu, Jing-Bing; Ma, Ying-Jun

    2016-08-01

    Based on tilted axis cranking relativistic mean-field theory within point-coupling interaction PC-PK1, the rotational structure and the characteristic features of antimagnetic rotation for ΔI = 2 bands in 108,110In are studied. Tilted axis cranking relativistic mean-field calculations reproduce the experimental energy spectrum well and are in agreement with the experimental I ∼ ω plot, although the calculated spin overestimates the experimental values. In addition, the two-shears-like mechanism in candidate antimagnetic rotation bands is clearly illustrated and the contributions from two-shears-like orbits, neutron (gd) orbits above Z = 50 shell and Z = 50, N = 50 core are investigated microscopically. The predicted B(E2), dynamic moment of inertia ℑ(2), deformation parameters β and γ, and ℑ(2)/B(E2) ratios in tilted axis cranking relativistic mean-field calculations are discussed and the characteristic features of antimagnetic rotation for the bands before and after alignment are shown. Supported by National Natural Science Foundation of China (11205068, 11205069, 11405072, 11475072, 11547308) and China Postdoctoral Science Foundation (2012M520667)

  19. Computer-Aided Design of Liquid Crystals: A Mean Field Approach

    NASA Astrophysics Data System (ADS)

    Weider, Titus; Glaser, Matthew A.; Clark, Noel A.

    1997-08-01

    The directed design of soft materials is challenging owing to their complex structure and interactions. A promising strategy for the modeling of organic materials involves the replacement of the explicit condensed phase environment of a molecule or group of molecules by an effective mean field potential. We have created mean field theory-based methods for the routine pre-synthesis prediction of materials properties of liquid crystals, including phase behavior, linear and nonlinear optical properties, and spontaneous polarization density. These methods are semi-empirical in the sense that they rely on experimental data (e.g. from NMR or FTIR measurements) for the development of transferable mean field potentials capable of yielding quantitative predictions for novel materials. Our calculations involve detailed quantum chemical studies of conformational energy surfaces and evaluation of statistical averages by exact enumeration (within an RIS approximation) or importance sampling (for fully flexible molecular models). This strategy appears to have great promise, and represents perhaps the only viable approach to computer-aided design of liquid crystalline materials.

  20. Communication: Electronic and transport properties of molecular junctions under a finite bias: A dual mean field approach

    SciTech Connect

    Liu, Shuanglong; Feng, Yuan Ping; Zhang, Chun

    2013-11-21

    We show that when a molecular junction is under an external bias, its properties cannot be uniquely determined by the total electron density in the same manner as the density functional theory for ground state properties. In order to correctly incorporate bias-induced nonequilibrium effects, we present a dual mean field (DMF) approach. The key idea is that the total electron density together with the density of current-carrying electrons are sufficient to determine the properties of the system. Two mean fields, one for current-carrying electrons and the other one for equilibrium electrons can then be derived. Calculations for a graphene nanoribbon junction show that compared with the commonly used ab initio transport theory, the DMF approach could significantly reduce the electric current at low biases due to the non-equilibrium corrections to the mean field potential in the scattering region.

  1. HELICITY CONSERVATION IN NONLINEAR MEAN-FIELD SOLAR DYNAMO

    SciTech Connect

    Pipin, V. V.; Sokoloff, D. D.; Zhang, H.; Kuzanyan, K. M.

    2013-05-01

    It is believed that magnetic helicity conservation is an important constraint on large-scale astrophysical dynamos. In this paper, we study a mean-field solar dynamo model that employs two different formulations of the magnetic helicity conservation. In the first approach, the evolution of the averaged small-scale magnetic helicity is largely determined by the local induction effects due to the large-scale magnetic field, turbulent motions, and the turbulent diffusive loss of helicity. In this case, the dynamo model shows that the typical strength of the large-scale magnetic field generated by the dynamo is much smaller than the equipartition value for the magnetic Reynolds number 10{sup 6}. This is the so-called catastrophic quenching (CQ) phenomenon. In the literature, this is considered to be typical for various kinds of solar dynamo models, including the distributed-type and the Babcock-Leighton-type dynamos. The problem can be resolved by the second formulation, which is derived from the integral conservation of the total magnetic helicity. In this case, the dynamo model shows that magnetic helicity propagates with the dynamo wave from the bottom of the convection zone to the surface. This prevents CQ because of the local balance between the large-scale and small-scale magnetic helicities. Thus, the solar dynamo can operate in a wide range of magnetic Reynolds numbers up to 10{sup 6}.

  2. Relativistic mean-field models and nuclear matter constraints

    SciTech Connect

    Dutra, M.; Lourenco, O.; Carlson, B. V.; Delfino, A.; Menezes, D. P.; Avancini, S. S.; Stone, J. R.; Providencia, C.; Typel, S.

    2013-05-06

    This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear {sigma}{sup 3}+{sigma}{sup 4} models, (iii) {sigma}{sup 3}+{sigma}{sup 4}+{omega}{sup 4} models, (iv) models containing mixing terms in the fields {sigma} and {omega}, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the {sigma} ({omega}) field. The isospin dependence of the interaction is modeled by the {rho} meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.

  3. Classical mutual information in mean-field spin glass models

    NASA Astrophysics Data System (ADS)

    Alba, Vincenzo; Inglis, Stephen; Pollet, Lode

    2016-03-01

    We investigate the classical Rényi entropy Sn and the associated mutual information In in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model in the n -sheet booklet. This is achieved by gluing together n independent copies of the model, and it is the main ingredient for constructing the Rényi entanglement-related quantities. We find a glassy phase at low temperatures, whereas at high temperatures the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends nontrivially on the geometry of the booklet. At high temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for Sn and In and for standard thermodynamic quantities. Both Sn and In exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities, Sn/N and In/N , in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.

  4. Antiferromagnetic and topological states in silicene: A mean field study

    NASA Astrophysics Data System (ADS)

    Liu, Feng; Liu, Cheng-Cheng; Yao, Yu-Gui

    2015-08-01

    It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron-electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling (SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K‧ for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state. Project supported by the National Key Basic Research Program of China (Grant Nos. 2014CB920903, 2013CB921903, 2011CBA00108, and 2012CB937500), the National Natural Science Foundation of China (Grant Nos. 11021262, 11172303, 11404022, 11225418, and 11174337), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20121101110046), the Excellent Young Scholars Research Fund of Beijing Institute of Technology (Grant No. 2014CX04028), and the Basic Research Funds of Beijing Institute of Technology (Grant No. 20141842001).

  5. Individual based and mean-field modeling of direct aggregation

    PubMed Central

    Burger, Martin; Haškovec, Jan; Wolfram, Marie-Therese

    2013-01-01

    We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the first-order model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. PMID:24926113

  6. Low density instability in relativistic mean field models

    NASA Astrophysics Data System (ADS)

    Sulaksono, A.; Mart, T.

    2006-10-01

    The effects of symmetry energy softening of relativistic mean field (RMF) models on the properties of matter with neutrino trapping are investigated. It is found that the effects are less significant than those in the case without neutrino trapping. The weak dependence of the equation of state on the symmetry energy is shown as the main reason for this finding. Using different RMF models the dynamical instabilities of uniform matters, with and without neutrino trapping, have been also studied. The interplay between the dominant contribution of the variation of matter composition and the role of effective masses of mesons and nucleons leads to higher critical densities for matter with neutrino trapping. Furthermore, the predicted critical density is insensitive to both the number of trapped neutrinos as well as the RMF model used in the investigation. It is also found that additional nonlinear terms in the Horowitz-Piekarewicz and Furnstahl-Serot-Tang models prevent another kind of instability, which occurs at relatively high densities, because the effective σ meson mass in their models increases as a function of matter density.

  7. Spectral Synthesis via Mean Field approach to Independent Component Analysis

    NASA Astrophysics Data System (ADS)

    Hu, Ning; Su, Shan-Shan; Kong, Xu

    2016-03-01

    We apply a new statistical analysis technique, the Mean Field approach to Independent Component Analysis (MF-ICA) in a Bayseian framework, to galaxy spectral analysis. This algorithm can compress a stellar spectral library into a few Independent Components (ICs), and the galaxy spectrum can be reconstructed by these ICs. Compared to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, the MF-ICA approach offers a large improvement in efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter recovery for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters derived with galaxies from the Sloan Digital Sky Survey. We find that our MF-ICA method can not only fit the observed galaxy spectra efficiently, but can also accurately recover the physical parameters of galaxies. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find it can provide excellent fitting results for low signal-to-noise spectra.

  8. Modeling distributed axonal delays in mean-field brain dynamics

    NASA Astrophysics Data System (ADS)

    Roberts, J. A.; Robinson, P. A.

    2008-11-01

    The range of conduction delays between connected neuronal populations is often modeled as a single discrete delay, assumed to be an effective value averaging over all fiber velocities. This paper shows the effects of distributed delays on signal propagation. A distribution acts as a linear filter, imposing an upper frequency cutoff that is inversely proportional to the delay width. Distributed thalamocortical and corticothalamic delays are incorporated into a physiologically based mean-field model of the cortex and thalamus to illustrate their effects on the electroencephalogram (EEG). The power spectrum is acutely sensitive to the width of the thalamocortical delay distribution, and more so than the corticothalamic distribution, because all input signals must travel along the thalamocortical pathway. This imposes a cutoff frequency above which the spectrum is overly damped. The positions of spectral peaks in the resting EEG depend primarily on the distribution mean, with only weak dependences on distribution width. Increasing distribution width increases the stability of fixed point solutions. A single discrete delay successfully approximates a distribution for frequencies below a cutoff that is inversely proportional to the delay width, provided that other model parameters are moderately adjusted. A pair of discrete delays together having the same mean, variance, and skewness as the distribution approximates the distribution over the same frequency range without needing parameter adjustment. Delay distributions with large fractional widths are well approximated by low-order differential equations.

  9. Resonating Valence Bonds and Mean-Field d-Wave Superconductivity in Graphite

    SciTech Connect

    Black-Schaffer, Annica M.

    2010-04-27

    We investigate the possibility of inducing superconductivity in a graphite layer by electronic correlation effects. We use a phenomenological microscopic Hamiltonian which includes nearest neighbor hopping and an interaction term which explicitly favors nearest neighbor spin-singlets through the well-known resonance valence bond (RVB) character of planar organic molecules. Treating this Hamiltonian in mean-field theory, allowing for bond-dependent variation of the RVB order parameter, we show that both s- and d-wave superconducting states are possible. The d-wave solution belongs to a two-dimensional representation and breaks time reversal symmetry. At zero doping there exists a quantum critical point at the dimensionless coupling J/t = 1.91 and the s- and d-wave solutions are degenerate for low temperatures. At finite doping the d-wave solution has a significantly higher T{sub c} than the s-wave solution. By using density functional theory we show that the doping induced from sulfur absorption on a graphite layer is enough to cause an electronically driven d-wave superconductivity at graphite-sulfur interfaces. We also discuss applying our results to the case of the intercalated graphites as well as the validity of a mean-field approach.

  10. Mean-field description of ionic size effects with nonuniform ionic sizes: a numerical approach.

    PubMed

    Zhou, Shenggao; Wang, Zhongming; Li, Bo

    2011-08-01

    Ionic size effects are significant in many biological systems. Mean-field descriptions of such effects can be efficient but also challenging. When ionic sizes are different, explicit formulas in such descriptions are not available for the dependence of the ionic concentrations on the electrostatic potential, that is, there is no explicit Boltzmann-type distributions. This work begins with a variational formulation of the continuum electrostatics of an ionic solution with such nonuniform ionic sizes as well as multiple ionic valences. An augmented Lagrange multiplier method is then developed and implemented to numerically solve the underlying constrained optimization problem. The method is shown to be accurate and efficient, and is applied to ionic systems with nonuniform ionic sizes such as the sodium chloride solution. Extensive numerical tests demonstrate that the mean-field model and numerical method capture qualitatively some significant ionic size effects, particularly those for multivalent ionic solutions, such as the stratification of multivalent counterions near a charged surface. The ionic valence-to-volume ratio is found to be the key physical parameter in the stratification of concentrations. All these are not well described by the classical Poisson-Boltzmann theory, or the generalized Poisson-Boltzmann theory that treats uniform ionic sizes. Finally, various issues such as the close packing, limitation of the continuum model, and generalization of this work to molecular solvation are discussed. PMID:21929014

  11. Evolution of primordial magnetic fields in mean-field approximation

    NASA Astrophysics Data System (ADS)

    Campanelli, Leonardo

    2014-01-01

    We study the evolution of phase-transition-generated cosmic magnetic fields coupled to the primeval cosmic plasma in the turbulent and viscous free-streaming regimes. The evolution laws for the magnetic energy density and the correlation length, both in the helical and the non-helical cases, are found by solving the autoinduction and Navier-Stokes equations in the mean-field approximation. Analytical results are derived in Minkowski spacetime and then extended to the case of a Friedmann universe with zero spatial curvature, both in the radiation- and the matter-dominated era. The three possible viscous free-streaming phases are characterized by a drag term in the Navier-Stokes equation which depends on the free-streaming properties of neutrinos, photons, or hydrogen atoms, respectively. In the case of non-helical magnetic fields, the magnetic intensity and the magnetic correlation length evolve asymptotically with the temperature, , as and . Here, , , and are, respectively, the temperature, the number of magnetic domains per horizon length, and the bulk velocity at the onset of the particular regime. The coefficients , , , , , and , depend on the index of the assumed initial power-law magnetic spectrum, , and on the particular regime, with the order-one constants and depending also on the cutoff adopted for the initial magnetic spectrum. In the helical case, the quasi-conservation of the magnetic helicity implies, apart from logarithmic corrections and a factor proportional to the initial fractional helicity, power-like evolution laws equal to those in the non-helical case, but with equal to zero.

  12. Magnetic material in mean-field dynamos driven by small scale helical flows

    NASA Astrophysics Data System (ADS)

    Giesecke, A.; Stefani, F.; Gerbeth, G.

    2014-07-01

    We perform kinematic simulations of dynamo action driven by a helical small scale flow of a conducting fluid in order to deduce mean-field properties of the combined induction action of small scale eddies. We examine two different flow patterns in the style of the G O Roberts flow but with a mean vertical component and with internal fixtures that are modelled by regions with vanishing flow. These fixtures represent either rods that lie in the center of individual eddies, or internal dividing walls that provide a separation of the eddies from each other. The fixtures can be made of magnetic material with a relative permeability larger than one which can alter the dynamo behavior. The investigations are motivated by the widely unknown induction effects of the forced helical flow that is used in the core of liquid sodium cooled fast reactors, and from the key role of soft iron impellers in the von-Kármán-sodium dynamo. For both examined flow configurations the consideration of magnetic material within the fluid flow causes a reduction of the critical magnetic Reynolds number of up to 25%. The development of the growth-rate in the limit of the largest achievable permeabilities suggests no further significant reduction for even larger values of the permeability. In order to study the dynamo behavior of systems that consist of tens of thousands of helical cells we resort to the mean-field dynamo theory (Krause and Rädler 1980 Mean-field Magnetohydrodynamics and Dynamo Theory (Oxford: Pergamon)) in which the action of the small scale flow is parameterized in terms of an α- and β-effect. We compute the relevant elements of the α- and the β-tensor using the so called testfield method. We find a reasonable agreement between the fully resolved models and the corresponding mean-field models for wall or rod materials in the considered range 1\\leqslant {{\\mu }_{r}}\\leqslant 20. Our results may be used for the development of global large scale models with recirculation

  13. Two-particle photoemission from strongly correlated systems: A dynamical mean-field approach

    SciTech Connect

    Napitu, B. D.; Berakdar, J.

    2010-05-15

    We study theoretically the simultaneous photoinduced two-particle excitations of strongly correlated systems on the basis of the Hubbard model. Under certain conditions specified in this work, the corresponding transition probability is related to the two-particle spectral function which we calculate using three different methods: the dynamical mean-field theory combined with quantum Monte Carlo technique, the first-order perturbation theory and the ladder approximations. The results are analyzed and compared for systems at the verge of the metal-insulator transitions. The dependencies on the electronic correlation strength and on doping are explored. In addition, the account for the orbital degeneracy allows an insight into the influence of interband correlations on the two-particle excitations. A suitable experimental realization is discussed.

  14. Nondiagonalizable and nondivergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions.

    PubMed

    Yamaguchi, Yoshiyuki Y

    2015-09-01

    We investigate the response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasistationary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with 0 means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for skew-normal distribution functions. PMID:26465428

  15. Nondiagonalizable and nondivergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions

    NASA Astrophysics Data System (ADS)

    Yamaguchi, Yoshiyuki Y.

    2015-09-01

    We investigate the response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasistationary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with 0 means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for skew-normal distribution functions.

  16. Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field

    NASA Astrophysics Data System (ADS)

    Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.; Rowlands, G.; Vyas, S.

    2016-08-01

    In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R=(b/{B}0)({{\\ell }}\\parallel /{{\\ell }}\\perp ) for rms magnetic fluctuation b, large-scale mean field {{\\boldsymbol{B}}}0, and coherence scales parallel ({{\\ell }}\\parallel ) and perpendicular ({{\\ell }}\\perp ) to {{\\boldsymbol{B}}}0. Here we use a nonperturbative analytic framework based on Corrsin’s hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B 0 with finite b and isotropic fluctuations with {{\\ell }}\\parallel /{{\\ell }}\\perp =1, instead of the well-studied route of varying {{\\ell }}\\parallel /{{\\ell }}\\perp for b \\ll {B}0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with b z = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B 0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with b z = 0, when different routes to R\\to ∞ are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.

  17. Relativistic mean-field hadronic models under nuclear matter constraints

    NASA Astrophysics Data System (ADS)

    Dutra, M.; Lourenço, O.; Avancini, S. S.; Carlson, B. V.; Delfino, A.; Menezes, D. P.; Providência, C.; Typel, S.; Stone, J. R.

    2014-11-01

    Background: The microscopic composition and properties of infinite hadronic matter at a wide range of densities and temperatures have been subjects of intense investigation for decades. The equation of state (EoS) relating pressure, energy density, and temperature at a given particle number density is essential for modeling compact astrophysical objects such as neutron stars, core-collapse supernovae, and related phenomena, including the creation of chemical elements in the universe. The EoS depends not only on the particles present in the matter, but, more importantly, also on the forces acting among them. Because a realistic and quantitative description of infinite hadronic matter and nuclei from first principles in not available at present, a large variety of phenomenological models has been developed in the past several decades, but the scarcity of experimental and observational data does not allow a unique determination of the adjustable parameters. Purpose: It is essential for further development of the field to determine the most realistic parameter sets and to use them consistently. Recently, a set of constraints on properties of nuclear matter was formed and the performance of 240 nonrelativistic Skyrme parametrizations was assessed [M. Dutra et al., Phys. Rev. C 85, 035201 (2012), 10.1103/PhysRevC.85.035201] in describing nuclear matter up to about three times nuclear saturation density. In the present work we examine 263 relativistic-mean-field (RMF) models in a comparable approach. These models have been widely used because of several important aspects not always present in nonrelativistic models, such as intrinsic Lorentz covariance, automatic inclusion of spin, appropriate saturation mechanism for nuclear matter, causality, and, therefore, no problems related to superluminal speed of sound in medium. Method: Three different sets of constraints related to symmetric nuclear matter, pure neutron matter, symmetry energy, and its derivatives were used. The

  18. Mean-field diffusion-limited aggregation: a "density" model for viscous fingering phenomena.

    PubMed

    Bogoyavlenskiy, V A

    2001-12-01

    We explore a universal "density" formalism to describe nonequilibrium growth processes, specifically, the immiscible viscous fingering in Hele-Shaw cells (usually referred to as the Saffman-Taylor problem). For that we develop an alternative approach to the viscous fingering phenomena, whose basic concepts have been recently published in a Rapid Communication [Phys. Rev. E 63, 045305(R) (2001)]. This approach uses the diffusion-limited aggregation (DLA) paradigm as a core: we introduce a mean-field DLA generalization in stochastic and deterministic formulations. The stochastic model, a quasicontinuum DLA, simulates Monte Carlo patterns, which demonstrate a striking resemblance to natural Hele-Shaw fingers and, for steady-state growth regimes, follow precisely the Saffman-Taylor analytical solutions in channel and sector configurations. The relevant deterministic theory, a complete set of differential equations for a time development of density fields, is derived from that stochastic model. As a principal conclusion, we prove an asymptotic equivalency of both the stochastic and deterministic mean-field DLA formulations to the classic Saffman-Taylor hydrodynamics in terms of an interface evolution. PMID:11736272

  19. Hyperons in a relativistic mean-field approach to asymmetric nuclear matter

    SciTech Connect

    Bunta, J. Kotulic; Gmuca, Stefan

    2004-11-01

    Relativistic mean-field theory with {delta} mesons, nonlinear isoscalar self-interactions, and isoscalar-isovector cross interaction terms with parametrizations obtained to reproduce Dirac-Brueckner-Hartree-Fock calculations for nuclear matter is used to study asymmetric nuclear matter properties in {beta} equilibrium, including hyperon degrees of freedom and (hidden) strange mesons. The influence of cross interactions on the composition of hyperon matter and the electron chemical potential is examined. Softening of the nuclear equation of state by cross interactions results in a lowering of the hyperonization, although simultaneously enhancing a hyperon-induced decrease of the electron chemical potential, thus indicating a further shift of the kaon condensate occurrence to higher densities.

  20. Beyond-mean-field boson-fermion model for odd-mass nuclei

    NASA Astrophysics Data System (ADS)

    Nomura, K.; Nikšić, T.; Vretenar, D.

    2016-05-01

    A novel method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is introduced, based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the even-even core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained in a self-consistent mean-field calculation determined by the choice of the energy density functional and pairing interaction. This method uniquely determines the parameters of the Hamiltonian of the boson core, and only the strength of the particle-core coupling is specifically adjusted to selected data for a particular nucleus. The approach is illustrated in a systematic study of low-energy excitation spectra and transition rates of axially deformed odd-mass Eu isotopes.

  1. Orbital magnetism of ultracold fermionic gases in a lattice: Dynamical mean-field approach

    NASA Astrophysics Data System (ADS)

    Cichy, Agnieszka; Sotnikov, Andrii

    2016-05-01

    We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-metal-like atoms in optical lattices that can be effectively described by the two-band spin-1 /2 Hubbard model including Hund's exchange coupling term. Our main goal is to investigate the effect of exchange interactions on finite-temperature magnetic phases for a wide range of lattice fillings. We use the dynamical mean-field theory approach and its real-space generalization to obtain finite-temperature phase diagrams including transitions to magnetically ordered phases. It allows to determine optimal experimental regimes for approaching long-range ferromagnetic ordering in ultracold gases. We also calculate the entropy in the vicinity of magnetically ordered phases, which provides quantitative predictions for ongoing and future experiments aiming at approaching and studying long-range ordered states in optical lattices.

  2. Critical temperature enhancement of topological superconductors: A dynamical mean-field study

    NASA Astrophysics Data System (ADS)

    Nagai, Yuki; Hoshino, Shintaro; Ota, Yukihiro

    2016-06-01

    We show that a critical temperature Tc for spin-singlet two-dimensional superconductivity is enhanced by a cooperation between the Zeeman magnetic field and the Rashba spin-orbit coupling, where a superconductivity becomes topologically nontrivial below Tc. The dynamical mean-field theory with the segment-based hybridization-expansion continuous-time quantum Monte Carlo impurity solver is used for accurately evaluating a critical temperature, without any fermion sign problem. A strong-coupling approach shows that spin-flip-driven local pair hopping leads to part of this enhancement, especially effects of the magnetic field. We propose physical settings suitable for verifying the present calculations, a one-atom-layer system on Si(111) and ionic-liquid-based electric double-layer transistors.

  3. Relativistic mean-field model with energy dependent self-energies

    SciTech Connect

    Antic, S.; Typel, S.

    2015-02-24

    Conventional relativistic mean-field theory is extended with the introduction of higher-order derivative couplings of nucleons with the meson fields. The Euler-Lagrange equations follow from the principle of stationary action. From invariance principles of the Lagrangian density the most general expressions for the conserved current and energy-momentum tensor are derived. The nucleon self-energies show the explicit dependence on the meson fields. They contain additional regulator functions which describe the energy dependence. The density dependence of meson-nucleon couplings causes the apperance of additional rearrangement contributions in the self-energies. The equation of state of infinite nuclear matter is obtained and the thermodynamical consistency of the model is demonstrated. This model is applied to the description of spherical, non-rotating stars in β-equilibrium. Stellar structure is calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations. The results for neutron stars are shown in terms of mass-radius relations.

  4. Mean-field dynamic criticality and geometric transition in the Gaussian core model

    NASA Astrophysics Data System (ADS)

    Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa

    2016-04-01

    We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.

  5. Mean-field dynamic criticality and geometric transition in the Gaussian core model.

    PubMed

    Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa

    2016-04-01

    We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model. PMID:27176347

  6. How self-organized criticality works: A unified mean-field picture

    NASA Astrophysics Data System (ADS)

    Vespignani, Alessandro; Zapperi, Stefano

    1998-06-01

    We present a unified dynamical mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF) models. In analogy with other nonequilibrium critical phenomena, we identify an order parameter with the density of ``active'' sites, and control parameters with the driving rates. Depending on the values of the control parameters, the system is shown to reach a subcritical (absorbing) or supercritical (active) stationary state. Criticality is analyzed in terms of the singularities of the zero-field susceptibility. In the limit of vanishing control parameters, the stationary state displays scaling characteristics of self-organized criticality (SOC). We show that this limit corresponds to the breakdown of space-time locality in the dynamical rules of the models. We define a complete set of critical exponents, describing the scaling of order parameter, response functions, susceptibility and correlation length in the subcritical and supercritical states. In the subcritical state, the response of the system to small perturbations takes place in avalanches. We analyze their scaling behavior in relation with branching processes. In sandpile models, because of conservation laws, a critical exponents subset displays mean-field values (ν=12 and γ=1) in any dimensions. We treat bulk and boundary dissipation and introduce a critical exponent relating dissipation and finite size effects. We present numerical simulations that confirm our results. In the case of the forest-fire model, our approach can distinguish between different regimes (SOC-FF and deterministic FF) studied in the literature, and determine the full spectrum of critical exponents.

  7. T-->0 mean-field population dynamics approach for the random 3-satisfiability problem.

    PubMed

    Zhou, Haijun

    2008-06-01

    During the past decade, phase-transition phenomena in the random 3-satisfiability ( 3 -SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random 3 -SAT problem by the mean-field first-step replica-symmetry-broken cavity theory at the limit of temperature T-->0 . The reweighting parameter y of the cavity theory is allowed to approach infinity together with the inverse temperature beta with fixed ratio r=ybeta . Focusing on the system's space of satisfiable configurations, we carry out extensive population dynamics simulations using the technique of importance sampling, and we obtain the entropy density s(r) and complexity Sigma(r) of zero-energy clusters at different r values. We demonstrate that the population dynamics may reach different fixed points with different types of initial conditions. By knowing the trends of s(r) and Sigma(r) with r , we can judge whether a certain type of initial condition is appropriate at a given r value. This work complements and confirms the results of several other very recent theoretical studies. PMID:18643331

  8. Chain architecture and micellization: A mean-field coarse-grained model for poly(ethylene oxide) alkyl ether surfactants

    NASA Astrophysics Data System (ADS)

    García Daza, Fabián A.; Colville, Alexander J.; Mackie, Allan D.

    2015-03-01

    Microscopic modeling of surfactant systems is expected to be an important tool to describe, understand, and take full advantage of the micellization process for different molecular architectures. Here, we implement a single chain mean field theory to study the relevant equilibrium properties such as the critical micelle concentration (CMC) and aggregation number for three sets of surfactants with different geometries maintaining constant the number of hydrophobic and hydrophilic monomers. The results demonstrate the direct effect of the block organization for the surfactants under study by means of an analysis of the excess energy and entropy which can be accurately determined from the mean-field scheme. Our analysis reveals that the CMC values are sensitive to branching in the hydrophilic head part of the surfactant and can be observed in the entropy-enthalpy balance, while aggregation numbers are also affected by splitting the hydrophobic tail of the surfactant and are manifested by slight changes in the packing entropy.

  9. Chain architecture and micellization: A mean-field coarse-grained model for poly(ethylene oxide) alkyl ether surfactants

    SciTech Connect

    García Daza, Fabián A.; Mackie, Allan D.; Colville, Alexander J.

    2015-03-21

    Microscopic modeling of surfactant systems is expected to be an important tool to describe, understand, and take full advantage of the micellization process for different molecular architectures. Here, we implement a single chain mean field theory to study the relevant equilibrium properties such as the critical micelle concentration (CMC) and aggregation number for three sets of surfactants with different geometries maintaining constant the number of hydrophobic and hydrophilic monomers. The results demonstrate the direct effect of the block organization for the surfactants under study by means of an analysis of the excess energy and entropy which can be accurately determined from the mean-field scheme. Our analysis reveals that the CMC values are sensitive to branching in the hydrophilic head part of the surfactant and can be observed in the entropy-enthalpy balance, while aggregation numbers are also affected by splitting the hydrophobic tail of the surfactant and are manifested by slight changes in the packing entropy.

  10. MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD

    SciTech Connect

    Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P.; Subedi, P.; Matthaeus, W. H.; Chuychai, P. E-mail: david.ruf@mahidol.ac.th E-mail: pat.wongpan@postgrad.otago.ac.nz E-mail: prasub@udel.edu

    2015-01-01

    In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.

  11. Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example

    NASA Astrophysics Data System (ADS)

    Bouchet, Freddy; Gawȩdzki, Krzysztof; Nardini, Cesare

    2016-06-01

    In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory (Freidlin and Wentzell, Random perturbations of dynamical systems, 2012). In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory (Bertini et al., arXiv:1404.6466 , 2014), which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to 1/√{N}, where N is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter λ , starting from a known quasi-potential for λ =0. In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner (Stochastics 20:247-308, 1987; Stochastic differential systems, vol 96, pp 1-10, 1987). Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example

  12. Deviation from mean-field behavior in a low molecular weight critical polymer blend

    NASA Astrophysics Data System (ADS)

    Hair, D. W.; Hobbie, E. K.; Nakatani, A. I.; Han, C. C.

    1992-06-01

    A deviation from mean-field behavior is observed in the static susceptibility and correlation length measured with small angle neutron scattering as a function of temperature near the phase boundary of a relatively low molecular weight critical polymer mixture. The possibility of a fluctuation influenced crossover from mean-field to nonmean-field behavior is considered.

  13. Limit Theorems for Monomer-Dimer Mean-Field Models with Attractive Potential

    NASA Astrophysics Data System (ADS)

    Alberici, Diego; Contucci, Pierluigi; Fedele, Micaela; Mingione, Emanuele

    2016-09-01

    The number of monomers in a monomer-dimer mean-field model with an attractive potential fluctuates according to the central limit theorem when the parameters are outside the critical curve. At the critical point the model belongs to the same universality class of the mean-field ferromagnet. Along the critical curve the monomer and dimer phases coexist.

  14. Mean-field dynamics of two-mode Bose-Einstein condensates in highly anisotropic potentials: interference, dimensionality and entanglement

    NASA Astrophysics Data System (ADS)

    Tacla, Alexandre B.; Caves, Carlton M.

    2013-02-01

    We study the mean-field dynamics and the reduced-dimension character of two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means of perturbative techniques, we show that the tightly confined (transverse) degrees of freedom can be decoupled from the dynamical equations at the expense of introducing additional effective three-body, attractive, intra- and inter-mode interactions into the dynamics of the loosely confined (longitudinal) degrees of freedom. These effective interactions are mediated by changes in the transverse wave function. The perturbation theory is valid as long as the nonlinear scattering energy is small compared to the transverse energy scales. This approach leads to reduced-dimension mean-field equations that optimally describe the evolution of a two-mode condensate in general quasi-one-dimensional (1D) and quasi-two-dimensional geometries. We use this model to investigate the relative phase and density dynamics of a two-mode, cigar-shaped 87Rb BEC. We study the relative-phase dynamics in the context of a nonlinear Ramsey interferometry scheme, which has recently been proposed as a novel platform for high-precision interferometry. Numerical integration of the coupled, time-dependent, three-dimensional, two-mode Gross-Pitaevskii equations for various atom numbers shows that this model gives a considerably more refined analytical account of the mean-field evolution than an idealized quasi-1D description.

  15. Kaon Condensation and Lambda-Nucleon Loop in the Relativistic Mean-Field Approach

    SciTech Connect

    Tomoyuki Maruyama; Takumi Muto; Toshitaka Tatsumi; Kazuo Tsushima; Anthony W. Thomas

    2005-02-24

    The possibility of kaon condensation in high-density symmetric nuclear matter is investigated including both s- and p-wave kaon-baryon interactions within the relativistic mean-field (RMF) theory. Above a certain density, we have a collective K{sub s} state carrying the same quantum numbers as the antikaon. The appearance of the K{sub s} state is caused by the time component of the axial-vector interaction between kaons and baryons. It is shown that the system becomes unstable with respect to condensation of K-Kbar{sub s} pairs. We consider how the effective baryon masses affect the kaon self-energy coming from the time component of the axial-vector interaction. Also, the role of the spatial component of the axial-vector interaction on the possible existence of the collective kaonic states is discussed in connection with Lambda-mixing effects in the ground state of high-density matter. Implications of K-Kbar{sub s} condensation for high-energy heavy-ion collisions are briefly mentioned.

  16. Singular-potential random-matrix model arising in mean-field glassy systems

    NASA Astrophysics Data System (ADS)

    Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo

    2014-06-01

    We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.

  17. Quantum Dynamics of Dark and Dark-Bright Solitons beyond the Mean-Field Approximation

    NASA Astrophysics Data System (ADS)

    Krönke, Sven; Schmelcher, Peter

    2014-05-01

    Dark solitons are well-known excitations in one-dimensional repulsively interacting Bose-Einstein condensates, which feature a characteristical phase-jump across a density dip and form stability in the course of their dynamics. While these objects are stable within the celebrated Gross-Pitaevskii mean-field theory, the situation changes dramatically in the full many-body description: The condensate being initially in a dark soliton state dynamically depletes and the density notch fills up with depleted atoms. We analyze this process in detail with a particular focus on two-body correlations and the fate of grey solitons (dark solitons with finite density in the notch) and thereby complement the existing results in the literature. Moreover, we extend these studies to mixtures of two repulsively interacting bosonic species with a dark-bright soliton (dark soliton in one component filled with localized atoms of the other component) as the initial state. All these many-body quantum dynamics simulations are carried out with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB).

  18. Singular-potential random-matrix model arising in mean-field glassy systems.

    PubMed

    Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo

    2014-06-01

    We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.

  19. Beyond-mean-field corrections within the second random-phase approximation

    NASA Astrophysics Data System (ADS)

    Grasso, M.; Gambacurta, D.; Engel, J.

    2016-06-01

    A subtraction procedure, introduced to overcome double-counting problems in beyond-mean-field theories, is used in the second random-phase approximation (SRPA). Doublecounting problems arise in the energy-density functional framework in all cases where effective interactions tailored at leading order are used for higher-order calculations, such as those done in the SRPA model. It was recently shown that this subtraction procedure also guarantees that the stability condition related to the Thouless theorem is verified in extended RPA models. We discuss applications of the subtraction procedure, introduced within the SRPA model, to the nucleus 16O. The application of the subtraction procedure leads to: (i) stable results that are weakly cutoff dependent; (ii) a considerable upwards correction of the SRPA spectra (which were systematically shifted downwards by several MeV with respect to RPA spectra, in all previous calculations). With this important implementation of the model, many applications may be foreseen to analyze the genuine impact of 2 particle-2 hole configurations (without any cutoff dependences and anomalous shifts) on the excitation spectra of medium-mass and heavy nuclei.

  20. Corrected mean-field models for spatially dependent advection-diffusion-reaction phenomena

    NASA Astrophysics Data System (ADS)

    Simpson, Matthew J.; Baker, Ruth E.

    2011-05-01

    In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion-process-based mechanisms motivated by applications from cell biology. Previous investigations that focused on relaxing the independence assumption have been limited to studying initially uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterized by moving fronts. Here we propose generalized methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion-process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave-type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

  1. Monogamy of entanglement and improved mean-field ansatz for spin lattices

    NASA Astrophysics Data System (ADS)

    Osterloh, Andreas; Schützhold, Ralf

    2015-03-01

    We consider rather general spin-1 /2 lattices with large coordination numbers Z . Based on the monogamy of entanglement and other properties of the concurrence C , we derive rigorous bounds for the entanglement between neighboring spins, such as C ≤1 /√{Z } , which show that C decreases for large Z . In addition, we demonstrate that the concurrence C measures the deviation from mean-field behavior and can only vanish if the mean-field ansatz yields an exact ground state of the Hamiltonian. Motivated by these findings, we propose an improved mean-field ansatz by adding entanglement.

  2. Combination of Hedin's GW and dynamical mean-field theory tested on H2 molecule

    NASA Astrophysics Data System (ADS)

    Lee, Juho; Haule, Kristjan

    We compare various flavors of `` GW +DMFT'' approach with LDA+DMFT for the simplest strongly correlated system, the H2 molecule. The following GW +DMFT methodologies are compared: (i) the fully self-consistent GW+DMFT, (ii) the quasi-particle self-consistent QS-GW+DMFT with dynamic double-counting, (iii) QS-GW+DMFT with static double-counting schemes. We found that fully self-consistent GW +DMFT with exact double-counting yields very precise spectra around equilibrium H-H distance, as well as reasonable total energy (comparable to LDA+DMFT). However, this scheme breaks down in the correlated regime due to causality violation. The QS-GW+DMFT approaches, which are not derivable from a functional, yield similar spectra as full GW+DMFT near equilibrium distance, and in static double-counting schemes, can also be extended into correlated regime. However, the total energy of these approaches is much worse than the total energy of LDA+DMFT. In summary, this toy model of correlated physics suggests that QS-GW+DMFT with constant double-counting should give accurate predictions of spectra, but not total energy, while LDA+DMFT gives very precise total energy, but somewhat less precise spectra.

  3. Nonequilibrium itinerant-electron magnetism: A time-dependent mean-field theory

    NASA Astrophysics Data System (ADS)

    Secchi, A.; Lichtenstein, A. I.; Katsnelson, M. I.

    2016-08-01

    We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation that is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the nonequilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of nonequilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of nonequilibrium single-electron Green's functions and self-energies. In the particular case of equilibrium, we recover previously known results.

  4. Dynamics of Labyrinthine Pattern Formation in Magnetic Fluids: A Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Otto, Felix

    A viscous ferroliquid is trapped between two narrowly spaced parallel sheets of glass, the Hele-Shaw cell. The ferroliquid fills a cylindrical domain with cross section Ω and the rest of the cell is filled with a fluid of negligible viscosity. In the absence of any other forces, the effect of surface tension at the interface between the fluids is such that the liquid is at rest if Ω is circular. Starting from time t=0 a strong magnetic field perpendicular to the cell is applied, so that the ferroliquid is instantaneously uniformly magnetized in this direction. For t>0, two competing forces act on the liquid: surface tension and magnetostatic repulsion. The liquid reacts to these forces by undergoing a strongly overdamped flow, preserving its volume and its uniform magnetization. In the regime of strong magnetization, it is observed that an initially disk-like phase configuration undergoes a fingering instability, that these fingers grow and form a labyrinth and that the domain covered by this microstructure spreads. We start from a model for the evolution of Ω proposed by Jackson, Goldstein & Cebers. Conventional analysis does not bridge the gap between the early stages (captured by the linearization) and the late stages of the evolution (described by a variational problem). Numerical analysis only captures the early stages. We present a new type of analysis for the intermediate stage. It allows us to introduce a coarse-grain description of this evolution of microstructure in a rational way: We derive an evolution equation for the local volume fraction of the gap filled by the ferroliquid. Our analysis is based on the discovery that this type of strongly overdamped flow problems can be considered as a gradient flux of the relevant energy functional.

  5. Linking phase behavior and reversible colloidal aggregation at low concentrations: simulations and stochastic mean field theory.

    PubMed

    Puertas, Antonio M; Odriozola, Gerardo

    2007-05-24

    We have studied the link between the kinetics of clustering and the phase behavior of dilute colloids with short range attractions of moderate strength. This was done by means of computer simulations and a theoretical kinetic model originally developed to deal with reversible colloidal aggregation. Three different regions of the phase diagram were accessed. For weak attractions, a gas phase of small clusters in equilibrium forms in the system. For intermediate attractions, the system undergoes liquid-gas separation, which is signatured by the formation of a few large droplike aggregates, a gas phase of small clusters, and an overall kinetics where a few seeds succeed in explosively growing at long times, after a lag time. Finally, for very strong attractions, fractal unbreakable clusters form and grow following DLCA-like (diffusion limited cluster aggregation) kinetics; liquid-gas separation is prevented by the strength of the bonds, which do not allow restructuration. Good qualitative and quantitative agreement is found between the dynamic simulations and the kinetic model in all the three regions.

  6. Light propagation beyond the mean-field theory of standard optics.

    PubMed

    Javanainen, Juha; Ruostekoski, Janne

    2016-01-25

    With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is, electrodynamics of a polarizable medium, and numerical simulations in an elementary problem of light propagating through a slab of matter. The standard optics fails already at quite low atom densities, and the failure becomes dramatic when the average interatomic separation is reduced to around k(-1), where k is the wave number of resonant light. The difference between the two solutions originates from correlations between the atoms induced by light-mediated dipole-dipole interactions. PMID:26832481

  7. Self-consistent Green's function embedding for advanced electronic structure methods based on a dynamical mean-field concept

    NASA Astrophysics Data System (ADS)

    Chibani, Wael; Ren, Xinguo; Scheffler, Matthias; Rinke, Patrick

    2016-04-01

    We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here a unit cell or a supercell) with advanced electronic structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self-consistent manner. Our scheme is based on the concept of dynamical mean-field theory formulated in terms of Green's functions. Our real-space dynamical mean-field embedding scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green's functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., computational supercell) size.

  8. Mean-field approximation for spacing distribution functions in classical systems

    NASA Astrophysics Data System (ADS)

    González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

    2012-01-01

    We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

  9. Can realistic interaction be useful for nuclear mean-field approaches?

    NASA Astrophysics Data System (ADS)

    Nakada, H.; Sugiura, K.; Inakura, T.; Margueron, J.

    2016-07-01

    Recent applications of the M3Y-type semi-realistic interaction to the nuclear mean-field approaches are presented: i) Prediction of magic numbers and ii) isotope shifts of nuclei with magic proton numbers. The results exemplify that the realistic interaction, which is derived from the bare 2 N and 3 N interaction, furnishes a new theoretical instrument for advancing nuclear mean-field approaches.

  10. Asymmetric Neutrino Emissions in Relativistic Mean-Field Approach and Observables: Pulsar Kick and Rapid Spin-Deceleration of Magnetized Proto-Neutron Stars

    NASA Astrophysics Data System (ADS)

    Maruyama, T.; Kajino, T.; Yasutake, N.; Hidaka, J.; Kuroda, T.; Cheoun, M. K.; Ryu, C. Y.; Mathews, G. J.

    2015-11-01

    We calculate absorption cross-sections of neutrino in proto-neutron stars with strong magnetic field in the relativistic mean-field theory. Then, we apply this result to the neutrino transfer in the matter, and study the pulsar kick and the rapid spin down of magnetars.

  11. Improved quasiparticle wave functions and mean field for G0W0 calculations: Initialization with the COHSEX operator

    NASA Astrophysics Data System (ADS)

    Jain, Manish; Deslippe, Jack; Samsonidze, Georgy; Cohen, Marvin L.; Chelikowsky, James R.; Louie, Steven G.

    2014-09-01

    The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the GW self-energy operator, Σ, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0W0 scheme. However, there are known situations in which this diagonal G0W0 approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc -COHSEX+GW, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW. In this scheme, frequency-dependent self energy Σ (ω), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX GW (od -COHSEX+GW). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the GW Σ in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc -COHSEX+GW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.

  12. Mean Field Strategies Induce Unrealistic Non-Linearities in Calcium Puffs

    PubMed Central

    Solovey, Guillermo; Fraiman, Daniel; Dawson, Silvina Ponce

    2011-01-01

    Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs). To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic non-linear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes. PMID:21869877

  13. Mean-field approach for a statistical mechanical model of proteins

    NASA Astrophysics Data System (ADS)

    Bruscolini, Pierpaolo; Cecconi, Fabio

    2003-07-01

    We study the thermodynamical properties of a topology-based model proposed by Galzitskaya and Finkelstein for the description of protein folding. We devise and test three different mean-field approaches for the model, that simplify the treatment without spoiling the description. The validity of the model and its mean-field approximations is checked by applying them to the β-hairpin fragment of the immunoglobulin-binding protein (GB1) and making a comparison with available experimental data and simulation results. Our results indicate that this model is a rather simple and reasonably good tool for interpreting folding experimental data, provided the parameters of the model are carefully chosen. The mean-field approaches substantially recover all the relevant exact results and represent reliable alternatives to the Monte Carlo simulations.

  14. A mean-field analysis of the simple model of evolving open systems

    NASA Astrophysics Data System (ADS)

    Shimada, Takashi; Ogushi, Fumiko

    2016-09-01

    A recently reported mechanism of letting evolving systems grow only if the interactions in it is moderately sparse is reviewed and examined. It is shown that the mean field analysis, which is known to give a good simple understanding for this transition from growing to non-growing phase but with about 30% difference in its position, is well improved by taking only mean field type information from the simulation of the original model. This supports the validity of the understanding for the mechanism of the transition, obtained from the mean field analysis. The transition stems from an essential balance of two effects: although having more interactions makes each node robust, it also increases the impact of the loss of a node.

  15. Carbon diffusion in supersaturated ferrite: a comparison of mean-field and atomistic predictions

    NASA Astrophysics Data System (ADS)

    Lawrence, B.; Sinclair, C. W.; Perez, M.

    2014-09-01

    Hillert's mean-field elastic prediction of the diffusivity of carbon in ferrite is regularly used to explain the experimental observation of slow diffusion of carbon in supersaturated ferrite. With increasing carbon supersaturation, the appropriateness of assuming that many-body carbon interactions can be ignored needs to be re-examined. In this work, we have sought to evaluate the limits of such mean-field predictions for activation barrier prediction by comparing such models with molecular dynamics simulations. The results of this analysis show that even at extremely high levels of supersaturation (up to 8 at% C), mean-field elasticity models can be used with confidence when the effects of carbon concentration on the energy of carbon at octahedral and tetrahedral sites are considered. The reasons for this finding and its consequences are discussed.

  16. Time-Dependent Green's Functions Description of One-Dimensional Nuclear Mean-Field Dynamics

    SciTech Connect

    Rios, Arnau; Danielewicz, Pawel; Barker, Brent

    2009-05-07

    The time-dependent Green's functions formalism provides a consistent description of the time evolution of quantum many-body systems, either in the mean-field approximation or in more sophisticated correlated approaches. We describe an attempt to apply this formalism to the mean-field dynamics of symmetric reactions for one-dimensional nuclear slabs. We pay particular attention to the off-diagonal elements of the Green's functions in real space representation. Their importance is quantified by means of an elimination scheme based on a super-operator cut-off field and their relevance for the global time evolution is assessed. The Wigner function and its structure in the mean-field approximation is also discussed.

  17. Streamlined mean field variational Bayes for longitudinal and multilevel data analysis.

    PubMed

    Lee, Cathy Yuen Yi; Wand, Matt P

    2016-07-01

    Streamlined mean field variational Bayes algorithms for efficient fitting and inference in large models for longitudinal and multilevel data analysis are obtained. The number of operations is linear in the number of groups at each level, which represents a two orders of magnitude improvement over the naïve approach. Storage requirements are also lessened considerably. We treat models for the Gaussian and binary response situations. Our algorithms allow the fastest ever approximate Bayesian analyses of arbitrarily large longitudinal and multilevel datasets, with little degradation in accuracy compared with Markov chain Monte Carlo. The modularity of mean field variational Bayes allows relatively simple extension to more complicated scenarios. PMID:27214238

  18. μ -symmetry breaking: An algebraic approach to finding mean fields of quantum many-body systems

    NASA Astrophysics Data System (ADS)

    Higashikawa, Sho; Ueda, Masahito

    2016-07-01

    One of the most fundamental problems in quantum many-body systems is the identification of a mean field in spontaneous symmetry breaking which is usually made in a heuristic manner. We propose a systematic method of finding a mean field based on the Lie algebra and the dynamical symmetry by introducing a class of symmetry-broken phases which we call μ -symmetry breaking. We show that for μ -symmetry breaking the quadratic part of an effective Lagrangian of Nambu-Goldstone modes can be block-diagonalized and that homotopy groups of topological excitations can be calculated systematically.

  19. Streamlined mean field variational Bayes for longitudinal and multilevel data analysis.

    PubMed

    Lee, Cathy Yuen Yi; Wand, Matt P

    2016-07-01

    Streamlined mean field variational Bayes algorithms for efficient fitting and inference in large models for longitudinal and multilevel data analysis are obtained. The number of operations is linear in the number of groups at each level, which represents a two orders of magnitude improvement over the naïve approach. Storage requirements are also lessened considerably. We treat models for the Gaussian and binary response situations. Our algorithms allow the fastest ever approximate Bayesian analyses of arbitrarily large longitudinal and multilevel datasets, with little degradation in accuracy compared with Markov chain Monte Carlo. The modularity of mean field variational Bayes allows relatively simple extension to more complicated scenarios.

  20. Non-mean-field effects in systems with long-range forces in competition.

    PubMed

    Bachelard, R; Staniscia, F

    2012-11-01

    We investigate the canonical equilibrium of systems with long-range forces in competition. These forces create a modulation in the interaction potential and modulated phases appear at the system scale. The structure of these phases differentiate this system from monotonic potentials, where only the mean-field and disordered phases exist. With increasing temperature, the system switches from one ordered phase to another through a first-order phase transition. Both mean-field and modulated phases may be stable, even at zero temperature, and the long-range nature of the interaction will lead to metastability characterized by extremely long time scales.

  1. Fragility of the mean-field scenario of structural glasses for disordered spin models in finite dimensions

    NASA Astrophysics Data System (ADS)

    Cammarota, Chiara; Biroli, Giulio; Tarzia, Marco; Tarjus, Gilles

    2013-02-01

    At the mean-field level, on fully connected lattices, several disordered spin models have been shown to belong to the universality class of “structural glasses” with a “random first-order transition” (RFOT) characterized by a discontinuous jump of the order parameter and no latent heat. However, their behavior in finite dimensions is often drastically different, displaying either no glassiness at all or a conventional spin-glass transition. We clarify the physical reasons for this phenomenon and stress the unusual fragility of the RFOT to short-range fluctuations, associated, e.g., with the mere existence of a finite number of neighbors. Accordingly, the solution of fully connected models is only predictive in very high dimension, whereas despite being also mean-field in character, the Bethe approximation provides valuable information on the behavior of finite-dimensional systems. We suggest that before embarking on a full blown account of fluctuations on all scales through computer simulation or renormalization-group approach, models for structural glasses should first be tested for the effect of short-range fluctuations and we discuss ways to do it. Our results indicate that disordered spin models do not appear to pass the test and are therefore questionable models for investigating the glass transition in three dimensions. This also highlights how nontrivial is the first step of deriving an effective theory for the RFOT phenomenology from a rigorous integration over the short-range fluctuations.

  2. Collective aspects deduced from time-dependent microscopic mean-field with pairing: Application to the fission process

    NASA Astrophysics Data System (ADS)

    Tanimura, Yusuke; Lacroix, Denis; Scamps, Guillaume

    2015-09-01

    Given a set of collective variables, a method is proposed to obtain the associated conjugated collective momenta and masses starting from a microscopic time-dependent mean-field theory. The construction of pairs of conjugated variables is the first step to bridge microscopic and macroscopic approaches. The method is versatile and can be applied to study a large class of nuclear processes. An illustration is given here with the fission of 258Fm. Using the quadrupole moment and eventually higher-order multipole moments, the associated collective masses are estimated along the microscopic mean-field evolution. When more than one collective variable is considered, it is shown that the off-diagonal matrix elements of the inertia play a crucial role. Using the information on the quadrupole moment and associated momentum, the collective evolution is studied. It is shown that dynamical effects beyond the adiabatic limit are important. Nuclei formed after fission tend to stick together for a longer time leading to a dynamical scission point at a larger distance between nuclei compared to the one anticipated from the adiabatic energy landscape. The effective nucleus-nucleus potential felt by the emitted nuclei is finally extracted.

  3. Multidimensionally constrained relativistic mean-field study of triple-humped barriers in actinides

    NASA Astrophysics Data System (ADS)

    Zhao, Jie; Lu, Bing-Nan; Vretenar, Dario; Zhao, En-Guang; Zhou, Shan-Gui

    2015-01-01

    Background: Potential energy surfaces (PES's) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier, the occurrence of a third barrier was predicted by macroscopic-microscopic model calculations in the 1970s, but contradictory results were later reported by a number of studies that used different methods. Purpose: Triple-humped barriers in actinide nuclei are investigated in the framework of covariant density functional theory (CDFT). Methods: Calculations are performed using the multidimensionally constrained relativistic mean field (MDC-RMF) model, with the nonlinear point-coupling functional PC-PK1 and the density-dependent meson exchange functional DD-ME2 in the particle-hole channel. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Results: Two-dimensional PES's of 226,228,230,232Th and 232,235,236,238U are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. The functional DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and 238U . The third minima in 230 ,232Th are very shallow, whereas those in 226 ,228Th and 238U are quite prominent. With the functional PC-PK1 a third barrier is found only in 226 ,228 ,230Th . Single-nucleon levels around the Fermi surface are analyzed in 226Th, and it is found that the formation of the third minimum is mainly due to the Z =90 proton energy gap at β20≈1.5 and β30≈0.7 . Conclusions: The possible occurrence of a third barrier on the PES's of actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases

  4. Gluon condensate in a pion superfluid beyond the mean-field approximation

    SciTech Connect

    Jiang Yin; Zhuang Pengfei

    2011-03-15

    We study gluon condensate in a pion superfluid by calculating the equation of state of the system in the Nambu-Jona-Lasinio model. While in mean-field approximation the growing pion condensate leads to an increasing gluon condensate, meson fluctuations reduce the gluon condensate, and the broken scalar symmetry can be smoothly restored at finite isospin density.

  5. A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach

    NASA Astrophysics Data System (ADS)

    Lacroix, Denis; Tanimura, Yusuke; Ayik, Sakir; Yilmaz, Bulent

    2016-04-01

    The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-, ..., N -body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for short time evolution. In that case, it gives information on the evolution time-scale close to a saddle point associated to a quantum phase-transition. For long time evolution and strong coupling, we observed that the simplified BBGKY hierarchy cannot be truncated and only the full SMF with initial sampling leads to reasonable results.

  6. a Mean-Field Version of the Ssb Model for X-Chromosome Inactivation

    NASA Astrophysics Data System (ADS)

    Gaeta, Giuseppe

    Nicodemi and Prisco recently proposed a model for X-chromosome inactivation in mammals, explaining this phenomenon in terms of a spontaneous symmetry-breaking mechanism [{\\it Phys. Rev. Lett.} 99 (2007), 108104]. Here we provide a mean-field version of their model.

  7. Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons

    PubMed Central

    Nicola, Wilten; Campbell, Sue Ann

    2013-01-01

    We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presence of heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons. PMID:24416013

  8. Charge and parity projected relativistic mean field model with pion for finite nuclei

    SciTech Connect

    Ogawa, Yoko; Toki, Hiroshi; Tamenaga, Setsuo; Sugimoto, Satoru; Ikeda, Kiyomi

    2006-03-15

    We construct a new relativistic mean field model by explicitly introducing a {pi}-meson mean field with charge number and parity projection. We call this model the charge and parity projected relativistic mean field (CPPRMF) model. We take the chiral {sigma} model Lagrangian for the construction of finite nuclei. We apply this framework first for the {sup 4}He nucleus as a pilot case and study the role of the {pi}-meson field on the structure of nuclei. We demonstrate that it is essential to solve the mean field equation with the variation introduced after the projection in order to take the pionic correlations into account explicitly. We study the ground-state properties of {sup 4}He by varying several parameters, such as the {sigma}-meson mass and the {omega}-meson coupling constant. We are able to construct a good ground state for {sup 4}He. A depression appears in the central region of the density distribution, and the second maximum and the position of the dip in the form factor of {sup 4}He are naturally obtained in the CPPRMF model.

  9. Self-consistent chaos in a mean-field Hamiltonian model of fluids and plasmas

    NASA Astrophysics Data System (ADS)

    del-Castillo-Negrete, D.; Firpo, Marie-Christine

    2002-11-01

    We present a mean-field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas. In plasmas, the model describes the self-consistent evolution of electron holes and clumps in phase space. In fluids, the model describes the dynamics of vortices with negative and positive circulation in shear flows. The mean-field nature of the system makes it a tractable model to study the dynamics of large degrees-of-freedom, coupled Hamiltonian systems. Here we focus in the role of self-consistent chaos in the formation and destruction of phase space coherent structures. Numerical simulations in the finite N and in the Narrow kinetic limit (where N is the number of particles) show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles, and show that the N = 2 limit has a family of rotating integrable solutions described by a one degree-of-freedom nontwist Hamiltonian. The coherence of the dipole is explained in terms of a parametric resonance between the rotation frequency of the macroparticles and the oscillation frequency of the self-consistent mean field. For a class of initial conditions, the mean field exhibits a self-consistent, elliptic-hyperbolic bifurcation that leads to the destruction of the dipole and violent mixing of the phase space.

  10. Towards a nonequilibrium Green's function description of nuclear reactions: One-dimensional mean-field dynamics

    SciTech Connect

    Rios, Arnau; Barker, Brent; Buchler, Mark; Danielewicz, Pawel

    2011-05-15

    Research Highlights: > Dynamics of central nuclear reactions. > Nonequilibrium Green's functions and Kadanoff-Baym formalism. > Adiabatic switching on of interactions. > Mean-field time evolution of nuclear slabs. > Off-diagonal spatial structure of a collision density matrix. - Abstract: Nonequilibrium Green's function methods allow for an intrinsically consistent description of the evolution of quantal many-body body systems, with inclusion of different types of correlations. In this paper, we focus on the practical developments needed to build a Green's function methodology for nuclear reactions. We start out by considering symmetric collisions of slabs in one dimension within the mean-field approximation. We concentrate on two issues of importance for actual reaction simulations. First, the preparation of the initial state within the same methodology as for the reaction dynamics is demonstrated by an adiabatic switching on of the mean-field interaction, which leads to the mean-field ground state. Second, the importance of the Green's function matrix-elements far away from the spatial diagonal is analyzed by a suitable suppression process that does not significantly affect the evolution of the elements close to the diagonal. The relative lack of importance of the far-away elements is tied to system expansion. We also examine the evolution of the Wigner function and verify quantitatively that erasing of the off-diagonal elements corresponds to averaging out of the momentum-space details in the Wigner function.

  11. Electronic and magnetic properties of TbNi4Si: Ab initio calculations, mean field approximation and Monte Carlo simulation

    NASA Astrophysics Data System (ADS)

    Bensadiq, A.; Zaari, H.; Benyoussef, A.; El Kenz, A.

    2016-09-01

    Using the density functional theory, the electronic structure; density of states, band structure and exchange couplings of Tb Ni4 Si compound have been investigated. Magnetic and magnetocaloric properties of this material have been studied using Monte Carlo Simulation (MCS) and Mean Field Approximation (MFA) within a three dimensional Ising model. We calculated the isothermal magnetic entropy change, adiabatic temperature change and relative cooling power (RCP) for different external magnetic field and temperature. The highest obtained isothermal magnetic entropy change is of -14.52 J kg-1 K-1 for a magnetic field of H=4 T. The adiabatic temperature reaches a maximum value equal to 3.7 K and the RCP maximum value is found to be 125.12 J kg-1 for a field magnetic of 14 T.

  12. Fractional Spin Fluctuations as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model

    NASA Astrophysics Data System (ADS)

    Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi

    2016-10-01

    Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the honeycomb Kitaev model whose ground state is a canonical example of the quantum spin liquid. We find that dynamical spin correlations show peculiar temperature and frequency dependence even below the temperature where static correlations saturate. The results provide the experimentally accessible symptoms of the fluctuating fractionalized spins evincing the quantum spin liquids.

  13. Mean field phase diagram of an SU(2){sub {ital L}}{times}SU(2){sub {ital R}} lattice Higgs-Yukawa model at finite {lambda}

    SciTech Connect

    Pryor, C.

    1996-02-01

    The phase diagram of an SU(2){sub {ital L}}{times}SU(2){sub {ital R}} lattice Higgs-Yukawa model with finite {lambda} is constructed using mean field theory. The phase diagram bears a superficial resemblance to that for {lambda}={infinity}; however, as {lambda} is decreased the paramagnetic region shrinks in size. For small {lambda} the phase transitions remain second order, and no new first order transitions are seen. {copyright} {ital 1996 The American Physical Society.}

  14. Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry.

    PubMed

    Haine, Simon A

    2016-06-10

    There has been considerable recent interest in the mean-field dynamics of various atom-interferometry schemes designed for precision sensing. In the field of quantum metrology, the standard tools for evaluating metrological sensitivity are the classical and quantum Fisher information. In this Letter, we show how these tools can be adapted to evaluate the sensitivity when the behavior is dominated by mean-field dynamics. As an example, we compare the behavior of four recent theoretical proposals for gyroscopes based on matter-wave interference in toroidally trapped geometries. We show that while the quantum Fisher information increases at different rates for the various schemes considered, in all cases it is consistent with the well-known Sagnac phase shift after the matter waves have traversed a closed path. However, we argue that the relevant metric for quantifying interferometric sensitivity is the classical Fisher information, which can vary considerably between the schemes. PMID:27341216

  15. Heterogeneous mean field for neural networks with short-term plasticity

    NASA Astrophysics Data System (ADS)

    di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro

    2014-08-01

    We report about the main dynamical features of a model of leaky integrate-and-fire excitatory neurons with short-term plasticity defined on random massive networks. We investigate the dynamics by use of a heterogeneous mean-field formulation of the model that is able to reproduce dynamical phases characterized by the presence of quasisynchronous events. This formulation allows one to solve also the inverse problem of reconstructing the in-degree distribution for different network topologies from the knowledge of the global activity field. We study the robustness of this inversion procedure by providing numerical evidence that the in-degree distribution can be recovered also in the presence of noise and disorder in the external currents. Finally, we discuss the validity of the heterogeneous mean-field approach for sparse networks with a sufficiently large average in-degree.

  16. H-mode transitions and limit cycle oscillations from mean field transport equations

    NASA Astrophysics Data System (ADS)

    Staebler, Gary M.; Groebner, R. J.

    2015-01-01

    The mean field toroidal and parallel momentum transport equations will be shown to admit both one-step transitions to suppressed transport (L/H) and limit cycle oscillations (LCO). Both types of transitions are driven by the suppression of turbulence by the mean field ExB velocity shear. Using experimental data to evaluate the coefficients of a reduced transport model, the observed frequency of the LCO can be matched. The increase in the H-mode power threshold above and below a minimum density agrees with the trends in the model. Both leading and lagging phase relations between the turbulent density fluctuation amplitude and the ExB velocity shear can occur depending on the evolution of the linear growth rate of the turbulence. The transport solutions match the initial phase of the L/H transition where the poloidal and ExB velocities are observed to change, and the density fluctuations drop, faster than the diamagnetic velocity.

  17. Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry

    NASA Astrophysics Data System (ADS)

    Haine, Simon A.

    2016-06-01

    There has been considerable recent interest in the mean-field dynamics of various atom-interferometry schemes designed for precision sensing. In the field of quantum metrology, the standard tools for evaluating metrological sensitivity are the classical and quantum Fisher information. In this Letter, we show how these tools can be adapted to evaluate the sensitivity when the behavior is dominated by mean-field dynamics. As an example, we compare the behavior of four recent theoretical proposals for gyroscopes based on matter-wave interference in toroidally trapped geometries. We show that while the quantum Fisher information increases at different rates for the various schemes considered, in all cases it is consistent with the well-known Sagnac phase shift after the matter waves have traversed a closed path. However, we argue that the relevant metric for quantifying interferometric sensitivity is the classical Fisher information, which can vary considerably between the schemes.

  18. Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry.

    PubMed

    Haine, Simon A

    2016-06-10

    There has been considerable recent interest in the mean-field dynamics of various atom-interferometry schemes designed for precision sensing. In the field of quantum metrology, the standard tools for evaluating metrological sensitivity are the classical and quantum Fisher information. In this Letter, we show how these tools can be adapted to evaluate the sensitivity when the behavior is dominated by mean-field dynamics. As an example, we compare the behavior of four recent theoretical proposals for gyroscopes based on matter-wave interference in toroidally trapped geometries. We show that while the quantum Fisher information increases at different rates for the various schemes considered, in all cases it is consistent with the well-known Sagnac phase shift after the matter waves have traversed a closed path. However, we argue that the relevant metric for quantifying interferometric sensitivity is the classical Fisher information, which can vary considerably between the schemes.

  19. Avalanche-size distributions in mean-field plastic yielding models.

    PubMed

    Jagla, E A

    2015-10-01

    We discuss the size distribution N(S) of avalanches occurring at the yielding transition of mean-field (i.e., Hebraud-Lequeux) models of amorphous solids. The size distribution follows a power law dependence of the form N(S)∼S(-τ). However (contrary to what is found in its depinning counterpart), the value of τ depends on details of the dynamic protocol used. For random triggering of avalanches we recover the τ=3/2 exponent typical of mean-field models, which, in particular, is valid for the depinning case. However, for the physically relevant case of external loading through a quasistatic increase of applied strain, a smaller exponent (close to 1) is obtained. This result is rationalized by mapping the problem to an effective random walk in the presence of a moving absorbing boundary. PMID:26565196

  20. Magnetic phase diagram of interacting nanoparticle systems under the mean-field model

    NASA Astrophysics Data System (ADS)

    Mao, Zhongquan; Chen, Xi

    2011-06-01

    The disordered random-anisotropy magnetic nanoparticle systems with competing dipolar interactions and ferromagnetic exchange couplings are investigated by Monte Carlo simulations. Superspin glass (SSG) and superferromagnetic (SFM) behaviors are found at low temperatures depending on the interactions. Based on the mean-field approximation, the Curie-Weiss temperature TCW = 0 is suggested as the phase boundary between the SSG systems and the SFM systems, which is evidenced by the spontaneous magnetizations and relaxations. The magnetic phase diagram is plotted.

  1. Mean-field overcharging of macromolecules via charge or surface modulation

    NASA Astrophysics Data System (ADS)

    Landy, Jonathan

    2010-03-01

    It is well known that multivalent counterions can at times overcharge macromolecules in electrolyte solutions. In this talk, I will discuss a simple mean-field mechanism that can allow for this effect: modulation of source charge and/or surface geometry can induce additional charge condensation sometimes resulting in overcharging. The qualitative features of this mechanism will be related to experimental observations. In addition, an experimental method by which one may be able test for modulation effects will be discussed.

  2. A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

    SciTech Connect

    Hosking, John Joseph Absalom

    2012-12-15

    We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

  3. Synchronization and Spin-Flop Transitions for a Mean-Field XY Model in Random Field

    NASA Astrophysics Data System (ADS)

    Collet, Francesca; Ruszel, Wioletta

    2016-08-01

    We characterize the phase space for the infinite volume limit of a ferromagnetic mean-field XY model in a random field pointing in one direction with two symmetric values. We determine the stationary solutions and detect possible phase transitions in the interaction strength for fixed random field intensity. We show that at low temperature magnetic ordering appears perpendicularly to the field. The latter situation corresponds to a spin-flop transition.

  4. A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics

    NASA Astrophysics Data System (ADS)

    Petrat, Sören; Pickl, Peter

    2016-03-01

    We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151-164 2011) for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence.

  5. TURBULENT CONVECTION IN STELLAR INTERIORS. III. MEAN-FIELD ANALYSIS AND STRATIFICATION EFFECTS

    SciTech Connect

    Viallet, Maxime; Meakin, Casey; Mocak, Miroslav; Arnett, David

    2013-05-20

    We present three-dimensional implicit large eddy simulations of the turbulent convection in the envelope of a 5 M{sub Sun} red giant star and in the oxygen-burning shell of a 23 M{sub Sun} supernova progenitor. The numerical models are analyzed in the framework of one-dimensional Reynolds-Averaged Navier-Stokes equations. The effects of pressure fluctuations are more important in the red giant model, owing to larger stratification of the convective zone. We show how this impacts different terms in the mean-field equations. We clarify the driving sources of kinetic energy, and show that the rate of turbulent dissipation is comparable to the convective luminosity. Although our flows have low Mach numbers and are nearly adiabatic, our analysis is general and can be applied to photospheric convection as well. The robustness of our analysis of turbulent convection is supported by the insensitivity of the mean-field balances to linear mesh resolution. We find robust results for the turbulent convection zone and the stable layers in the oxygen-burning shell model, and robust results everywhere in the red giant model, but the mean fields are not well converged in the narrow boundary regions (which contain steep gradients) in the oxygen-burning shell model. This last result illustrates the importance of unresolved physics at the convective boundary, which governs the mixing there.

  6. Forward approximation as a mean-field approximation for the Anderson and many-body localization transitions

    NASA Astrophysics Data System (ADS)

    Pietracaprina, Francesca; Ros, Valentina; Scardicchio, Antonello

    2016-02-01

    In this paper we analyze the predictions of the forward approximation in some models which exhibit an Anderson (single-body) or many-body localized phase. This approximation, which consists of summing over the amplitudes of only the shortest paths in the locator expansion, is known to overestimate the critical value of the disorder which determines the onset of the localized phase. Nevertheless, the results provided by the approximation become more and more accurate as the local coordination (dimensionality) of the graph, defined by the hopping matrix, is made larger. In this sense, the forward approximation can be regarded as a mean-field theory for the Anderson transition in infinite dimensions. The sum can be efficiently computed using transfer matrix techniques, and the results are compared with the most precise exact diagonalization results available. For the Anderson problem, we find a critical value of the disorder which is 0.9 % off the most precise available numerical value already in 5 spatial dimensions, while for the many-body localized phase of the Heisenberg model with random fields the critical disorder hc=4.0 ±0.3 is strikingly close to the most recent results obtained by exact diagonalization. In both cases we obtain a critical exponent ν =1 . In the Anderson case, the latter does not show dependence on the dimensionality, as it is common within mean-field approximations. We discuss the relevance of the correlations between the shortest paths for both the single- and many-body problems, and comment on the connections of our results with the problem of directed polymers in random medium.

  7. Construction of traveling clusters in the Hamiltonian mean-field model by nonequilibrium statistical mechanics and Bernstein-Greene-Kruskal waves.

    PubMed

    Yamaguchi, Yoshiyuki Y

    2011-07-01

    Traveling clusters are ubiquitously observed in the Hamiltonian mean-field model for a wide class of initial states, which are not predicted to become spatially inhomogeneous states by nonequilibrium statistical mechanics and by nonlinear Landau damping. To predict such a cluster state from a given initial state, we combine nonequilibrium statistical mechanics and a construction method of Bernstein-Greene-Kruskal (BGK) waves with the aid of phenomenological assumptions. The phenomenological theory is partially successful, and the theoretically constructed cluster states are in good agreement with N-body simulations. Robustness of the theory is also discussed for unsuccessful initial states. PMID:21867277

  8. Eliminating the mean-field shift in two-component bose-einstein condensates

    PubMed

    Goldstein; Moore; Pu; Meystre

    2000-12-11

    We demonstrate that the nonlinear mean-field shift in a multicomponent Bose-Einstein condensate may be eliminated by controlling the two-body interaction coefficients. This modification can be achieved by engineering the environment of the condensate. We consider the case of a two-component condensate in a quasi-one-dimensional atomic waveguide, achieving modification of the atom-atom interactions by varying the transverse wave functions of the components. Eliminating the density-dependent phase shift represents a promising potential application for multicomponent condensates in atom interferometry and precision measurements.

  9. The cumulative overlap distribution function in spin glasses: mean field vs. three dimensions

    NASA Astrophysics Data System (ADS)

    Yllanes, David; Billoire, Alain; Maiorano, Andrea; Marinari, Enzo; Martin-Mayor, Victor

    2015-03-01

    We use a sample-dependent analysis, based on medians and quantiles, to analyze the behavior of the overlap probability distribution in spin glasses. Using analytical and numerical mean-field results for the Sherrington-Kirkpatrick model, as well as data from toy models, we show that this approach is an effective tool to distinguish the low-temperature behavior of replica symmmetry breaking systems from that expected in the droplet picture. An application of the method to the three-dimensional Edwards-Anderson models shows agreement with the replica symmetry breaking predictions. Supported by ERC Grant No. 247328 and from MINECO (Spain), Contract No. FIS2012-35719-C02.

  10. Critical temperature for {alpha}-particle condensation within a momentum-projected mean-field approach

    SciTech Connect

    Sogo, T.; Roepke, G.; Lazauskas, R.

    2009-05-15

    {alpha}-particle (quartet) condensation in homogeneous spin-isospin symmetric nuclear matter is investigated. The usual Thouless criterion for the critical temperature is extended to the quartet case. The in-medium four-body problem is strongly simplified by the use of a momentum-projected mean-field ansatz for the quartet. The self-consistent single-particle wave functions are shown and discussed for various values of the density at the critical temperature. Excellent agreement of the critical temperature with a numerical solution of the Faddeev-Yakubovsky equation is obtained.

  11. Mean-field microrheology of a very soft colloidal suspension: Inertia induces shear thickening.

    PubMed

    Démery, Vincent

    2015-06-01

    Colloidal suspensions have a rich rheology and can exhibit shear thinning as well as shear thickening. Numerical simulations recently suggested that shear-thickening may be attributed to the inertia of the colloids, besides the hydrodynamic interactions between them. Here, we consider the ideal limit of a dense bath of soft colloids following an underdamped Langevin dynamics. We use a mean-field equation for the colloidal density to get an analytical expression of the drag force felt by a probe pulled at constant velocity through the suspension. Our results show that inertia can indeed induce shear thickening by allowing density waves to propagate through the suspension.

  12. Study of shape transitions in N{approx}90 isotopes with beyond mean field calculations

    SciTech Connect

    Rodriguez, Tomas R.; Egido, J. L.

    2009-01-28

    We study the spherical to prolate-deformed shape transition in {sup 144-158}Sm and {sup 146-160}Gd isotopes with modern calculations beyond the mean field with the Gogny D1S force. We compare the results with the shape-phase transition predicted by the collective Hamiltonian model and with the experimental data. Our calculations do not support the existence of a first order phase transition in these isotopic chains in the viewpoint of the Bohr Hamiltonian neither the interpretation of the nuclei N = 90 as critical points.

  13. Asymmetric neutrino production in magnetized proto-neutron stars in fully relativistic mean-field approach

    SciTech Connect

    Maruyama, Tomoyuki; Kajino, Toshitaka; Hidaka, Jun; Takiwaki, Tomoya; Yasutake, Nobutoshi; Kuroda, Takami; Cheoun, Myung-Ki; Ryu, Chung-Yeol; Mathews, Grant J.

    2014-05-02

    We calculate the neutrino production cross-section in the proto-neutron-star matter under a strong magnetic field in the relativistic mean-field approach. We introduce a new parameter-set which can reproduce the 1.96 solar mass neutron star. We find that the production process increases emitted neutrinos along the direction parallel to the magnetic field and decrease those along its opposite direction. It means that resultant asymmetry due to the neutrino absorption and scattering process in the magnetic field becomes larger by the addition of the neutrino production process.

  14. The Vlasov-Poisson Dynamics as the Mean Field Limit of Extended Charges

    NASA Astrophysics Data System (ADS)

    Lazarovici, Dustin

    2016-10-01

    The paper treats the validity problem of the nonrelativistic Vlasov-Poisson equation in {d ≥ 2} dimensions. It is shown that the Vlasov-Poisson dynamics can be derived as a combined mean field and point-particle limit of an N-particle Coulomb system of extended charges. This requires a sufficiently fast convergence of the initial empirical distributions. If the electron radius decreases slower than {N^{-{1/d(d+2)}}}, the corresponding initial configurations are typical. This result entails propagation of molecular chaos for the respective dynamics.

  15. Hot and dense hadronic matter in an effective mean-field approach

    SciTech Connect

    Lavagno, A.

    2010-04-15

    We investigate the equation of state of hadronic matter at finite values of baryon density and temperature reachable in high-energy heavy-ion collisions. The analysis is performed by requiring the Gibbs conditions on the global conservation of baryon number, electric charge fraction, and zero net strangeness. We consider an effective relativistic mean-field model with the inclusion of DELTA isobars, hyperons, and the lightest pseudoscalar and vector meson degrees of freedom. In this context, we study the influence of the DELTA-isobar degrees of freedom in the hadronic equation of state and, in connection, the behavior of different particle-antiparticle ratios and strangeness production.

  16. Beyond the relativistic mean-field approximation. III. Collective Hamiltonian in five dimensions

    SciTech Connect

    Niksic, T.; Li, Z. P.; Vretenar, D.; Prochniak, L.; Meng, J.; Ring, P.

    2009-03-15

    The framework of relativistic energy density functionals is extended to include correlations related to the restoration of broken symmetries and fluctuations of collective variables. A new implementation is developed for the solution of the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The model is tested in a series of illustrative calculations of potential energy surfaces and the resulting collective excitation spectra and transition probabilities of the chain of even-even gadolinium isotopes.

  17. Cluster dynamic mean-field study on the superconductivity in doped honeycomb lattice Hubbard model

    NASA Astrophysics Data System (ADS)

    Xu, Xiao Yan; Dang, Hung T.; Wessel, Stefen; Meng, Zi Yang

    The issue of superconductivities emerging from doped honeycomb lattice Mott insulator remains inconclusive. Existing proposals, such as p+ip triplet pairing driven by ferromagnetic fluctuations, d+id singlet pairing driven by antiferromagnetic fluctuations or van Hove singularities in the band structure, are not compatible. This is mainly due to the limitation of various approximated techniques employed in addressing such question with inherent strongly correlated nature. Trying to clarify the situation, we perform large-scale cluster dynamic mean-field simulations to explore the superconductivity instabilities in the doped honeycomb lattice Hubbard model, from medium to strong coupling. To benchmark, we make use of both interaction- and hybridization-expansion continuous time quantum Monte Carlo methods to exactly solve the quantum cluster embedded in self-consistently determined mean-field bath. Temperature dependence of various superconducting susceptibilities are calculated, hence, we provide the least biased results of the competition of the superconductivity in different channels in the phase diagram spanned by doping and electronic interaction.

  18. A mean-field approach to the propagation of field patterns in stratified magnetorotational turbulence

    NASA Astrophysics Data System (ADS)

    Gressel, Oliver

    2010-06-01

    Local shearing box simulations of stratified magnetorotational turbulence invariably exhibit cyclic field patterns which propagate away from the disc mid-plane. A common explanation for this is magnetic buoyancy. The recent analysis by Shi et al. however shows that the flow is buoyantly stable below one disc scaleheight H, necessitating an alternative explanation in this region. We here conduct and analyse direct numerical simulations to explain the observed behaviour by means of a mean-field description. Apart from the mean radial and azimuthal field, we monitor the small-scale current helicity, which we propose as a key indicator for saturation. Reconstructing the horizontally averaged field, we demonstrate that the problem can be reduced to a 1D induction equation. By means of the so-called test field method, we then determine the underlying closure parameters. Our analysis shows that, apart from a possible direct magnetorotational instability (MRI) dynamo, two distinct indirect dynamo mechanisms operate in the disc. This resolves the issue of the `wrong' sign of the MRI dynamo effect. Finally, we use the obtained closure parameters to run a dynamically quenched dynamo model. This model approximately recovers the observed field patterns in the mean fields. Moreover, the model reproduces the prevailing parity and the distinct phase pattern in the small-scale current helicity. The latter property might open a potential route to understand the saturation of MRI induced turbulence.

  19. Finite-size critical scaling in Ising spin glasses in the mean-field regime

    NASA Astrophysics Data System (ADS)

    Aspelmeier, T.; Katzgraber, Helmut G.; Larson, Derek; Moore, M. A.; Wittmann, Matthew; Yeo, Joonhyun

    2016-03-01

    We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.

  20. Modeling and computation of mean field equilibria in producers' game with emission permits trading

    NASA Astrophysics Data System (ADS)

    Zhang, Shuhua; Wang, Xinyu; Shanain, Aleksandr

    2016-08-01

    In this paper, we present a mean field game to model the production behaviors of a very large number of producers, whose carbon emissions are regulated by government. Especially, an emission permits trading scheme is considered in our model, in which each enterprise can trade its own permits flexibly. By means of the mean field equilibrium, we obtain a Hamilton-Jacobi-Bellman (HJB) equation coupled with a Kolmogorov equation, which are satisfied by the adjoint state and the density of producers (agents), respectively. Then, we propose a so-called fitted finite volume method to solve the HJB equation and the Kolmogorov equation. The efficiency and the usefulness of this method are illustrated by the numerical experiments. Under different conditions, the equilibrium states as well as the effects of the emission permits price are examined, which demonstrates that the emission permits trading scheme influences the producers' behaviors, that is, more populations would like to choose a lower rather than a higher emission level when the emission permits are expensive.

  1. Preequilibrium neutron emission in heavy ion reaction: Mean field effect and multiple emission

    NASA Astrophysics Data System (ADS)

    Paul, Sabyasachi; Nandy, Maitreyee; Mohanty, A. K.; Gambhir, Y. K.

    2016-09-01

    Effects of nuclear mean field and of multiple preequilibrium (PEQ) emission on double differential neutron multiplicity distribution from heavy ion reactions (12C+165Ho and 20Ne+165Ho ) at 10-30 MeV/u have been investigated in the framework of the semiclassical formalism for heavy ion reaction (henceforth termed "HION") developed earlier. HION follows the equilibration of a target+projectile composite system through the kinematics of two-body scattering. In the present work nuclear density distribution in the composite system is estimated in the relativistic mean field (RMF) approach. The nucleon-nucleon collision rates and subsequently the nucleon emission probability are calculated from this density distribution. A second approach based on a semiphenomenological formalism is also used for nuclear density distribution. Energy-angle distribution of neutron multiplicities calculated with this modified HION model coupled with multiple PEQ emission could reproduce the measured data of earlier workers in the projectile energy range of 10-30 MeV/u.

  2. Finite-size critical scaling in Ising spin glasses in the mean-field regime.

    PubMed

    Aspelmeier, T; Katzgraber, Helmut G; Larson, Derek; Moore, M A; Wittmann, Matthew; Yeo, Joonhyun

    2016-03-01

    We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent. PMID:27078308

  3. Correcting mean-field approximations for birth-death-movement processes

    NASA Astrophysics Data System (ADS)

    Baker, Ruth E.; Simpson, Matthew J.

    2010-10-01

    On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

  4. Connecting mean field models of neural activity to EEG and fMRI data.

    PubMed

    Bojak, Ingo; Oostendorp, Thom F; Reid, Andrew T; Kötter, Rolf

    2010-06-01

    Progress in functional neuroimaging of the brain increasingly relies on the integration of data from complementary imaging modalities in order to improve spatiotemporal resolution and interpretability. However, the usefulness of merely statistical combinations is limited, since neural signal sources differ between modalities and are related non-trivially. We demonstrate here that a mean field model of brain activity can simultaneously predict EEG and fMRI BOLD with proper signal generation and expression. Simulations are shown using a realistic head model based on structural MRI, which includes both dense short-range background connectivity and long-range specific connectivity between brain regions. The distribution of modeled neural masses is comparable to the spatial resolution of fMRI BOLD, and the temporal resolution of the modeled dynamics, importantly including activity conduction, matches the fastest known EEG phenomena. The creation of a cortical mean field model with anatomically sound geometry, extensive connectivity, and proper signal expression is an important first step towards the model-based integration of multimodal neuroimages.

  5. Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems

    NASA Astrophysics Data System (ADS)

    Jin, Jiasen; Biella, Alberto; Viyuela, Oscar; Mazza, Leonardo; Keeling, Jonathan; Fazio, Rosario; Rossini, Davide

    2016-07-01

    We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1 /2 on a lattice interacting through an X Y Z Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.

  6. Relativistic mean-field study on proton skins and proton halos in exotic nuclei

    NASA Astrophysics Data System (ADS)

    Ren, Zhongzhou; Mittig, W.; Sarazin, F.

    1999-06-01

    We investigate the ground state properties of proton-rich nuclei in the framework of the relativistic mean-field model. Calculations show that the experimental proton halo in the nuclei 26,27,28P can be reproduced by the model. The proton halos can appear in proton-rich nuclei because the total nuclear potential is attractive up to the radial distance r ≈ 5.5 fm. But the size of proton halos is finite due to the limitation of the Coulomb potential barrier. The mean-square radius of a halo proton is not very sensitive to the separation energy of the last proton in some very proton-rich nuclei due to the effect of the Coulomb barrier. This behavior is different from the case of a neutron halo where the mean-square radius of a halo neutron is inversely proportional to the separation energy of the last halo neutron. We have also analysed the differences of the relativistic mean-field potentials of 25Al and 26P and found that the isovector potential from the p meson has an important effect on the differences.

  7. Mean field approximation for biased diffusion on Japanese inter-firm trading network.

    PubMed

    Watanabe, Hayafumi

    2014-01-01

    By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7. PMID:24626149

  8. The application of the Gibbs-Bogoliubov-Feynman inequality in mean field calculations for Markov random fields.

    PubMed

    Zhang, J

    1996-01-01

    The Gibbs-Bogoliubov-Feynman (GBF) inequality of statistical mechanics is adopted, with an information-theoretic interpretation, as a general optimization framework for deriving and examining various mean field approximations for Markov random fields (MRF's). The efficacy of this approach is demonstrated through the compound Gauss-Markov (CGM) model, comparisons between different mean field approximations, and experimental results in image restoration.

  9. A soft, mean-field potential derived from crystal contacts for predicting protein-protein interactions.

    PubMed

    Robert, C H; Janin, J

    1998-11-13

    We derive a series of novel mean-field potentials from statistical analyses of protein-protein contact regions in crystal structures. These potentials are parameterized in terms of the number of contacts made by an atom in an interface region. Such an explicit number dependence avoids the pairwise assumption and is intrinsically softer than distance-based approaches. It appears well suited to protein-protein docking applications, for which detailed interface geometry is generally lacking. In tests including protein complex reconstitution and docking of independently determined protein structures, we show that a hydrophobic potential of this type performs remarkably well, identifying native-like complexes by their favourable potential energies and in several cases demonstrating a recognition energy gap of 4-8 kcal/mol according to the system.

  10. Aspects of the decoherence in high-spin environments: Breakdown of the mean-field approximation

    NASA Astrophysics Data System (ADS)

    Hamdouni, Yamen

    2016-08-01

    The study of the decoherence of qubits in spin systems is almost restricted to environments whose constituents are spin-1/2 particles. In this paper we consider environments that are composed of particles of higher spin, and we investigate the consequences on the dynamics of a qubit coupled to such baths via Heisenberg X Y and Ising interactions. It is shown that, while the short time decay in both cases gets faster as the magnitude of the spin increases, the asymptotic behavior exhibits an improvement of the suppression of the decoherence when the coupling is through Heisenberg X Y interactions. In the case of a transverse Ising model, we find that the mean-field approximation breaks down for high values of the spin.

  11. Mean-field dynamics of spin-orbit coupled Bose-Einstein condensates.

    PubMed

    Zhang, Yongping; Mao, Li; Zhang, Chuanwei

    2012-01-20

    Spin-orbit coupling (SOC), the interaction between the spin and momentum of a quantum particle, is crucial for many important condensed matter phenomena. The recent experimental realization of SOC in neutral bosonic cold atoms provides a new and ideal platform for investigating spin-orbit coupled quantum many-body physics. In this Letter, we derive a generic Gross-Pitaevskii equation as the starting point for the study of many-body dynamics in spin-orbit coupled Bose-Einstein condensates. We show that different laser setups for realizing the same SOC may lead to different mean-field dynamics. Various ground state phases (stripe, phase separation, etc.) of the condensate are found in different parameter regions. A new oscillation period induced by the SOC, similar to the Zitterbewegung oscillation, is found in the center-of-mass motion of the condensate.

  12. Modeling of coherent ultrafast magneto-optical experiments: Light-induced molecular mean-field model

    SciTech Connect

    Hinschberger, Y.; Hervieux, P.-A.

    2015-12-28

    We present calculations which aim to describe coherent ultrafast magneto-optical effects observed in time-resolved pump-probe experiments. Our approach is based on a nonlinear semi-classical Drude-Voigt model and is used to interpret experiments performed on nickel ferromagnetic thin film. Within this framework, a phenomenological light-induced coherent molecular mean-field depending on the polarizations of the pump and probe pulses is proposed whose microscopic origin is related to a spin-orbit coupling involving the electron spins of the material sample and the electric field of the laser pulses. Theoretical predictions are compared to available experimental data. The model successfully reproduces the observed experimental trends and gives meaningful insight into the understanding of magneto-optical rotation behavior in the ultrafast regime. Theoretical predictions for further experimental studies are also proposed.

  13. Angular momentum projection for a Nilsson mean-field plus pairing model

    NASA Astrophysics Data System (ADS)

    Wang, Yin; Pan, Feng; Launey, Kristina D.; Luo, Yan-An; Draayer, J. P.

    2016-06-01

    The angular momentum projection for the axially deformed Nilsson mean-field plus a modified standard pairing (MSP) or the nearest-level pairing (NLP) model is proposed. Both the exact projection, in which all intrinsic states are taken into consideration, and the approximate projection, in which only intrinsic states with K = 0 are taken in the projection, are considered. The analysis shows that the approximate projection with only K = 0 intrinsic states seems reasonable, of which the configuration subspace considered is greatly reduced. As simple examples for the model application, low-lying spectra and electromagnetic properties of 18O and 18Ne are described by using both the exact and approximate angular momentum projection of the MSP or the NLP, while those of 20Ne and 24Mg are described by using the approximate angular momentum projection of the MSP or NLP.

  14. Occupation numbers of spherical orbits in self-consistent beyond-mean-field methods

    NASA Astrophysics Data System (ADS)

    Rodríguez, Tomás R.; Poves, Alfredo; Nowacki, Frédéric

    2016-05-01

    We present a method to compute the number of particles occupying spherical single-particle (SSP) levels within the energy density functional (EDF) framework. These SSP levels are defined for each nucleus by performing self-consistent mean-field calculations. The nuclear many-body states, in which the occupation numbers are evaluated, are obtained with a symmetry conserving configuration mixing (SCCM) method based on the Gogny EDF. The method allows a closer comparison between EDF and shell model with configuration mixing in large valence spaces (SM-CI) results, and can serve as a guidance to define physically sound valence spaces for SM-CI calculations. As a first application of the method, we analyze the onset of deformation in neutron-rich N =40 isotones and the role of the SSP levels around this harmonic oscillator magic number, with particular emphasis in the structure of 64Cr.

  15. Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing

    PubMed Central

    Yoshida, Ryo; West, Mike

    2010-01-01

    We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate “artificial” posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data. PMID:20890391

  16. Onset of synchronization in the disordered Hamiltonian mean-field model

    NASA Astrophysics Data System (ADS)

    Restrepo, Juan G.; Meiss, James D.

    2014-05-01

    We study the Hamiltonian mean field (HMF) model of coupled Hamiltonian rotors with a heterogeneous distribution of moments of inertia and coupling strengths. We show that when the parameters of the rotors are heterogeneous, finite-size fluctuations can greatly modify the coupling strength at which the incoherent state loses stability by inducing correlations between the momenta and parameters of the rotors. When the distribution of initial frequencies of the oscillators is sufficiently narrow, an analytical expression for the modification in critical coupling strength is obtained that confirms numerical simulations. We find that heterogeneity in the moments of inertia tends to stabilize the incoherent state, while heterogeneity in the coupling strengths tends to destabilize the incoherent state. Numerical simulations show that these effects disappear for a wide, bimodal frequency distribution.

  17. Ground state phase transition in the Nilsson mean-field plus standard pairing model

    NASA Astrophysics Data System (ADS)

    Guan, Xin; Xu, Haocheng; Zhang, Yu; Pan, Feng; Draayer, Jerry P.

    2016-08-01

    The ground state phase transition in Nd, Sm, and Gd isotopes is investigated by using the Nilsson mean-field plus standard pairing model based on the exact solutions obtained from the extended Heine-Stieltjes correspondence. The results of the model calculations successfully reproduce the critical phenomena observed experimentally in the odd-even mass differences, odd-even differences of two-neutron separation energy, and the α -decay and double β--decay energies of these isotopes. Since the odd-even effects are the most important signatures of pairing interactions in nuclei, the model calculations yield microscopic insight into the nature of the ground state phase transition manifested by the standard pairing interaction.

  18. Isospin-symmetry-breaking effects in A∼70 nuclei within beyond-mean-field approach

    SciTech Connect

    Petrovici, A.; Andrei, O.

    2015-02-24

    Particular isospin-symmetry-breaking probes including Coulomb energy differences (CED), mirror energy differences (MED), and triplet energy differences (TED) manifest anomalies in the A∼70 isovector triplets of nuclei. The structure of proton-rich nuclei in the A∼70 mass region suggests shape coexistence and competition between pairing correlations in different channels. Recent results concerning the interplay between isospin-mixing and shape-coexistence effects on exotic phenomena in A∼70 nuclei obtained within the beyond-mean-field complex Excited Vampir variational model with symmetry projection before variation using a realistic effective interaction in a relatively large model space are presented. Excited Vampir predictions concerning the Gamow-Teller β decay to the odd-odd N=Z {sup 66}As and {sup 70}Br nuclei correlated with the pair structure analysis in the T=1 and T=0 channel of the involved wave functions are discussed.

  19. Economic dynamics with financial fragility and mean-field interaction: A model

    NASA Astrophysics Data System (ADS)

    Di Guilmi, C.; Gallegati, M.; Landini, S.

    2008-06-01

    Following Aoki’s statistical mechanics methodology [Masanao Aoki, New Approaches to Macroeconomic Modeling, Cambridge University Press, 1996; Masanao Aoki, Modeling Aggregate Behaviour and Fluctuations in Economics, Cambridge University Press, 2002; Masanao Aoki, and Hiroshi Yoshikawa, Reconstructing Macroeconomics, Cambridge University Press, 2006], we provide some insights into the well-known works of [Bruce Greenwald, Joseph Stiglitz, Macroeconomic models with equity and credit rationing, in: R. Hubbard (Ed.), Information, Capital Markets and Investment, Chicago University Press, Chicago, 1990; Bruce Greenwald, Joseph Stiglitz, Financial markets imperfections and business cycles, Quarterly journal of Economics (1993)]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea is to represent the economy as an evolving complex system, composed by heterogeneous interacting agents, that can be partitioned into a space of macroscopic states. This meso level of aggregation permits to adopt mean-field interaction modeling and master equation techniques.

  20. Antikaons in neutron star studied with recent versions of relativistic mean-field models

    NASA Astrophysics Data System (ADS)

    Gupta, Neha; Arumugam, P.

    2013-03-01

    We study the impact of additional couplings in the relativistic mean field (RMF) models, in conjunction with antikaon condensation, on various neutron star properties. We analyze different properties such as in-medium antikaon and nucleon effective masses, antikaon energies, chemical potentials and the mass-radius relations of neutron star (NS). We calculate the NS properties with the RMF (NL3), E-RMF (G1, G2) and FSU2.1 models, which are quite successful in explaining several finite nuclear properties. Our results show that the onset of kaon condensation in NS strongly depends on the parameters of the Lagrangian, especially the additional couplings which play a significant role at higher densities where antikaons dominate the behavior of equation of state.

  1. Dimensional effects in a relativistic mean-field approach. II. Finite temperatures

    SciTech Connect

    Sa Martins, J. S.; Delfino, A.

    2000-04-01

    The Walecka model is studied at finite temperatures in one, two, and three spatial dimensions. The critical temperatures (T{sub c}) and densities ({rho}{sub c}) for the liquid-gas phase transition are calculated in these dimensions. As expected from a mean-field approach, the phase diagram in the T/T{sub c} versus {rho}/{rho}{sub c} plane is dimension independent in the vicinity of the critical point. An interesting finding is that, because the critical and ''flash'' temperatures are proportional, within numerical errors, dimension-independent curves can also be obtained for the incompressibility by scaling with the ''flash'' point coordinates (T{sub f},{rho}{sub f}). At the high-temperature regime, only the two- and three-dimensional systems present a phase transition. (c) 2000 The American Physical Society.

  2. β-decay of magic nuclei: Beyond mean-field description

    SciTech Connect

    Niu, Yifei; Niu, Zhongming; Colò, Gianluca; Vigezzi, Enrico

    2015-10-15

    Nuclear β-decay plays an important role not only in nuclear physics but also in astrophysics. The widely used self-consistent Random Phase Approximation (RPA) models tend to overestimate the half-lives of magic nuclei. To overcome this problem, we go beyond the mean-field description and include the effects of particle-vibration coupling (PVC) on top of the RPA model. The β-decay half-lives of {sup 34}Si, {sup 68}Ni, {sup 78}Ni, and {sup 132}Sn are studied within this approach in the case of the Skyrme interaction SkM*. It is found that the low-lying Gamow-Teller (GT) strength is shifted downwards with the inclusion of the PVC effect, and as a consequence, the half-lives are reduced due to the increase of the phase space available for β-decay, which leads to a good agreement between theoretical and experimental lifetimes.

  3. Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

    NASA Astrophysics Data System (ADS)

    del-Castillo-Negrete, Diego

    We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

  4. Critical wetting of a class of nonequilibrium interfaces: a mean-field picture.

    PubMed

    de Los Santos, Francisco; Romera, Elvira; Al Hammal, Omar; Muñoz, Miguel Angel

    2007-03-01

    A self-consistent mean-field method is used to study critical wetting transitions under nonequilibrium conditions by analyzing Kardar-Parisi-Zhang (KPZ) interfaces in the presence of a bounding substrate. In the case of positive KPZ nonlinearity a single (Gaussian) regime is found. On the contrary, interfaces corresponding to negative nonlinearities lead to three different regimes of critical behavior for the surface order parameter: (i) a trivial Gaussian regime, (ii) a weak-fluctuation regime with a trivially located critical point and nontrivial exponents, and (iii) a highly nontrivial strong-fluctuation regime, for which we provide a full solution by finding the zeros of parabolic-cylinder functions. These analytical results are also verified by solving numerically the self-consistent equation in each case. Analogies with and differences from equilibrium critical wetting as well as nonequilibrium complete wetting are also discussed.

  5. Mean-field approach for the B phase of (La,Ca)MnO{sub 3}

    SciTech Connect

    Schlottmann, P.

    2001-06-01

    I consider a simple cubic lattice of mixed valent Mn ions (Mn{sup 4+} and Mn{sup 3+}) and calculate the ground state energy for the ferromagnetic B phase using a slave-boson mean-field approach. Each Mn ion has three localized t{sub 2g} electrons with their spins ferromagnetically coupled to form a spin S=3/2. Ions in the Mn{sup 3+} configuration have an additional e{sub g} electron to form a total spin of (S+1/2). The e{sub g} electrons are allowed to hop between the Mn sites (giving rise to the double exchange), but the multiple occupancy of the e{sub g} levels is excluded at each site. Five slave bosons per site are introduced to take into account the correlations between the e{sub g} electrons. {copyright} 2001 American Institute of Physics.

  6. Weiss mean-field approximation for multicomponent stochastic spatially extended systems.

    PubMed

    Kurushina, Svetlana E; Maximov, Valerii V; Romanovskii, Yurii M

    2014-08-01

    We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system, which describes a well-known model of autocatalytic chemical reaction (brusselator) with spatially correlated multiplicative noise, and to study the evolution of probability density and statistical characteristics of the system in the process of spatial pattern formation. We propose the finite-difference method for the numerical solving of a general class of multivariate nonlinear self-consistent time-dependent Fokker-Planck equations. We illustrate the accuracy and reliability of the method by applying it to an exactly solvable nonlinear Fokker-Planck equation (NFPE) for the Shimizu-Yamada model [Prog. Theor. Phys. 47, 350 (1972)] and nonlinear Fokker-Planck equation [Desai and Zwanzig, J. Stat. Phys. 19, 1 (1978)] obtained for a nonlinear stochastic mean-field model introduced by Kometani and Shimizu [J. Stat. Phys. 13, 473 (1975)]. Taking the problems indicated above as an example, the accuracy of the method is compared with the accuracy of Hermite distributed approximating functional method [Zhang et al., Phys. Rev. E 56, 1197 (1997)]. Numerical study of the NFPE solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple "repumping" of probability density through bimodality. Additionally, we study the behavior of the order parameter of the system under consideration and show that the second type of solution arises in the supercritical region if noise intensity values are close to the values appropriate for the transition from bimodal stationary probability density for the order parameter to the unimodal one. PMID:25215716

  7. Weiss mean-field approximation for multicomponent stochastic spatially extended systems

    NASA Astrophysics Data System (ADS)

    Kurushina, Svetlana E.; Maximov, Valerii V.; Romanovskii, Yurii M.

    2014-08-01

    We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system, which describes a well-known model of autocatalytic chemical reaction (brusselator) with spatially correlated multiplicative noise, and to study the evolution of probability density and statistical characteristics of the system in the process of spatial pattern formation. We propose the finite-difference method for the numerical solving of a general class of multivariate nonlinear self-consistent time-dependent Fokker-Planck equations. We illustrate the accuracy and reliability of the method by applying it to an exactly solvable nonlinear Fokker-Planck equation (NFPE) for the Shimizu-Yamada model [Prog. Theor. Phys. 47, 350 (1972), 10.1143/PTP.47.350] and nonlinear Fokker-Planck equation [Desai and Zwanzig, J. Stat. Phys. 19, 1 (1978), 10.1007/BF01020331] obtained for a nonlinear stochastic mean-field model introduced by Kometani and Shimizu [J. Stat. Phys. 13, 473 (1975), 10.1007/BF01013146]. Taking the problems indicated above as an example, the accuracy of the method is compared with the accuracy of Hermite distributed approximating functional method [Zhang et al., Phys. Rev. E 56, 1197 (1997), 10.1103/PhysRevE.56.1197]. Numerical study of the NFPE solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple "repumping" of probability density through bimodality. Additionally, we study the behavior of the order parameter of the system under consideration and show that the second type of solution arises in the supercritical region if noise intensity values are close to the values appropriate for the transition from bimodal stationary probability density

  8. Mean-field thalamocortical modeling of longitudinal EEG acquired during intensive meditation training.

    PubMed

    Saggar, Manish; Zanesco, Anthony P; King, Brandon G; Bridwell, David A; MacLean, Katherine A; Aichele, Stephen R; Jacobs, Tonya L; Wallace, B Alan; Saron, Clifford D; Miikkulainen, Risto

    2015-07-01

    Meditation training has been shown to enhance attention and improve emotion regulation. However, the brain processes associated with such training are poorly understood and a computational modeling framework is lacking. Modeling approaches that can realistically simulate neurophysiological data while conforming to basic anatomical and physiological constraints can provide a unique opportunity to generate concrete and testable hypotheses about the mechanisms supporting complex cognitive tasks such as meditation. Here we applied the mean-field computational modeling approach using the scalp-recorded electroencephalogram (EEG) collected at three assessment points from meditating participants during two separate 3-month-long shamatha meditation retreats. We modeled cortical, corticothalamic, and intrathalamic interactions to generate a simulation of EEG signals recorded across the scalp. We also present two novel extensions to the mean-field approach that allow for: (a) non-parametric analysis of changes in model parameter values across all channels and assessments; and (b) examination of variation in modeled thalamic reticular nucleus (TRN) connectivity over the retreat period. After successfully fitting whole-brain EEG data across three assessment points within each retreat, two model parameters were found to replicably change across both meditation retreats. First, after training, we observed an increased temporal delay between modeled cortical and thalamic cells. This increase provides a putative neural mechanism for a previously observed reduction in individual alpha frequency in these same participants. Second, we found decreased inhibitory connection strength between the TRN and secondary relay nuclei (SRN) of the modeled thalamus after training. This reduction in inhibitory strength was found to be associated with increased dynamical stability of the model. Altogether, this paper presents the first computational approach, taking core aspects of physiology and

  9. Effects of anisotropies in turbulent magnetic diffusion in mean-field solar dynamo models

    SciTech Connect

    Pipin, V. V.; Kosovichev, A. G.

    2014-04-10

    We study how anisotropies of turbulent diffusion affect the evolution of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magnetohydrodynamics framework assuming that triple correlations provide relaxation to the turbulent electromotive force (so-called the 'minimal τ-approximation'). We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model and a distributed-dynamo model with a subsurface rotational shear layer. For both models, we investigate effects of the double- and triple-cell meridional circulation, recently suggested by helioseismology and numerical simulations. To characterize the anisotropy effects, we introduce a parameter of anisotropy as a ratio of the radial and horizontal intensities of turbulent mixing. It is found that the anisotropy affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the dynamo period approach to constant values for large values of the anisotropy parameter. The anisotropy reduces the overlap of toroidal magnetic fields generated in subsequent dynamo cycles, in the time-latitude 'butterfly' diagram. If we assume that sunspots are formed in the vicinity of the subsurface shear layer, then the distributed dynamo model with the anisotropic diffusivity satisfies the observational constraints from helioseismology and is consistent with the value of effective turbulent diffusion estimated from the dynamics of surface magnetic fields.

  10. Mean-field analysis of an inductive reasoning game: Application to influenza vaccination

    NASA Astrophysics Data System (ADS)

    Breban, Romulus; Vardavas, Raffaele; Blower, Sally

    2007-09-01

    Recently we have introduced an inductive reasoning game of voluntary yearly vaccination to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. Here, we analyze our model to describe the dynamics of the collective yearly vaccination uptake. We discuss the mean-field equations of our model and first order effects of fluctuations. We explain why our model predicts that severe epidemics are periodically expected even without the introduction of pandemic strains. We find that fluctuations in the collective yearly vaccination uptake induce severe epidemics with an expected periodicity that depends on the number of independent decision makers in the population. The mean-field dynamics also reveal that there are conditions for which the dynamics become robust to the fluctuations. However, the transition between fluctuation-sensitive and fluctuation-robust dynamics occurs for biologically implausible parameters. We also analyze our model when incentive-based vaccination programs are offered. When a family-based incentive is offered, the expected periodicity of severe epidemics is increased. This results from the fact that the number of independent decision makers is reduced, increasing the effect of the fluctuations. However, incentives based on the number of years of prepayment of vaccination may yield fluctuation-robust dynamics where severe epidemics are prevented. In this case, depending on prepayment, the transition between fluctuation-sensitive and fluctuation-robust dynamics may occur for biologically plausible parameters. Our analysis provides a practical method for identifying how many years of free vaccination should be provided in order to successfully ameliorate influenza epidemics.

  11. A multiscale variational approach to the kinetics of viscous classical liquids: The coarse-grained mean field approximation

    SciTech Connect

    Sereda, Yuriy V.; Ortoleva, Peter J.

    2014-04-07

    A closed kinetic equation for the single-particle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarse-grained mean-field (CGMF) ansatz. The CGMF ansatz is based on the notion that during the characteristic time of deformation a given particle interacts with many others so that it experiences an average interaction. A trial function for the N-particle probability density is constructed using a multiscale perturbation method and the CGMF ansatz is applied to it. The multiscale perturbation scheme is based on the ratio of the average nearest-neighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is mass-conserving and closed in the single-particle density. The kinetic equation has much of the character of the Vlasov equation except that true viscous, and not Landau, damping is accounted for. The theory captures condensation kinetics and takes much of the character of the Gross-Pitaevskii equation in the weak-gradient short-range force limit.

  12. Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion.

    PubMed

    Banerjee, Tanmoy; Biswas, Debabrata

    2013-12-01

    We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.

  13. Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion

    NASA Astrophysics Data System (ADS)

    Banerjee, Tanmoy; Biswas, Debabrata

    2013-12-01

    We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.

  14. Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies.

    PubMed

    Kamala Latha, B; Jose, Regina; Murthy, K P N; Sastry, V S S

    2015-07-01

    Investigations of the phase diagram of biaxial liquid-crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed toward an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realizing such a system unambiguously, despite encouraging predictions from MFT, for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free-energy dependences on relevant observables as the system is driven through the transitions. The recent paper from this group [Kamala Latha et al., Phys. Rev. E 89, 050501(R) (2014)], summarizing the outcome of detailed Monte Carlo simulations carried out employing an entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven toward the so-called partly repulsive regions. It was argued that the degree of (cross) coupling between the uniaxial and biaxial tensor components of neighboring molecules plays a crucial role in facilitating a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidence from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions.

  15. Biopolymers under large external forces and mean-field RNA virus evolutionary dynamics

    NASA Astrophysics Data System (ADS)

    Ahsan, Syed Amir

    The modeling of the mechanical response of single-molecules of DNA and RNA under large external forces through statistical mechanical methods is central to this thesis with a small portion devoted to modeling the evolutionary dynamics of positive-sense single-stranded RNA viruses. In order to develop and test models of biopolymer mechanics and illuminate the mechanisms underlying biological processes where biopolymers undergo changes in energy on the order of the thermal energy, , entails measuring forces and lengths on the scale of piconewtons (pN) and nanometers (nm), respectively. A capacity achieved in the past two decades at the single-molecule level through the development of micromanipulation techniques such as magnetic and optical tweezers, atomic force microscopy, coupled with advances in micro- and nanofabrication. The statistical mechanical models of biopolymers developed in this dissertation are dependent upon and the outcome of these advancements and resulting experiments. The dissertation begins in chapter 1 with an introduction to the structure and thermodynamics of DNA and RNA, highlighting the importance and effectiveness of simple, two-state models in their description as a prelude to the emergence of two-state models in the research manuscripts. In chapter 2 the standard models of the elasticity of polymers and of a polymer gel are reviewed, characterizing the continuum and mean-field models, including the scaling behavior of DNA in confined spaces. The research manuscript presented in the last section of chapter 2 (section 2.5), subsequent to a review of a Flory gel and in contrast to it, is a model of the elasticity of RNA as a gel, with viral RNA illustrating an instance of such a network, and shown to exhibit anomalous elastic behavior, a negative Poisson ratio, and capable of facilitating viral RNA encapsidation with further context provided in section 5.1. In chapter 3 the experimental methods and behavior of DNA and RNA under mechanical

  16. Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field

    NASA Astrophysics Data System (ADS)

    Brandenburg, A.; Gressel, O.; Jabbari, S.; Kleeorin, N.; Rogachevskii, I.

    2014-02-01

    Context. Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a large-scale negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding growth rate, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached, resulting in magnetic spots that are reminiscent of sunspots. Aims: We determine under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. Methods: We use a combination of MFS, DNS, and implicit large-eddy simulations (ILES) to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. Results: Using DNS, we confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using ILES, we find that magnetic flux concentrations occur for Mach numbers between 0.1 and 0.7. They occur also for weaker stratification and larger turbulent eddies if the domain is wide enough. Using MFS, the size and aspect ratio of magnetic structures are determined as functions of two input parameters characterizing the parameterization of the effective magnetic pressure. DNS, ILES, and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. These tubes can reach a length of about

  17. Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches.

    PubMed

    Moosavi, S Amin; Montakhab, Afshin

    2015-01-01

    Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches.

  18. Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches

    NASA Astrophysics Data System (ADS)

    Moosavi, S. Amin; Montakhab, Afshin

    2015-11-01

    Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014), 10.1103/PhysRevE.89.052139] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches.

  19. Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches.

    PubMed

    Moosavi, S Amin; Montakhab, Afshin

    2015-01-01

    Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches. PMID:26651741

  20. Nuclear mean field and double-folding model of the nucleus-nucleus optical potential

    NASA Astrophysics Data System (ADS)

    Khoa, Dao T.; Phuc, Nguyen Hoang; Loan, Doan Thi; Loc, Bui Minh

    2016-09-01

    Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on a local density approximation, the double-folding model of the nucleus-nucleus optical potential has been extended to take into account consistently the rearrangement effect and energy dependence of the nuclear mean-field potential, using the modified CDM3Yn interactions. The extended double-folding model was applied to study the elastic 12C+12C and 16O+12C scattering at the refractive energies, where the Airy structure of the nuclear rainbow has been well established. The RT was found to affect significantly the real nucleus-nucleus optical potential at small internuclear distances, giving a potential strength close to that implied by the realistic optical model description of the Airy oscillation.

  1. Monte Carlo Mean Field Treatment of Microbunching Instability in the FERMI@Elettra First Bunch Compressor

    SciTech Connect

    Bassi, G.; Ellison, J.A.; Heinemann, K.; Warnock, R.; /SLAC

    2009-05-07

    Bunch compressors, designed to increase the peak current, can lead to a microbunching instability with detrimental effects on the beam quality. This is a major concern for free electron lasers (FELs) where very bright electron beams are required, i.e. beams with low emittance and energy spread. In this paper, we apply our self-consistent, parallel solver to study the microbunching instability in the first bunch compressor system of FERMI{at}Elettra. Our basic model is a 2D Vlasov-Maxwell system. We treat the beam evolution through a bunch compressor using our Monte Carlo mean field approximation. We randomly generate N points from an initial phase space density. We then calculate the charge density using a smooth density estimation procedure, from statistics, based on Fourier series. The electric and magnetic fields are calculated from the smooth charge/current density using a novel field formula that avoids singularities by using the retarded time as a variable of integration. The points are then moved forward in small time steps using the beam frame equations of motion, with the fields frozen during a time step, and a new charge density is determined using our density estimation procedure. We try to choose N large enough so that the charge density is a good approximation to the density that would be obtained from solving the 2D Vlasov-Maxwell system exactly. We call this method the Monte Carlo Particle (MCP) method.

  2. Critical behavior of a tumor growth model: Directed percolation with a mean-field flavor

    NASA Astrophysics Data System (ADS)

    Lipowski, Adam; Ferreira, António Luis; Wendykier, Jacek

    2012-10-01

    We examine the critical behavior of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report [Ferreira , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.010901 85, 010901(R) (2012)], which suggested that the critical behavior of the model differs from the expected directed percolation (DP) universality class. Surprisingly, only some of the critical exponents (β, α, ν⊥, and z) take non-DP values while some others (β', ν||, and spreading-dynamics exponents Θ, δ, z') remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations β=αν||, β'=δν||, and the generalized hyperscaling relation Θ+α+δ=d/z, where the dynamical exponent z is, however, used instead of the spreading exponent z'. Both in d=1 and d=2 versions of our model, the exponent β most likely takes the mean-field value β=1, and we speculate that it might be due to the roulette-wheel selection, which is used to choose the site to supply a nutrient.

  3. Generalized mean-field description of entanglement in dimerized spin systems

    NASA Astrophysics Data System (ADS)

    Boette, A.; Rossignoli, R.; Canosa, N.; Matera, J. M.

    2015-02-01

    We discuss a generalized self-consistent mean-field (MF) treatment, based on the selection of an arbitrary subset of operators for representing the system density matrix, and its application to the problem of entanglement evaluation in composite quantum systems. As a specific example, we examine in detail a pair MF approach to the ground state (GS) of dimerized spin-1 /2 systems with anisotropic ferromagnetic-type X Y and X Y Z couplings in a transverse field, including chains and arrays with first neighbor and also longer range couplings. The approach is fully analytic and able to capture the main features of the GS of these systems, in contrast with the conventional single-spin MF. Its phase diagram differs significantly from that of the latter, exhibiting (Sz) parity breaking just in a finite field window if the coupling between pairs is sufficiently weak, together with a fully dimerized phase below this window and a partially aligned phase above it. It is then shown that through symmetry restoration, the approach is able to correctly predict not only the concurrence of a pair, but also its entanglement with the rest of the chain, which shows a pronounced peak in the parity breaking window. Perturbative corrections allow to reproduce more subtle observables like the entanglement between weakly coupled spins and the low lying energy spectrum. All predictions are tested against exact results for finite systems.

  4. Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

    NASA Astrophysics Data System (ADS)

    Yasuhiko Igarashi,; Masafumi Oizumi,; Masato Okada,

    2010-08-01

    We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing-state variable and a synaptic variable. In these equations, the average product of thesevariables is decoupled as the product of their averages because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight Jij is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady-state equations for a network with uniform connections and for a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady-state solutions. An oscillatory uniform state was observed in the network with uniform connections owing to a Hopf instability. For the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading to two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previously unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.

  5. Cluster mean-field signature of entanglement entropy in bosonic superfluid-insulator transitions

    NASA Astrophysics Data System (ADS)

    Zhang, Li; Qin, Xizhou; Ke, Yongguan; Lee, Chaohong

    2016-08-01

    Entanglement entropy (EE), a fundamental concept in quantum information for characterizing entanglement, has been extensively employed to explore quantum phase transitions (QPTs). Although the conventional single-site mean-field (MF) approach successfully predicts the emergence of QPTs, it fails to include any entanglement. Here, in the framework of a cluster MF treatment, we extract the signature of EE in bosonic superfluid-insulator (SI) transitions. We consider a trimerized Kagomé lattice of interacting bosons, in which each trimer is treated as a cluster, and implement the cluster MF treatment by decoupling all intertrimer hopping. In addition to superfluid and integer insulator phases, we find that fractional insulator phases appear when the tunneling is dominated by the intratrimer part. To quantify the residual bipartite entanglement in a cluster, we calculate the second-order Rényi entropy, which can be experimentally measured by quantum interference of many-body twins. The second-order Rényi entropy itself is continuous everywhere, however, the continuousness of its first-order derivative breaks down at the phase boundary. This means that the bosonic SI transitions can still be efficiently captured by the residual entanglement in our cluster MF treatment. Besides to the bosonic SI transitions, our cluster MF treatment may also be used to capture the signature of EE for other QPTs in quantum superlattice models.

  6. Mean-field simulation of metal oxide antiferromagnetic films and multilayers

    NASA Astrophysics Data System (ADS)

    Charilaou, M.; Hellman, F.

    2013-05-01

    In this work the magnetization in antiferromagnetic thin films and multilayers with interlayer exchange coupling is simulated using mean-field approximation. Transition-metal oxide antiferromagnets are modeled as multiplane magnetic systems with 1 to 11 planes and the magnetization M is calculated as a function of temperature T. The antiferromagnetic films exhibit ferromagnetism when the number of monolayers is odd, i.e., when there is an uncompensated plane, but the net magnetization is lower than that of any single uncompensated plane due to cancellations and finite-size effects. With increasing film thickness the Néel temperature increases monotonically and the magnetic moment near the surface is reduced compared to that of the core, changing the form of the M(T) curve. When antiferromagnetic films are exchange coupled to each other, as in a multilayer with a nonmagnetic intervening layer, the surface magnetization of each film increases and the ferromagnetism of odd-numbered systems is enhanced. These results are shown to be experimentally testable by comparing magnetometry and neutron diffraction.

  7. Stable nonequilibrium probability densities and phase transitions for mean-field models in the thermodynamic limit

    SciTech Connect

    Bonilla, L.L.

    1987-02-01

    A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of a infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as nonequilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Gruener-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered.

  8. Self-consistent mean-field model for palmitoyloleoylphosphatidylcholine-palmitoyl sphingomyelin–cholesterol lipid bilayers

    PubMed Central

    Tumaneng, Paul W.; Pandit, Sagar A.; Zhao, Guijun; Scott, H. L.

    2012-01-01

    The connection between membrane inhomogeneity and the structural basis of lipid rafts has sparked interest in the lateral organization of model lipid bilayers of two and three components. In an effort to investigate anisotropic lipid distribution in mixed bilayers, a self-consistent mean-field theoretical model is applied to palmitoyloleoylphosphatidylcholine (POPC)–palmitoyl sphingomyelin (PSM)–cholesterol mixtures. The compositional dependence of lateral organization in these mixtures is mapped onto a ternary plot. The model utilizes molecular dynamics simulations to estimate interaction parameters and to construct chain conformation libraries. We find that at some concentration ratios the bilayers separate spatially into regions of higher and lower chain order coinciding with areas enriched with PSM and POPC, respectively. To examine the effect of the asymmetric chain structure of POPC on bilayer lateral inhomogeneity, we consider POPC-lipid interactions with and without angular dependence. Results are compared with experimental data and with results from a similar model for mixtures of dioleoylphosphatidylcholine, steroyl sphingomyelin, and cholesterol. PMID:21517541

  9. Correlations between bulk parameters in relativistic and nonrelativistic hadronic mean-field models

    NASA Astrophysics Data System (ADS)

    Santos, B. M.; Dutra, M.; Lourenço, O.; Delfino, A.

    2015-07-01

    In this work, we study the arising of correlations among some isoscalar (Ko, Qo, and Io) and isovector (J , Lo, Ksymo, Qsymo, and Isymo) bulk parameters in nonrelativistic and relativistic hadronic mean-field models. For the former, we investigate correlations in Skyrme and Gogny parametrizations, as well as in the nonrelativistic (NR) limit of relativistic point-coupling models. We provide analytical correlations among bulk parameters for the NR limit, discussing the conditions in which they are linear ones. Based on a recent study [Santos et al., Phys. Rev. C 90, 035203 (2014), 10.1103/PhysRevC.90.035203], we also show that some correlations presented in the NR limit are reproduced for relativistic models presenting cubic and quartic self-interactions in the scalar field σ , mostly studied in this work in the context of the relativistic framework. We also discuss how the crossing points, observed in the density dependence of some bulk parameters, can be seen as a signature of linear correlations between the specific bulk quantity presenting the crossing and its immediately next order parameter.

  10. Constraining mean-field models of the nuclear matter equation of state at low densities

    NASA Astrophysics Data System (ADS)

    Voskresenskaya, M. D.; Typel, S.

    2012-08-01

    An extension of the generalized relativistic mean-field (gRMF) model with density dependent couplings is introduced in order to describe thermodynamical properties and the composition of dense nuclear matter for astrophysical applications. Bound states of light nuclei and two-nucleon scattering correlations are considered as explicit degrees of freedom in the thermodynamical potential. They are represented by quasiparticles with medium-dependent properties. The model describes the correct low-density limit given by the virial equation of state (VEoS) and reproduces RMF results around nuclear saturation density where clusters are dissolved. A comparison between the fugacity expansions of the VEoS and the gRMF model provides consistency relations between the quasiparticles properties, the nucleon-nucleon scattering phase shifts and the meson-nucleon couplings of the gRMF model at zero density. Relativistic effects are found to be important at temperatures that are typical in astrophysical applications. Neutron matter and symmetric nuclear matter are studied in detail.

  11. Impacts of Parameters Adjustment of Relativistic Mean Field Model on Neutron Star Properties

    NASA Astrophysics Data System (ADS)

    Kasmudin; Sulaksono, A.

    Analysis of the parameters adjustment effects in isovector as well as in isoscalar sectors of effective field based relativistic mean field (E-RMF) model in the symmetric nuclear matter and neutron-rich matter properties has been performed. The impacts of the adjustment on slowly rotating neutron star are systematically investigated. It is found that the mass-radius relation obtained from adjusted parameter set G2** is compatible not only with neutron stars masses from 4U 0614+09 and 4U 1636-536, but also with the ones from thermal radiation measurement in RX J1856 and with the radius range of canonical neutron star of X7 in 47 Tuc, respectively. It is also found that the moment inertia of PSR J073-3039A and the strain amplitude of gravitational wave at the Earth's vicinity of PSR J0437-4715 as predicted by the E-RMF parameter sets used are in reasonable agreement with the extracted constraints of these observations from isospin diffusion data.

  12. Mass predictions of the relativistic mean-field model with the radial basis function approach

    NASA Astrophysics Data System (ADS)

    Zheng, J. S.; Wang, N. Y.; Wang, Z. Y.; Niu, Z. M.; Niu, Y. F.; Sun, B.

    2014-07-01

    The radial basis function (RBF) is a powerful tool to improve mass predictions of nuclear models. By combining the RBF approach with the relativistic mean-field (RMF) model, the systematic deviations between mass predictions of the RMF model and the experimental data are eliminated to a large extent and the resulting rms deviation is reduced from 2.217 to 0.488 MeV. Furthermore, it is found that the RBF approach has a relatively reliable extrapolative power along the distance from the β-stability line except for a large uncertainty around the region at magic number. From the deduced neutron separation energies, we found that the description of the nuclear shell structure and shape transition is also significantly improved by the RBF approach, thus improving agreement with the solar r-process abundances before A =130 and speeding up the r-matter flow. Therefore, a shorter irradiation time is enough to reproduce the solar r-process abundance distribution for the improved RMF mass model, which is closer to the irradiation time for those sophisticated mass models.

  13. A mean field description of the kinetics of precipitate free zone formation

    SciTech Connect

    Hoyt, J.J.

    1997-12-15

    A precipitate free zone (PFZ) refers to the dissolution of second phase particles in the vicinity of a grain boundary, interphase boundary or free surface due to the local depletion of solute concentration. Since the early work of Thomas and Nutting, it is well known that the presence of PFZ`s can have an adverse effect on the mechanical behavior, fracture resistance and stress corrosion cracking resistance of several Al-based alloys. The purpose of the present work is to describe the diffusion process valid for PFZ growth in a more rigorous fashion by treating the precipitates as point sources for solute. A Greens function solution to the diffusion equation together with a mean field description of the precipitate spatial distribution leads to an expression for the dissolution rate of the particles and in turn predicts a kinetic expression for the PFZ growth rate. It will be shown that the growth rate constant derived from the model agrees well with previously published experimental measurements from the Al-Li and the Al-Zn systems.

  14. Cranking in Isospace --- Towards a Consistent Mean-Field Description of N=Z Nuclei

    NASA Astrophysics Data System (ADS)

    Satula, Wojciech; Wyss, Ramon A.

    2001-09-01

    Excitation spectra {Δ } ET of T=0,1,2 states in even-even (e-e) and odd-odd (o-o) N=Z nuclei are analyzed within a mean-field based model involving isovector and isoscalar pairing interactions and the iso-cranking formalism applied to restore approximately isospin symmetry. It is shown that T=0 states in o-o and T=1 states in e-e nuclei correspond to two-quasiparticle, time-reversal symmetry breaking excitations since their angular momenta are Inot =0. On the other hand the lowest T=2 states in e-e and T=1 states in o-o nuclei, which both are similar in structure to their even-even isobaric analogue states, are described as e-e type vacua excited (iso-cranked) in isospace. It appears that in all cases isoscalar pairing plays a crucial role in restoring the proper value of the inertia parameter in isospace i.e. {Δ } ET.

  15. Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy*

    NASA Astrophysics Data System (ADS)

    Kechedzhi, Kostyantyn; Smelyanskiy, Vadim N.

    2016-04-01

    Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p -spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.

  16. Self-consistent mean-field model for palmitoyloleoylphosphatidylcholine-palmitoyl sphingomyelin-cholesterol lipid bilayers

    NASA Astrophysics Data System (ADS)

    Tumaneng, Paul W.; Pandit, Sagar A.; Zhao, Guijun; Scott, H. L.

    2011-03-01

    The connection between membrane inhomogeneity and the structural basis of lipid rafts has sparked interest in the lateral organization of model lipid bilayers of two and three components. In an effort to investigate anisotropic lipid distribution in mixed bilayers, a self-consistent mean-field theoretical model is applied to palmitoyloleoylphosphatidylcholine (POPC)-palmitoyl sphingomyelin (PSM)-cholesterol mixtures. The compositional dependence of lateral organization in these mixtures is mapped onto a ternary plot. The model utilizes molecular dynamics simulations to estimate interaction parameters and to construct chain conformation libraries. We find that at some concentration ratios the bilayers separate spatially into regions of higher and lower chain order coinciding with areas enriched with PSM and POPC, respectively. To examine the effect of the asymmetric chain structure of POPC on bilayer lateral inhomogeneity, we consider POPC-lipid interactions with and without angular dependence. Results are compared with experimental data and with results from a similar model for mixtures of dioleoylphosphatidylcholine, steroyl sphingomyelin, and cholesterol.

  17. A mean-field study of the Hubbard model on the kagome lattice

    NASA Astrophysics Data System (ADS)

    Enjalran, Matthew

    The experimental work on the herbertsmithite compound, ZnCu3(OH)6Cl2, almost a decade ago ignited intense interest in the field of frustrated magnetism because it represented the best material realization of a spin- 1 / 2 Heisenberg antiferromagnet (AFM) on the kagome lattice and its ground state was a gapless spin liquid. Many theoretical and numerical studies of the quantum Heisenberg AFM on the kagome lattice have been performed since and have coalesced around the general consensus of a small gapped spin liquid ground state for the model. Although there is not currently a metallic kagome material system, the work on ZnCu3(OH)6Cl2 has motivated theoretical and numerical investigations of itinerant electrons on the kagome lattice. We contribute to this pursuit by studying the single band Hubbard model on the kagome lattice, where the frustration can be tuned by adjusting the hopping along different bonds, t1 and t2; however, we are mainly interested in the isotropic limit, t1 =t2 = t . We report preliminary results on the low temperature correlations in the half filled model as a function of frustration and interaction strength in the mean-field, Hartree-Fock, limit. CSU Research Grant.

  18. Correlation patterns of NIKKEI index constituents. Towards a mean-field model

    NASA Astrophysics Data System (ADS)

    Hayashi, Katsuhiko; Kaizoji, Taisei; Pichl, Lukáš

    2007-09-01

    An analysis of minute-tick data from the Japanese stock index market is reported for a three-year period of 2000/7/4-2003/6/30. Correlation patterns and principal component distributions were determined for 180 constituents of the NIKKEI 225 index, excluding the effects of after-hours trading and constituent revisions. The first principal component describes about 30% of the total variance in constituent log returns (subject to slow decrease with the size of the correlation window), suggesting that a small number of physical parameters may describe the internal dynamics of the index, allowing for an adiabatic representation of index dynamics, and a self-consistent mean-field model of its constituents. Finally, it is shown that the introduction of a time gap into minute-tick data significantly improves the correlations of the price-weighed index with its constituents, even when such gap inserts are strictly penalized. This phenomenon corresponds to a heterogenous response time of index constituents to the adiabatic collective motion and also demonstrates the inhomogeneous nature of equidistant time ticks in financial trading.

  19. Asymmetric nuclear matter and neutron skin in an extended relativistic mean-field model

    SciTech Connect

    Agrawal, B. K.

    2010-03-15

    The density dependence of the symmetry energy, instrumental in understanding the behavior of the asymmetric nuclear matter, is investigated within the extended relativistic mean-field (ERMF) model, which includes the contributions from the self- and mixed-interaction terms for the scalar-isoscalar ({sigma}), vector-isoscalar ({omega}), and vector-isovector ({rho}) mesons up to the quartic order. Each of the 26 different parametrizations of the ERMF model employed is compatible with the bulk properties of the finite nuclei. The behavior of the symmetry energy for several parameter sets is found to be consistent with the empirical constraints on them as extracted from the analyses of the isospin diffusion data. The neutron-skin thickness in the {sup 208}Pb nucleus for these parameter sets of the ERMF model lies in the range of {approx}0.20-0.24 fm, which is in harmony with the thickness predicted by the Skyrme Hartree-Fock model. We also investigate the role of various mixed-interaction terms that are crucial for the density dependence of the symmetry energy.

  20. Hamiltonian mean field model: Effect of network structure on synchronization dynamics

    NASA Astrophysics Data System (ADS)

    Virkar, Yogesh S.; Restrepo, Juan G.; Meiss, James D.

    2015-11-01

    The Hamiltonian mean field model of coupled inertial Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony begins when the coupling constant K is inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors. When K is just beyond the transition to synchronization, we find that the degree of synchronization is highly dependent on the network's heterogeneity, but that for large K the degree of synchronization is robust to changes in the degree distribution. Our results are illustrated with numerical simulations on Erdös-Renyi networks and networks with power-law degree distributions.

  1. Competing orders in a dipolar Bose-Fermi mixture on a square optical lattice: mean-field perspective

    NASA Astrophysics Data System (ADS)

    Scaramazza, Jasen A.; Kain, Ben; Ling, Hong Y.

    2016-07-01

    We consider a mixture of a two-component Fermi gas and a single-component dipolar Bose gas in a square optical lattice and reduce it into an effective Fermi system where the Fermi-Fermi interaction includes the attractive interaction induced by the phonons of a uniform dipolar Bose-Einstein condensate. Focusing on this effective Fermi system in the parameter regime that preserves the symmetry of D4, the point group of a square, we explore, within the Hartree-Fock-Bogoliubov mean-field theory, the phase competition among density wave orderings and superfluid pairings. We construct the matrix representation of the linearized gap equation in the irreducible representations of D4. We show that in the weak coupling regime, each matrix element, which is a four-dimensional (4D) integral in momentum space, can be put in a separable form involving a 1D integral, which is only a function of temperature and the chemical potential, and a pairing-specific "effective" interaction, which is an analytical function of the parameters that characterize the Fermi-Fermi interactions in our system. We analyze the critical temperatures of various competing orders as functions of different system parameters in both the absence and presence of the dipolar interaction. We find that close to half filling, the dx2 - y2-wave pairing with a critical temperature in the order of a fraction of Fermi energy (at half filling) may dominate all other phases, and at a higher filling factor, the p-wave pairing with a critical temperature in the order of a hundredth of Fermi energy may emerge as a winner. We find that tuning a dipolar interaction can dramatically enhance the pairings with dxy- and g-wave symmetries but not enough for them to dominate other competing phases.

  2. Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies

    NASA Astrophysics Data System (ADS)

    Kamala Latha, B.; Jose, Regina; Murthy, K. P. N.; Sastry, V. S. S.

    2015-07-01

    Investigations of the phase diagram of biaxial liquid-crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed toward an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realizing such a system unambiguously, despite encouraging predictions from MFT, for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free-energy dependences on relevant observables as the system is driven through the transitions. The recent paper from this group [Kamala Latha et al., Phys. Rev. E 89, 050501(R) (2014), 10.1103/PhysRevE.89.050501], summarizing the outcome of detailed Monte Carlo simulations carried out employing an entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven toward the so-called partly repulsive regions. It was argued that the degree of (cross) coupling between the uniaxial and biaxial tensor components of neighboring molecules plays a crucial role in facilitating a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidence from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions.

  3. Double Dynamo Signatures in a Global MHD Simulation and Mean-field Dynamos

    NASA Astrophysics Data System (ADS)

    Beaudoin, Patrice; Simard, Corinne; Cossette, Jean-François; Charbonneau, Paul

    2016-08-01

    The 11 year solar activity cycle is the most prominent periodic manifestation of the magnetohydrodynamical (MHD) large-scale dynamo operating in the solar interior, yet longer and shorter (quasi-) periodicities are also present. The so-called “quasi-biennial” signal appearing in many proxies of solar activity has been gaining increasing attention since its detection in p-mode frequency shifts, which suggests a subphotospheric origin. A number of candidate mechanisms have been proposed, including beating between co-existing global dynamo modes, dual dynamos operating in spatially separated regions of the solar interior, and Rossby waves driving short-period oscillations in the large-scale solar magnetic field produced by the 11 year activity cycle. In this article, we analyze a global MHD simulation of solar convection producing regular large-scale magnetic cycles, and detect and characterize shorter periodicities developing therein. By constructing kinematic mean-field α 2Ω dynamo models incorporating the turbulent electromotive force (emf) extracted from that same simulation, we find that dual-dynamo behavior materializes in fairly wide regions of the model’s parameters space. This suggests that the origin of the similar behavior detected in the MHD simulation lies with the joint complexity of the turbulent emf and differential rotation profile, rather that with dynamical interactions such as those mediated by Rossby waves. Analysis of the simulation also reveals that the dual dynamo operating therein leaves a double-period signature in the temperature field, consistent with a dual-period helioseismic signature. Order-of-magnitude estimates for the magnitude of the expected frequency shifts are commensurate with helioseismic measurements. Taken together, our results support the hypothesis that the solar quasi-biennial oscillations are associated with a secondary dynamo process operating in the outer reaches of the solar convection zone.

  4. Relativistic mean field model for entrainment in general relativistic superfluid neutron stars

    NASA Astrophysics Data System (ADS)

    Comer, G. L.; Joynt, R.

    2003-07-01

    General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic σ-ω mean field model for the nucleons and their interactions. In this context there are two notions of “relativistic”: relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro’s number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons.

  5. Second relativistic mean field and virial equation of state for astrophysical simulations

    SciTech Connect

    Shen, G.; Horowitz, C. J.; O'Connor, E.

    2011-06-15

    We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the virial expansion of a nonideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100 000 grid points in the temperature range T=0 to 80 MeV, the density range n{sub B}=10{sup -8} to 1.6 fm{sup -3}, and the proton fraction range Y{sub p}=0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3-based EOS, and previous EOSs by Lattimer-Swesty and H. Shen et al. for the thermodynamic properties, composition, and neutron star structure. The original FSUGold interaction produces an EOS, which we call FSU1.7, that has a maximum neutron star mass of 1.7 solar masses. A modification in the high-density EOS is introduced to increase the maximum neutron star mass to 2.1 solar masses and results in a slightly different EOS that we call FSU2.1. The EOS tables for FSU1.7 and FSU2.1 are available for download.

  6. EFFECTS OF LARGE-SCALE NON-AXISYMMETRIC PERTURBATIONS IN THE MEAN-FIELD SOLAR DYNAMO

    SciTech Connect

    Pipin, V. V.; Kosovichev, A. G.

    2015-11-10

    We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R{sub ⊙} has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number R{sub m}. In the range of R{sub m} = 10{sup 4}–10{sup 6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.

  7. Mean-field modeling of the basal ganglia-thalamocortical system. II Dynamics of parkinsonian oscillations.

    PubMed

    van Albada, S J; Gray, R T; Drysdale, P M; Robinson, P A

    2009-04-21

    Neuronal correlates of Parkinson's disease (PD) include a shift to lower frequencies in the electroencephalogram (EEG) and enhanced synchronized oscillations at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a recent physiologically based mean-field model of the basal ganglia-thalamocortical system, and shows how it accounts for many key electrophysiological correlates of PD. Its detailed functional connectivity comprises partially segregated direct and indirect pathways through two populations of striatal neurons, a hyperdirect pathway involving a corticosubthalamic projection, thalamostriatal feedback, and local inhibition in striatum and external pallidum (GPe). In a companion paper, realistic steady-state firing rates were obtained for the healthy state, and after dopamine loss modeled by weaker direct and stronger indirect pathways, reduced intrapallidal inhibition, lower firing thresholds of the GPe and subthalamic nucleus (STN), a stronger projection from striatum to GPe, and weaker cortical interactions. Here it is shown that oscillations around 5 and 20 Hz can arise with a strong indirect pathway, which also causes increased synchronization throughout the basal ganglia. Furthermore, increased theta power with progressive nigrostriatal degeneration is correlated with reduced alpha power and peak frequency, in agreement with empirical results. Unlike the hyperdirect pathway, the indirect pathway sustains oscillations with phase relationships that coincide with those found experimentally. Alterations in the responses of basal ganglia to transient stimuli accord with experimental observations. Reduced cortical gains due to both nigrostriatal and mesocortical dopamine loss lead to slower changes in cortical activity and may be related to bradykinesia. Finally, increased EEG power found in some studies may be partly explained by a lower effective GPe firing threshold, reduced GPe-GPe inhibition, and/or weaker

  8. Thermodynamic properties of rhodium at high temperature and pressure by using mean field potential approach

    NASA Astrophysics Data System (ADS)

    Kumar, Priyank; Bhatt, Nisarg K.; Vyas, Pulastya R.; Gohel, Vinod B.

    2016-10-01

    The thermophysical properties of rhodium are studied up to melting temperature by incorporating anharmonic effects due to lattice ions and thermally excited electrons. In order to account anharmonic effects due to lattice vibrations, we have employed mean field potential (MFP) approach and for thermally excited electrons Mermin functional. The local form of the pseudopotential with only one effective adjustable parameter rc is used to construct MFP and hence vibrational free energy due to ions - Fion. We have studied equation of state at 300 K and further, to access the applicability of present conjunction scheme, we have also estimated shock-Hugoniot and temperature along principle Hugoniot. We have carried out the study of temperature variation of several thermophysical properties like thermal expansion (βP), enthalpy (EH), specific heats at constant pressure and volume (CP and CV), specific heats due to lattice ions and thermally excited electrons ( and , isothermal and adiabatic bulk moduli (BT and Bs) and thermodynamic Gruneisen parameter (γth) in order to examine the inclusion of anharmonic effects in the present study. The computed results are compared with available experimental results measured by using different methods and previously obtained theoretical results using different theoretical philosophy. Our computed results are in good agreement with experimental findings and for some physical quantities better or comparable with other theoretical results. We conclude that local form of the pseudopotential used accounts s-p-d hybridization properly and found to be transferable at extreme environment without changing the values of the parameter. Thus, even the behavior of transition metals having complexity in electronic structure can be well understood with local pseudopotential without any modification in the potential at extreme environment. Looking to the success of present scheme (MFP + pseudopotential) we would like to extend it further for the

  9. A mean field approach for computing solid-liquid surface tension for nanoscale interfaces.

    PubMed

    Chiu, Chi-cheng; Ranatunga, R J K Udayana; Torres Flores, David; Pérez, D Vladimir; Moore, Preston B; Shinoda, Wataru; Nielsen, Steven O

    2010-02-01

    The physical properties of a liquid in contact with a solid are largely determined by the solid-liquid surface tension. This is especially true for nanoscale systems with high surface area to volume ratios. While experimental techniques can only measure surface tension indirectly for nanoscale systems, computer simulations offer the possibility of a direct evaluation of solid-liquid surface tension although reliable methods are still under development. Here we show that using a mean field approach yields great physical insight into the calculation of surface tension and into the precise relationship between surface tension and excess solvation free energy per unit surface area for nanoscale interfaces. Previous simulation studies of nanoscale interfaces measure either excess solvation free energy or surface tension, but these two quantities are only equal for macroscopic interfaces. We model the solid as a continuum of uniform density in analogy to Hamaker's treatment of colloidal particles. As a result, the Hamiltonian of the system is imbued with parametric dependence on the size of the solid object through the integration limits for the solid-liquid interaction energy. Since the solid-liquid surface area is a function of the size of the solid, and the surface tension is the derivative of the system free energy with respect to this surface area, we obtain a simple expression for the surface tension of an interface of arbitrary shape. We illustrate our method by modeling a thin nanoribbon and a solid spherical nanoparticle. Although the calculation of solid-liquid surface tension is a demanding task, the method presented herein offers new insight into the problem, and may prove useful in opening new avenues of investigation.

  10. Investigation of band termination in the lower fp shell within the cranked relativistic mean field model

    NASA Astrophysics Data System (ADS)

    Bhagwat, A.; Wyss, R.; Satuła, W.; Meng, J.; Gambhir, Y. K.

    2013-04-01

    The excitation energy difference (ΔE) between the terminating states built on the f7/2n and d3/2-1f7/2n+1 configurations (here, 'n' denotes the number of valence particles outside the 40Ca core and the particle hole excitation across the magic gap 20 is of proton type) in the lower fp shell are studied systematically within the framework of the cranked relativistic mean field model. The ΔE thus defined, depends predominantly on the f7/2 - d3/2 shell gap, and its evolution as a function of neutron - proton asymmetry. The latter, in turn, depends on the isoscalar - isovector balance in the spin - orbit potential. Therefore, a systematic investigation of the difference ΔE is expected to test quantitatively the predicted shell gaps as a function of isospin. We find that: 1) the conventional NL3 parameter set over estimates the ΔE values, implying that the said shell gap is over - estimated in this parametrization and 2) the largest deviation between the calculated and the experimental values of ΔE is obtained for the nucleus with the smallest asymmetry value in the set of nuclei considered, and that the deviation decreases with increasing asymmetry, indicating that the in RMF parametrization considered, the isoscalar - isovector balance in the spin - orbit potential requires improvement. We carry out a re - fit of the RMF parameters to attempt a remedy to these two problems. We find that in addition to the binding energies and charge radii, if a constraint is put on the f7/2 - d3/2 shell gap in the fit to the Lagrangian parameters, the overall agreement of ΔE with the experiment improves significantly, without disturbing the agreement already achieved for the bulk properties of the nuclei spanning the entire periodic table. At a finer level, however, it is found that the isoscalar - isovector balance in the spin orbit interaction is required to be improved further. A detailed work in this direction is in progress.

  11. Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states.

    PubMed

    Decelle, Aurélien; Ricci-Tersenghi, Federico

    2016-07-01

    In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and spiking regimes in neural networks). Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference (e.g., in the low-temperature phase of the Curie-Weiss model). In this work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures (low-temperature phases of Curie-Weiss and Hopfield models). PMID:27575082

  12. Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states

    NASA Astrophysics Data System (ADS)

    Decelle, Aurélien; Ricci-Tersenghi, Federico

    2016-07-01

    In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and spiking regimes in neural networks). Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference (e.g., in the low-temperature phase of the Curie-Weiss model). In this work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures (low-temperature phases of Curie-Weiss and Hopfield models).

  13. Differences between Mean-Field Dynamics and N-Particle Quantum Dynamics as a Signature of Entanglement

    SciTech Connect

    Weiss, Christoph; Teichmann, Niklas

    2008-04-11

    A Bose-Einstein condensate in a tilted double-well potential under the influence of time-periodic potential differences is investigated in the regime where the mean-field (Gross-Pitaevskii) dynamics become chaotic. For some parameters near stable regions, even averaging over several condensate oscillations does not remove the differences between mean-field and N-particle results. While introducing decoherence via piecewise deterministic processes reduces those differences, they are due to the emergence of mesoscopic entangled states in the chaotic regime.

  14. Quantum Chemistry for Large Molecules: Linear-Scaling Mean-Field and Correlated Approaches

    NASA Astrophysics Data System (ADS)

    Ochsenfeld, Christian

    2009-03-01

    A brief review of our work to attain linear scaling computational effort for Hartree-Fock (HF), Density-Functional Theory (DFT), and second-order Mo/ller-Plesset perturbation theory (MP2) is presented. While we describe linear-scaling methods for calculating molecular response properties of large molecules for HF and DFT, we focus on energetics and energy gradients at the MP2 level. A key element of our approach is the use of multipole-based integral estimates (MBIE) which allow to rigorously preselect four-center two-electron integrals ubiquitous in quantum chemistry. MBIE does not only account for the exponential coupling between basis functions forming charge distributions, but also for the 1/R coupling between the charge distributions. In context of an atomic-orbital based formulation of MP2 theory, the MBIE preselection of significant contributions opens the way to achieve linear scaling, while numerical errors remain fully controlled. The largest system computed sofar at the MP2 level is a DNA strand with 16 base pairs, 1052 atoms, and 10 674 basis functions.

  15. Deviations from mean-field behavior in disordered nanoscale superconductor normal-metal superconductor arrays

    NASA Astrophysics Data System (ADS)

    Kouh, Taejoon; Valles, J. M.

    2003-04-01

    We have fabricated quasi-two-dimensional disordered arrays of nanoscale Pb grains coupled by an overlayer of Ag grains. Their temperature-dependent resistive transitions follow predictions for an array of mesoscopic superconductor normal-metal superconductor junctions. The decrease of their transition temperatures with Ag overlayer thickness systematically deviates from the Cooper limit theory of the proximity effect as the Pb grain size decreases. The deviations occur when the estimated number of Cooper pairs per grain is <1 and suggest the approach to a superconductor-to-metal transition.

  16. Spatial Correlation in the Three-band Copper Oxide Model: Dynamical Mean-field Study with Configuration Interaction Based Impurity Solver

    NASA Astrophysics Data System (ADS)

    Go, Ara; Millis, Andrew J.

    2014-03-01

    The three-band copper oxide model is studied using the single-site and four-site dynamical mean-field theory with configuration interaction based impurity solver. Comparison of the single and four site approximations shows that short ranged antiferromagnetic correlations are crucial to the physics. In the undoped case, they increase the gap size, shift the metal-insulator phase boundary and enhance the conductivity at the gap edge. The relation of antiferromagnetism and the pseudogap is discussed for the doped case. The new solver permits the inclusion of more bath orbitals which are crucial for accurate studies of spectral properties near the gap edge. This work was supported by the US Department of Energy under Grants No. DOE FG02-04ER46169 and DE-SC0006613.

  17. Stochastic approach to correlations beyond the mean field with the Skyrme interaction

    SciTech Connect

    Fukuoka, Y.; Nakatsukasa, T.; Funaki, Y.; Yabana, K.

    2012-10-20

    Large-scale calculation based on the multi-configuration Skyrme density functional theory is performed for the light N=Z even-even nucleus, {sup 12}C. Stochastic procedures and the imaginary-time evolution are utilized to prepare many Slater determinants. Each state is projected on eigenstates of parity and angular momentum. Then, performing the configuration mixing calculation with the Skyrme Hamiltonian, we obtain low-lying energy-eigenstates and their explicit wave functions. The generated wave functions are completely free from any assumption and symmetry restriction. Excitation spectra and transition probabilities are well reproduced, not only for the ground-state band, but for negative-parity excited states and the Hoyle state.

  18. Model-free test of local-density mean-field behavior in electric double layers

    NASA Astrophysics Data System (ADS)

    Giera, Brian; Henson, Neil; Kober, Edward M.; Squires, Todd M.; Shell, M. Scott

    2013-07-01

    We derive a self-similarity criterion that must hold if a planar electric double layer (EDL) can be captured by a local-density approximation (LDA), without specifying any specific LDA. Our procedure generates a similarity coordinate from EDL profiles (measured or computed), and all LDA EDL profiles for a given electrolyte must collapse onto a master curve when plotted against this similarity coordinate. Noncollapsing profiles imply the inability of any LDA theory to capture EDLs in that electrolyte. We demonstrate our approach with molecular simulations, which reveal dilute electrolytes to collapse onto a single curve, and semidilute ions to collapse onto curves specific to each electrolyte, except where size-induced correlations arise.

  19. Building relativistic mean field models for finite nuclei and neutron stars

    NASA Astrophysics Data System (ADS)

    Chen, Wei-Chia; Piekarewicz, J.

    2014-10-01

    Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed χ2 objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, "FSUGold2," is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron-star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter, suggesting a fairly large neutron-skin thickness in Pb208 and a moderate value of the nuclear incompressibility. Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme—properly supplemented by a covariance analysis—provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.

  20. Dynamics and termination cost of spatially coupled mean-field models

    NASA Astrophysics Data System (ADS)

    Caltagirone, Francesco; Franz, Silvio; Morris, Richard G.; Zdeborová, Lenka

    2014-01-01

    This work is motivated by recent progress in information theory and signal processing where the so-called spatially coupled design of systems leads to considerably better performance. We address relevant open questions about spatially coupled systems through the study of a simple Ising model. In particular, we consider a chain of Curie-Weiss models that are coupled by interactions up to a certain range. Indeed, it is well known that the pure (uncoupled) Curie-Weiss model undergoes a first-order phase transition driven by the magnetic field, and furthermore in the spinodal region such systems are unable to reach equilibrium in subexponential time if initialized in the metastable state. In contrast, the spatially coupled system is instead able to reach the equilibrium even when initialized to the metastable state. The equilibrium phase propagates along the chain in the form of a traveling wave. Here we study the speed of the wave front and the so-called termination cost—i.e., the conditions necessary for the propagation to occur. We reach several interesting conclusions about optimization of the speed and the cost.

  1. Beyond mean-field bistability in driven-dissipative lattices: Bunching-antibunching transition and quantum simulation

    NASA Astrophysics Data System (ADS)

    Mendoza-Arenas, J. J.; Clark, S. R.; Felicetti, S.; Romero, G.; Solano, E.; Angelakis, D. G.; Jaksch, D.

    2016-02-01

    In the present work we investigate the existence of multiple nonequilibrium steady states in a coherently driven X Y lattice of dissipative two-level systems. A commonly used mean-field ansatz, in which spatial correlations are neglected, predicts a bistable behavior with a sharp shift between low- and high-density states. In contrast one-dimensional matrix product methods reveal these effects to be artifacts of the mean-field approach, with both disappearing once correlations are taken fully into account. Instead, a bunching-antibunching transition emerges. This indicates that alternative approaches should be considered for higher spatial dimensions, where classical simulations are currently infeasible. Thus we propose a circuit QED quantum simulator implementable with current technology to enable an experimental investigation of the model considered.

  2. Poisson-Boltzmann equation and electro-convective instability in ferroelectric liquid crystals: a mean-field approach

    NASA Astrophysics Data System (ADS)

    Lahiri, T.; Pal Majumder, T.; Ghosh, N. K.

    2014-07-01

    Commercialization of ferroelectric liquid crystal displays (FLCDs) suffers from mechanical and electro-convective instabilities. Impurity ions play a pivotal role in the latter case, and therefore we developed a mean-field type model to understand the complex role of space charges, particularly ions in a ferroelectric liquid crystal. Considering an effective ion-chirality relation, we obtained a modified Poisson-Boltzmann equation for ions dissolved into a chiral solvent like the ferroelectric smectic phase. A nonuniform director profile induced by the mean electrostatic potential of the ions is then calculated by solving an Euler-Lagrange equation for a helically twisted smectic state. A combination of effects resulting from molecular chirality and an electrostatically driven twist created by the ions seems to produce this nonuniform fluctuation in the director orientation. Finally, both theoretical and experimental points of view are presented on the prediction of this mean-field model.

  3. Neural networks with excitatory and inhibitory components: Direct and inverse problems by a mean-field approach.

    PubMed

    di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro

    2016-01-01

    We study the dynamics of networks with inhibitory and excitatory leak-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a heterogeneous mean-field approximation, which allows us to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, which give rise to a rich dynamical phase diagram as a function of the fraction of inhibitory neurons. Using the same mean-field approach, we study and solve a global inverse problem: reconstructing the degree probability distributions of the inhibitory and excitatory components and the fraction of inhibitory neurons from the knowledge of the average synaptic activity field. This approach unveils new perspectives on the numerical study of neural network dynamics and the possibility of using these models as a test bed for the analysis of experimental data. PMID:26871090

  4. Neural networks with excitatory and inhibitory components: Direct and inverse problems by a mean-field approach

    NASA Astrophysics Data System (ADS)

    di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro

    2016-01-01

    We study the dynamics of networks with inhibitory and excitatory leak-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a heterogeneous mean-field approximation, which allows us to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, which give rise to a rich dynamical phase diagram as a function of the fraction of inhibitory neurons. Using the same mean-field approach, we study and solve a global inverse problem: reconstructing the degree probability distributions of the inhibitory and excitatory components and the fraction of inhibitory neurons from the knowledge of the average synaptic activity field. This approach unveils new perspectives on the numerical study of neural network dynamics and the possibility of using these models as a test bed for the analysis of experimental data.

  5. MEAN-FIELD MODELING OF AN α{sup 2} DYNAMO COUPLED WITH DIRECT NUMERICAL SIMULATIONS OF RIGIDLY ROTATING CONVECTION

    SciTech Connect

    Masada, Youhei; Sano, Takayoshi E-mail: sano@ile.osaka-u.ac.jp

    2014-10-10

    The mechanism of large-scale dynamos in rigidly rotating stratified convection is explored by direct numerical simulations (DNS) in Cartesian geometry. A mean-field dynamo model is also constructed using turbulent velocity profiles consistently extracted from the corresponding DNS results. By quantitative comparison between the DNS and our mean-field model, it is demonstrated that the oscillatory α{sup 2} dynamo wave, excited and sustained in the convection zone, is responsible for large-scale magnetic activities such as cyclic polarity reversal and spatiotemporal migration. The results provide strong evidence that a nonuniformity of the α-effect, which is a natural outcome of rotating stratified convection, can be an important prerequisite for large-scale stellar dynamos, even without the Ω-effect.

  6. Brownian regime of finite-N corrections to particle motion in the XY Hamiltonian mean field model

    NASA Astrophysics Data System (ADS)

    Ribeiro, Bruno V.; Amato, Marco A.; Elskens, Yves

    2016-08-01

    We study the dynamics of the N-particle system evolving in the XY Hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent Brownian noises over a time scale diverging not slower than {N}2/5 as N\\to ∞ , which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.

  7. Mean-field interactions between nucleic-acid-base dipoles can drive the formation of the double helix

    PubMed Central

    He, Yi; Maciejczyk, Maciej; Ołdziej, Stanisław; Scheraga, Harold A.; Liwo, Adam

    2013-01-01

    A proposed coarse-grained model of nucleic acids demonstrates that average interactions between base dipoles, together with chain connectivity and excluded-volume interactions, are sufficient to form double-helical structures of DNA and RNA molecules. Additionally, local interactions determine helix handedness and direction of strand packing. This result, and earlier research on reduced protein models, suggest that mean-field multipole-multipole interactions are the principal factors responsible for the formation of regular structure of biomolecules. PMID:23496746

  8. Sedimentation of shelf sandstones in Queen Formation, McFarland and Means fields, central basin platform of Permian basin

    SciTech Connect

    Malicse, A.; Mazzullo, J.; Holley, C.; Mazzullo, S.J.

    1988-01-01

    The Queen Formation is a sequence of carbonates, evaporites, and sandstones of Permian (Guadalupian) age that is found across the subsurface of the Central Basin platform of the Permian basin. The formation is a major hydrocarbon reservoir in this region, and its primary reservoir facies are porous shelf sandstones and dolomites. Cores and well logs from McFarland and Means fields (on the northwest margin of the Central Basin platform) were examined to determine the sedimentary history of the shelf sandstones.

  9. Organic crystal polymorphism: a benchmark for dispersion-corrected mean-field electronic structure methods.

    PubMed

    Brandenburg, Jan Gerit; Grimme, Stefan

    2016-08-01

    We analyze the energy landscape of the sixth crystal structure prediction blind test targets with various first principles and semi-empirical quantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pairwise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko-Scheffler (TS) method, and the density-dependent dispersion correction dDsC. Recent methodological progress includes higher-order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod-Teller-Muto type three-body contribution, the TS based many-body dispersion (MBD), and the nonlocal van der Waals density functional (vdW-DF2). The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As a computationally less demanding method, we test our recently presented minimal basis Hartree-Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted. PMID:27484372

  10. Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions

    NASA Astrophysics Data System (ADS)

    Touboul, Jonathan

    2012-08-01

    In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate stochastic delayed integro-differential McKean-Vlasov equation that remain impenetrable, leaving the stochastic collective dynamics of such networks poorly understood. In order to study these macroscopic dynamics, we analyze networks of firing-rate neurons, i.e. with linear intrinsic dynamics and sigmoidal interactions. In that case, we prove that the solution of the mean-field equation is Gaussian, hence characterized by its two first moments, and that these two quantities satisfy a set of coupled delayed integro-differential equations. These equations are similar to usual neural field equations, and incorporate noise levels as a parameter, allowing analysis of noise-induced transitions. We identify through bifurcation analysis several qualitative transitions due to noise in the mean-field limit. In particular, stabilization of spatially homogeneous solutions, synchronized oscillations, bumps, chaotic dynamics, wave or bump splitting are exhibited and arise from static or dynamic Turing-Hopf bifurcations. These surprising phenomena allow further exploring the role of noise in the nervous system.

  11. Brain activity modeling in general anesthesia: Enhancing local mean-field models using a slow adaptive firing rate

    NASA Astrophysics Data System (ADS)

    Molaee-Ardekani, B.; Senhadji, L.; Shamsollahi, M. B.; Vosoughi-Vahdat, B.; Wodey, E.

    2007-10-01

    In this paper, an enhanced local mean-field model that is suitable for simulating the electroencephalogram (EEG) in different depths of anesthesia is presented. The main building elements of the model (e.g., excitatory and inhibitory populations) are taken from Steyn-Ross [M. L. Steyn-Ross , Phys. Rev. E 64, 011917 (2001), D. A. Steyn-Ross , Phys. Rev. E 64, 011918 (2001)] and Bojak and Liley [I. Bojak and D. T. Liley, Phys. Rev. E 71, 041902 (2005)] mean-field models and a new slow ionic mechanism is included in the main model. Generally, in mean-field models, some sigmoid-shape functions determine firing rates of neural populations according to their mean membrane potentials. In the enhanced model, the sigmoid function corresponding to excitatory population is redefined to be also a function of the slow ionic mechanism. This modification adapts the firing rate of neural populations to slow ionic activities of the brain. When an anesthetic drug is administered, the slow mechanism may induce neural cells to alternate between two levels of activity referred to as up and down states. Basically, the frequency of up-down switching is in the delta band (0-4Hz) and this is the main reason behind high amplitude, low frequency fluctuations of EEG signals in anesthesia. Our analyses show that the enhanced model may have different working states driven by anesthetic drug concentration. The model is settled in the up state in the waking period, it may switch to up and down states in moderate anesthesia while in deep anesthesia it remains in the down state.

  12. Mean-field dispersion-induced spatial synchrony, oscillation and amplitude death, and temporal stability in an ecological model

    NASA Astrophysics Data System (ADS)

    Banerjee, Tanmoy; Dutta, Partha Sharathi; Gupta, Anubhav

    2015-05-01

    One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems.

  13. Mean-field dispersion-induced spatial synchrony, oscillation and amplitude death, and temporal stability in an ecological model.

    PubMed

    Banerjee, Tanmoy; Dutta, Partha Sharathi; Gupta, Anubhav

    2015-05-01

    One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems. PMID:26066241

  14. Lars Onsager Prize: The mean field solution for Hard Sphere Jamming and a new scenario for the low temperature landscape of glasses

    NASA Astrophysics Data System (ADS)

    Parisi, Giorgio

    In a hard spheres systems particles cannot overlap. Increasing the density we reach a point where most of the particles are blocked and the density cannot be increased any more: this is the jamming point. The jamming point separates the phase, where all the constraint can be satisfied, from an unsatifiable phase, where spheres do have to overlap. A scaling theory of the behavior around the jamming critical point has been formulated and a few critical exponents have been introduced. The exponents are apparently super-universal, as far as they do seem to be independent from the space dimensions. The mean field version of the model (i.e. the infinite dimensions limit) has been solved analytically using broken replica symmetry techniques and the computed critical exponents have been found in a remarkable agreement with three-dimensional and two-dimensional numerical results and experiments. The theory predicts in hard spheres (in glasses) a new transition (the Gardener transition) from the replica symmetric phase to the replica broken phase at high density (at low temperature), in agreement with simulations on hard sphere systems. I will briefly discuss the possible consequences of this new picture on the very low temperature behavior of glasses in the quantum regime.

  15. Mean-field coarse-grained model for poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer systems.

    PubMed

    García Daza, Fabián A; Colville, Alexander J; Mackie, Allan D

    2015-03-31

    The microscopic modeling of surfactant systems is of the utmost importance in understanding the mechanisms related to the micellization process because it allows for prediction and comparison with experimental data of diverse equilibrium system properties. In this work, we present a coarse-grained model for Pluronics, a trademarked type of triblock copolymer, from simulations based on a single-chain mean-field theory (SCMF). This microscopic model is used to quantify the micellization process of these nonionic surfactants at 37 °C and has been shown to be able to quantitatively reproduce experimental data of the critical micelle concentration (CMC) along with other equilibrium properties. In particular, these results correctly capture the experimental behavior with respect to the lengths of the hydrophobic and hydrophilic moieties of the surfactants for low and medium hydrophobicities. However, for the more highly hydrophobic systems with low CMCs, a deviation is found which has been previously attributed to nonequilibrium effects in the experimental data (Garcı́a Daza, F. A.; Mackie, A. D. Low Critical Micelle Concentration Discrepancy between Theory and Experiment. J. Phys. Chem. Lett. 2014, 5, 2027-2032).

  16. Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices.

    PubMed

    Morsch, O; Müller, J H; Cristiani, M; Ciampini, D; Arimondo, E

    2001-10-01

    We have loaded Bose-Einstein condensates into one-dimensional, off-resonant optical lattices and accelerated them by chirping the frequency difference between the two lattice beams. For small values of the lattice well depth, Bloch oscillations were observed. Reducing the potential depth further, Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied and used as a probe for the effective potential resulting from mean-field interactions as predicted by Choi and Niu [Phys. Rev. Lett. 82, 2022 (1999)]. The effective potential was measured for various condensate densities and trap geometries, yielding good qualitative agreement with theoretical calculations.

  17. Mean-field studies of time reversal breaking states in super-heavy nuclei with the Gogny force

    SciTech Connect

    Robledo, L. M.

    2015-10-15

    Recent progress on the description of time reversal breaking (odd mass and multi-quasiparticle excitation) states in super-heavy nuclei within a mean field framework and using several flavors of the Gogny interaction is reported. The study includes ground and excited states in selected odd mass isotopes of nobelium and mendelevium as well as high K isomeric states in {sup 254}No. These are two and four-quasiparticle excitations that are treated in the same self-consistent HFB plus blocking framework as the odd mass states.

  18. A Mean Field Analysis of the Exchange Coupling (J) For 2- and 3-D Structured Tetracyanoethylenide (TCNE -)-based Magnets

    SciTech Connect

    McConnell, Amber C.; Fishman, Randy Scott; Miller, Joel S.

    2012-01-01

    Mean field expressions based on the simple Heisenberg model were derived to correlate the inter- and intralayer exchange coupling to the critical temperatures, Tc, for several TCNE (tetracyanoethylene) based magnets with extended 2- and 3-D structure types. These expressions were used to estimate the exchange coupling, J, for 2-D ferrimagnetic [MII(TCNE)(NCMe)2]+ (M = Mn, Fe), 3-D antiferromagnetic MnII(TCNE)[C4(CN)8]1/2, and 3-D ferrimagnetic MnII(TCNE)3/2(I3)1/2. The sign and magnitude of the exchange coupling are in accord with previously reported magnetic data.

  19. Mean-Field and RPA Approaches to Stable and Unstable Nuclei with Semi-Realistic NN Interaction

    SciTech Connect

    Nakada, H.

    2011-05-06

    A M3Y-type semi-realistic NN interaction has been applied to the mean-field and the RPA calculations. Explicitly including the tensor force and the central part of the one-pion exchange potential, the semi-realistic interaction is useful in studying the Z or N dependence of the nuclear shell structure. The magicity of N = 32, 40 and 58 in the neutron-rich Ca and Ni nuclei has been investigated, and the Z = 28 magicity in {sup 78}Ni has been argued. Significance of the tensor force in magnetic transitions is demonstrated by the M1 excitation of {sup 208}Pb.

  20. Mean-field studies of time reversal breaking states in super-heavy nuclei with the Gogny force

    NASA Astrophysics Data System (ADS)

    Robledo, L. M.

    2015-10-01

    Recent progress on the description of time reversal breaking (odd mass and multi-quasiparticle excitation) states in super-heavy nuclei within a mean field framework and using several flavors of the Gogny interaction is reported. The study includes ground and excited states in selected odd mass isotopes of nobelium and mendelevium as well as high K isomeric states in 254No. These are two and four-quasiparticle excitations that are treated in the same self-consistent HFB plus blocking framework as the odd mass states.

  1. Connection between the nuclear matter mean-field equation of state and the quark and gluon condensates at high density

    SciTech Connect

    Malheiro, M.; Dey, M.; Delfino, A.; Dey, J. |||

    1997-01-01

    It is known now that chiral symmetry restoration requires the meson-nucleon couplings to be density-dependent in nuclear-matter mean-field models. We further show that, quite generally, the quark and gluon condensates in medium are related to the trace of the energy-momentum tensor of nuclear matter and in these models the incompressibility K must be less than 3 times the chemical potential {mu}. In the critical density {rho}{sub c}, the gluon condensate is only reduced by 20{percent}, indicating a larger effective nucleon mass. {copyright} {ital 1997} {ital The American Physical Society}

  2. A Mean-Field Photoreaction Model for the Pretilt Generation of a Liquid Crystal on Photopolymer Layers upon Ultraviolet Exposure

    NASA Astrophysics Data System (ADS)

    Na, Jun-Hee; Pae, Hyungwu; Kim, Jinyool; Yu, Chang-Jae; Lee, Sin-Doo

    2011-03-01

    We present a mean-field photoreaction model for the pretilt generation of a nematic liquid crystal (NLC) on the surfaces of photopolymers upon the exposure of ultraviolet (UV) light. The angular distribution function of photopolymer side chains, calculated in the photoreaction model, is used for determining the surface anchoring energy within the Rapini-Papoular approximation. The pretilt angle transition from the homeotropic alignment to the planar alignment of the NLC is demonstrated in two photopolymers with different alkyl chain lengths as a function of the UV exposure time. The main features of the experimental results agree well with theoretical predictions.

  3. Mean-field plus various types of pairing models and an exact boson mapping of the standard pairing model

    SciTech Connect

    Pan Feng; Wang Yin; Guan Xin; Jia Lu; Chen Xiangrong; Draayer, J. P.

    2011-06-28

    Exact solutions of Nilsson mean-field with various pairing interactions are reviewed. Some even-odd mass differences and moments of inertia of low-lying states for rare earth and actinide nuclei are calculated for the nearest-orbit pairing approximation as well as for the extended pairing model and compared to available experimental data. An exact boson mapping of the standard pairing Hamiltonian is also reported. Under the mapping, fermion pair operators are mapped exactly onto corresponding bosons. The image of the mapping is a Bose-Hubbard model with orbit-dependent hopping.

  4. A statistical mechanical model of cell membrane ion channels in electric fields: The mean-field approximation

    NASA Astrophysics Data System (ADS)

    Yang, Y. S.; Thompson, C. J.; Anderson, V.; Wood, A. W.

    A statistical mechanical model of cell membrane ion channels is proposed which incorporates interactions between ion channels and external electric fields. The model provides a physical explanation of trans-membrane ion transport. Under a mean-field approximation, the maximum fractions of open potassium and sodium channels are obtained by solving a self-consistent nonlinear algebraic equation. Using known parameters for the squid giant axon, the model gives excellent agreement with experimental measurements for potassium and sodium trans-membrane conductance. The numerical results imply that the chemical potential of open channels and the interaction energy between channels are well above the thermal noise.

  5. Solvent electronic polarization effects on a charge transfer excitation studied by the mean-field QM/MM method

    SciTech Connect

    Nakano, Hiroshi

    2015-12-31

    Electronic polarization effects of a medium can have a significant impact on a chemical reaction in condensed phases. We discuss the effects on the charge transfer excitation of a chromophore, N,N-dimethyl-4-nitroaniline, in various solvents using the mean-field QM/MM method with a polarizable force field. The results show that the explicit consideration of the solvent electronic polarization effects is important especially for a solvent with a low dielectric constant when we study the solvatochromism of the chromophore.

  6. Mean-field methods in evolutionary duplication-innovation-loss models for the genome-level repertoire of protein domains

    NASA Astrophysics Data System (ADS)

    Angelini, A.; Amato, A.; Bianconi, G.; Bassetti, B.; Cosentino Lagomarsino, M.

    2010-02-01

    We present a combined mean-field and simulation approach to different models describing the dynamics of classes formed by elements that can appear, disappear, or copy themselves. These models, related to a paradigm duplication-innovation model known as Chinese restaurant process, are devised to reproduce the scaling behavior observed in the genome-wide repertoire of protein domains of all known species. In view of these data, we discuss the qualitative and quantitative differences of the alternative model formulations, focusing in particular on the roles of element loss and of the specificity of empirical domain classes.

  7. Stable mean-field solution of a short-range interacting SO(3) quantum Heisenberg spin glass.

    PubMed

    da Conceição, C M S; Marino, E C

    2008-07-18

    We present a mean-field solution for a quantum, short-range interacting, disordered, SO(3) Heisenberg spin model, in which the Gaussian distribution of couplings is centered in an antiferromagnetic (AF) coupling J[over ]>0, and which, for weak disorder, can be treated as a perturbation of the pure AF Heisenberg system. The phase diagram contains, apart from a Néel phase at T=0, spin-glass and paramagnetic phases whose thermodynamic stability is demonstrated by an analysis of the Hessian matrix of the free-energy. The magnetic susceptibilities exhibit the typical cusp of a spin-glass transition.

  8. Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights

    PubMed Central

    Nicola, Wilten; Tripp, Bryan; Scott, Matthew

    2016-01-01

    A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks. PMID:26973503

  9. MEAN-FIELD SOLAR DYNAMO MODELS WITH A STRONG MERIDIONAL FLOW AT THE BOTTOM OF THE CONVECTION ZONE

    SciTech Connect

    Pipin, V. V.; Kosovichev, A. G.

    2011-09-01

    This paper presents a study of kinematic axisymmetric mean-field dynamo models for the case of meridional circulation with a deep-seated stagnation point and a strong return flow at the bottom of the convection zone. This kind of circulation follows from mean-field models of the angular momentum balance in the solar convection zone. The dynamo models include turbulent sources of the large-scale poloidal magnetic field production due to kinetic helicity and a combined effect due to the Coriolis force and large-scale electric current. In these models the toroidal magnetic field, which is responsible for sunspot production, is concentrated at the bottom of the convection zone and is transported to low-latitude regions by a meridional flow. The meridional component of the poloidal field is also concentrated at the bottom of the convection zone, while the radial component is concentrated in near-polar regions. We show that it is possible for this type of meridional circulation to construct kinematic dynamo models that resemble in some aspects the sunspot magnetic activity cycle. However, in the near-equatorial regions the phase relation between the toroidal and poloidal components disagrees with observations. We also show that the period of the magnetic cycle may not always monotonically decrease with the increase of the meridional flow speed. Thus, for further progress it is important to determine the structure of the meridional circulation, which is one of the critical properties, from helioseismology observations.

  10. Vlasov formalism for extended relativistic mean field models: The crust-core transition and the stellar matter equation of state

    NASA Astrophysics Data System (ADS)

    Pais, Helena; Providência, Constança

    2016-07-01

    The Vlasov formalism is extended to relativistic mean field hadron models with nonlinear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear ω ρ and σ ρ coupling terms on the crust-core transition density and pressure and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6 ±0.3 km and a crust thickness of 1.36 ±0.06 km for a 1.4 M⊙ star.

  11. Supercritical Mean Field Equations on Convex Domains and the Onsager's Statistical Description of Two-Dimensional Turbulence

    NASA Astrophysics Data System (ADS)

    Bartolucci, Daniele; De Marchis, Francesca

    2015-08-01

    We are motivated by the study of the Microcanonical Variational Principle within Onsager's description of two-dimensional turbulence in the range of energies where the equivalence of statistical ensembles fails. We obtain sufficient conditions for the existence and multiplicity of solutions for the corresponding Mean Field Equation on convex and "thin" enough domains in the supercritical (with respect to the Moser-Trudinger inequality) regime. This is a brand new achievement since existence results in the supercritical region were previously known only on multiply connected domains. We then study the structure of these solutions by the analysis of their linearized problems and we also obtain a new uniqueness result for solutions of the Mean Field Equation on thin domains whose energy is uniformly bounded from above. Finally we evaluate the asymptotic expansion of those solutions with respect to the thinning parameter and, combining it with all the results obtained so far, we solve the Microcanonical Variational Principle in a small range of supercritical energies where the entropy is shown to be concave.

  12. Microstructure for ferroelastic transitions from strain pseudo-spin clock models in two and three dimensions: a mean field analysis

    SciTech Connect

    Lookman, Turab; Vasseur, Romain

    2009-01-01

    We obtain the microstructure of ferroelastic transitions in two and three dimensions from the solution of their corresponding discrete pseudo-spin models. In two dimensions we consider two transitions each from the high symmetry square and triangle symmetries: square-to-rectangle (SR), square-to-oblique (SO), triangle-to-centered rectangle (TR) and triangle-to-oblique (TO). In three dimensions we study the corresponding spin model for the cubic to tetragonal transition. The Landau free energies for these transitions result in N+ I states clock models (Z{sub N}) with long range interactions and we derive mean-field self-consistency equations for the clock model Hamiltonians. The microstructures from the mean-field solutions of the models are very similar to those obtained from the original continuum models or Monte Carlo simulations on the spin models (in the SR case), illustrating that these discrete models capture the salient physics. The models, in the presence of disorder, provide the basis for the study of the strain glass phase observed in martensitic alloys.

  13. Modeling MHD accretion-ejection: episodic ejections of jets triggered by a mean-field disk dynamo

    SciTech Connect

    Stepanovs, Deniss; Fendt, Christian; Sheikhnezami, Somayeh E-mail: fendt@mpia.de

    2014-11-20

    We present MHD simulations exploring the launching, acceleration, and collimation of jets and disk winds. The evolution of the disk structure is consistently taken into account. Extending our earlier studies, we now consider the self-generation of the magnetic field by an α{sup 2}Ω mean-field dynamo. The disk magnetization remains on a rather low level, which helps to evolve the simulations for T > 10, 000 dynamical time steps on a domain extending 1500 inner disk radii. We find the magnetic field of the inner disk to be similar to the commonly found open field structure, favoring magneto-centrifugal launching. The outer disk field is highly inclined and predominantly radial. Here, differential rotation induces a strong toroidal component, which plays a key role in outflow launching. These outflows from the outer disk are slower, denser, and less collimated. If the dynamo action is not quenched, magnetic flux is continuously generated, diffuses outward through the disk, and fills the entire disk. We have invented a toy model triggering a time-dependent mean-field dynamo. The duty cycles of this dynamo lead to episodic ejections on similar timescales. When the dynamo is suppressed as the magnetization falls below a critical value, the generation of the outflows and also accretion is inhibited. The general result is that we can steer episodic ejection and large-scale jet knots by a disk-intrinsic dynamo that is time-dependent and regenerates the jet-launching magnetic field.

  14. Universality and anomalous mean-field breakdown of symmetry-breaking transitions in a coupled two-component Bose-Einstein condensate.

    PubMed

    Lee, Chaohong

    2009-02-20

    We study both mean-field and full quantum dynamics of symmetry-breaking transitions (SBTs) in a coupled two-component Bose-Einstein condensate. By controlling s-wave scattering lengths and the coupling strength, it is possible to stimulate SBTs between normal and spontaneously polarized ground states. In static transitions, the probability maxima of full quantum ground states correspond to the mean-field ground states. In dynamical transitions, due to the vanishing of excitation gaps, the mean-field dynamics shows universal scalings obeying the Kibble-Zurek mechanism. Both mean-field and full quantum defect modes appear as damped oscillations, but they appear at different critical points and undergo different oscillation regimes. The anomalous breakdown of mean-field dynamics induced by SBTs depends on the approaching direction.

  15. Universality and Anomalous Mean-Field Breakdown of Symmetry-Breaking Transitions in a Coupled Two-Component Bose-Einstein Condensate

    SciTech Connect

    Lee, Chaohong

    2009-02-20

    We study both mean-field and full quantum dynamics of symmetry-breaking transitions (SBTs) in a coupled two-component Bose-Einstein condensate. By controlling s-wave scattering lengths and the coupling strength, it is possible to stimulate SBTs between normal and spontaneously polarized ground states. In static transitions, the probability maxima of full quantum ground states correspond to the mean-field ground states. In dynamical transitions, due to the vanishing of excitation gaps, the mean-field dynamics shows universal scalings obeying the Kibble-Zurek mechanism. Both mean-field and full quantum defect modes appear as damped oscillations, but they appear at different critical points and undergo different oscillation regimes. The anomalous breakdown of mean-field dynamics induced by SBTs depends on the approaching direction.

  16. Gap junctions mediate large-scale Turing structures in a mean-field cortex driven by subcortical noise

    NASA Astrophysics Data System (ADS)

    Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Wilson, M. T.; Sleigh, J. W.

    2007-07-01

    One of the grand puzzles in neuroscience is establishing the link between cognition and the disparate patterns of spontaneous and task-induced brain activity that can be measured clinically using a wide range of detection modalities such as scalp electrodes and imaging tomography. High-level brain function is not a single-neuron property, yet emerges as a cooperative phenomenon of multiply-interacting populations of neurons. Therefore a fruitful modeling approach is to picture the cerebral cortex as a continuum characterized by parameters that have been averaged over a small volume of cortical tissue. Such mean-field cortical models have been used to investigate gross patterns of brain behavior such as anesthesia, the cycles of natural sleep, memory and erasure in slow-wave sleep, and epilepsy. There is persuasive and accumulating evidence that direct gap-junction connections between inhibitory neurons promote synchronous oscillatory behavior both locally and across distances of some centimeters, but, to date, continuum models have ignored gap-junction connectivity. In this paper we employ simple mean-field arguments to derive an expression for D2 , the diffusive coupling strength arising from gap-junction connections between inhibitory neurons. Using recent neurophysiological measurements reported by Fukuda [J. Neurosci. 26, 3434 (2006)], we estimate an upper limit of D2≈0.6cm2 . We apply a linear stability analysis to a standard mean-field cortical model, augmented with gap-junction diffusion, and find this value for the diffusive coupling strength to be close to the critical value required to destabilize the homogeneous steady state. Computer simulations demonstrate that larger values of D2 cause the noise-driven model cortex to spontaneously crystalize into random mazelike Turing structures: centimeter-scale spatial patterns in which regions of high-firing activity are intermixed with regions of low-firing activity. These structures are consistent with the

  17. Approximate analytical solution for nuclear matter in a mean-field Walecka model and Coester line behavior

    SciTech Connect

    Delfino, A.; Silva, J.B.; Malheiro, M.

    2006-03-15

    We study nuclear matter, at the mean-field approximation, by considering as equal the values of the scalar and the vector density in the Walecka model, which is a very reasonable approximation up to the nuclear matter saturation density. It turns out that the model has an analytical solution for the scalar and vector couplings as functions only of the nuclear matter density and binding energy. The nuclear matter properties are very close to the original version of the model. This solution allows us to show that the correlation between the binding energy and the saturation density is Coester line like. The liquid-gas phase transition is also studied and the critical and flash temperatures are again very similar to the original ones.

  18. Phase transitions in scale-free neural networks: Departure from the standard mean-field universality class

    SciTech Connect

    Aldana, Maximino; Larralde, Hernan

    2004-12-01

    We investigate the nature of the phase transition from an ordered to a disordered state that occurs in a family of neural network models with noise. These models are closely related to the majority voter model, where a ferromagneticlike interaction between the elements prevails. Each member of the family is distinguished by the network topology, which is determined by the probability distribution of the number of incoming links. We show that for homogeneous random topologies, the phase transition belongs to the standard mean-field universality class, characterized by the order parameter exponent {beta}=1/2. However, for scale-free networks we obtain phase transition exponents ranging from 1/2 to infinity. Furthermore, we show the existence of a phase transition even for values of the scale-free exponent in the interval (1.5,2], where the average network connectivity diverges.

  19. Non-thermal quenched damage phenomena: The application of the mean-field approach for the three-dimensional case

    NASA Astrophysics Data System (ADS)

    Abaimov, Sergey G.; Akhatov, Iskander S.

    2016-09-01

    In this study, we apply the mean-field approach to the three-dimensional damage phenomena. The model approximates a solid as a polycrystalline material where grains are assumed isotropic. While the stiffness properties are considered homogeneous, the heterogeneous distribution of grains' strengths provides the quenched statistical variability generating non-thermal fluctuations in the ensemble. Studying the statistical properties of the fluctuations, we introduce the concept of susceptibility of damage. Its divergence in the vicinity of the point of material failure can be treated as a catastrophe predictor. In accordance with this criterion, we find that damage growth in reality is much faster than it could be expected from intuitive engineering considerations. Also, we consider avalanches of grain failures and find that due to the slowing down effect the characteristic time of the relaxation processes diverges in the vicinity of the point of material failure.

  20. Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

    NASA Astrophysics Data System (ADS)

    Ku, Wai Lim; Girvan, Michelle; Ott, Edward

    2015-12-01

    In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

  1. Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

    SciTech Connect

    Ku, Wai Lim; Girvan, Michelle; Ott, Edward

    2015-12-15

    In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is “extensive” in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

  2. Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states.

    PubMed

    Ku, Wai Lim; Girvan, Michelle; Ott, Edward

    2015-12-01

    In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

  3. Circulating current in 1D Hubbard rings with long-range hopping: Comparison between exact diagonalization method and mean-field approach

    NASA Astrophysics Data System (ADS)

    Saha, Madhumita; Maiti, Santanu K.

    2016-10-01

    The interplay between Hubbard interaction, long-range hopping and disorder on persistent current in a mesoscopic one-dimensional conducting ring threaded by a magnetic flux ϕ is analyzed in detail. Two different methods, exact numerical diagonalization and Hartree-Fock mean field theory, are used to obtain numerical results from the many-body Hamiltonian. The current in a disordered ring gets enhanced as a result of electronic correlation and it becomes more significant when contributions from higher order hoppings, even if they are too small compared to nearest-neighbor hopping, are taken into account. Certainly this can be an interesting observation in the era of long-standing controversy between theoretical and experimental results of persistent current amplitudes. Along with these we also find half-flux quantum periodic current for some typical electron fillings and kink-like structures at different magnetic fluxes apart from ϕ = 0 and ±ϕ0 / 2. The scaling behavior of current is also discussed for the sake of completeness of our present analysis.

  4. Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases

    SciTech Connect

    Pekalski, J.; Ciach, A.; Almarza, N. G.

    2014-03-21

    The short-range attraction and long-range repulsion between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces, or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion. At the ground state of the model (T = 0) the lattice is empty for small values of the chemical potential μ, and fully occupied for large μ. For intermediate values of μ periodically distributed clusters, bubbles, or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For T > 0 we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.

  5. Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes

    NASA Astrophysics Data System (ADS)

    Sampaio Filho, C. I. N.; dos Santos, T. B.; Moreira, A. A.; Moreira, F. G. B.; Andrade, J. S.

    2016-05-01

    We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which directed long-range connections are randomly added according to the probability Pi j˜r-α , where ri j is the Manhattan distance between nodes i and j , and the exponent α is a controlling parameter [J. M. Kleinberg, Nature (London) 406, 845 (2000), 10.1038/35022643]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent α . Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For α ≤3 the critical behavior is described by mean-field exponents, while for α ≥4 it belongs to the Ising universality class. Finally, in the region where the crossover occurs, 3 <α <4 , the critical exponents are dependent on α .

  6. Influence of memory in deterministic walks in random media: analytical calculation within a mean-field approximation.

    PubMed

    Terçariol, César Augusto Sangaletti; Martinez, Alexandre Souto

    2008-09-01

    Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2 , as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N1) is just n=e=2.72... while in the mu=2 case, the mean number n of visited points grows proportionally to N;{12} . Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones. PMID:18850997

  7. Fock-space diagonalization of the state-dependent pairing Hamiltonian with the Woods-Saxon mean field

    NASA Astrophysics Data System (ADS)

    Molique, H.; Dudek, J.

    1997-10-01

    A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian H⁁pair=∑αβGαβc†αc†α ¯cβ ¯cβ with an arbitrary set of matrix elements Gαβ. Symmetries of the Hamiltonians on the many-body level are discussed using the language of P symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of P symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to p~40 particles on n~80 levels and for several dozens of lowest lying states with precision ~(1-2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority s=0 solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei.

  8. An incremental-secant mean-field homogenization method with second statistical moments for elasto-plastic composite materials

    NASA Astrophysics Data System (ADS)

    Wu, L.; Doghri, I.; Noels, L.

    2015-10-01

    In this paper, the incremental-secant mean-field homogenization (MFH) scheme recently developed by the authors is extended to account for second statistical moments. The incremental-secant MFH method possesses several advantages compared to other MFH methods. Indeed the method can handle non-proportional and non-monotonic loadings, while the instantaneous stiffness operators used in the Eshelby tensor are naturally isotropic, avoiding the isotropization approximation required by the affine and incremental-tangent methods. Moreover, the incremental-secant MFH formalism was shown to be able to account for material softening when extended to include a non-local damage model in the matrix phase, thus enabling an accurate simulation of the onset and evolution of damage across the scales. In this work, by accounting for a second statistical moment estimation of the current yield stress in the composite phases, the plastic flow computation allows capturing with a better accuracy the plastic yield in the composite material phases, which in turn improves the accuracy of the predictions, mainly in the case of short fibre composite materials. The incremental-secant MFH can thus be used to model a wide variety of composite material systems with a good accuracy.

  9. Temperature and density dependence of asymmetric nuclear matter and protoneutron star properties within an extended relativistic mean field model

    NASA Astrophysics Data System (ADS)

    Mahajan, Gulshan; Dhiman, Shashi K.

    2011-10-01

    The effect of temperature and density dependence of the asymmetric nuclear matter properties is studied within the extended relativistic mean field (ERMF) model, which includes the contribution from the self and mixed interaction terms by using different parametrizations obtained by varying the neutron skin thickness Δr and ω-meson self-coupling (ζ). We observed that the symmetry energy and its slope and incompressibility coefficients decrease with increasing temperatures up to saturation densities. The ERMF parametrizations were employed to obtain a new set of equations of state (EOS) of the protoneutron star (PNS) with and without inclusion of hyperons. In our calculations, in comparison with cold compact stars, we obtained that the gravitational mass of the protoneutron star with and without hyperons increased by ˜0.4M⊙ and its radius increased by ˜3 km. Whereas in case of the rotating PNS, the mass shedding limit decreased with increasing temperature, and this suggested that the keplerian frequency of the PNS at T=10 MeV should be smaller by 14%-20% for the EOS with hyperon, as compared to the keplerian frequency of a cold compact star.

  10. Multiple ionization of neon atoms in collisions with bare and dressed ions: A mean-field description considering target response

    NASA Astrophysics Data System (ADS)

    Schenk, Gerald; Kirchner, Tom

    2015-05-01

    We investigate projectile-charge-state-differential electron removal from neon atoms by impact of He2+, Li3+, B2+, and C3+ ions at intermediate projectile energies (25 keV/u to 1 MeV/u ). The many-electron problem is described with an independent electron model in which active electrons at both collision centers are propagated in a common mean-field potential. Response to electron removal is taken into account in terms of a time-dependent screening potential, and a Slater-determinant-based method is used for the final-state analysis. Total cross sections for net recoil ion production, multiple ionization, and capture channels are mostly in good agreement with published experimental data. Results from equicharged bare and dressed ions are compared and the net recoil ion production cross section is broken down into contributions associated with different final projectile charge states in order to shed light on the role of the projectile electrons.

  11. Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

    NASA Astrophysics Data System (ADS)

    Moosavi, S. Amin; Montakhab, Afshin

    2014-05-01

    Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (nonconservative) local dynamics on the critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibits true criticality for a wide range of noise in various dimensions, given that conservation is respected on the average. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for a sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, the addition of noise does not affect the exponents at the upper critical dimension (D =4). In addition to an extensive finite-size scaling analysis of our systems, we also employ a useful time-series analysis method to establish true criticality of noisy systems. Finally, we discuss the implications of our work in neuroscience as well as some implications for the general phenomena of criticality in nonequilibrium systems.

  12. Periodic mean-field solutions and the spectra of discrete bosonic fields: Trace formula for Bose-Hubbard models.

    PubMed

    Engl, Thomas; Urbina, Juan Diego; Richter, Klaus

    2015-12-01

    We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number N. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, nonperturbative solutions of the, typically nonlinear, wave equation of the classical (mean-field) limit. To this end, we construct the semiclassical approximation for both the smooth and oscillatory parts of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects such as vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommensurable frequencies, our formulas are generically valid also in the free-field case of noninteracting bosons. PMID:26764774

  13. Ultracold bosons with cavity-mediated long-range interactions: A local mean-field analysis of the phase diagram

    NASA Astrophysics Data System (ADS)

    Niederle, Astrid E.; Morigi, Giovanna; Rieger, Heiko

    2016-09-01

    Ultracold bosonic atoms in optical lattices self-organize into a variety of structural and quantum phases when placed into a single-mode cavity and pumped by a laser. Cavity optomechanical effects induce an atom density modulation at the cavity-mode wavelength that competes with the optical lattice arrangement. Simultaneously short-range interactions via particle hopping promote superfluid order such that a variety of structural and quantum coherent phases can occur. We analyze the emerging phase diagram in two dimensions by means of an extended Bose-Hubbard model using a local mean-field approach combined with a superfluid cluster analysis. For commensurate ratios of the cavity and external lattice wavelengths, the Mott insulator-superfluid transition is modified by the appearance of charge density wave and supersolid phases, at which the atomic density supports the buildup of a cavity field. For incommensurate ratios, the optomechanical forces induce the formation of Bose-glass and superglass phases, namely, nonsuperfluid and superfluid phases, respectively, displaying quasiperiodic density modulations, which in addition can exhibit structural and superfluid stripe formation. The onset of such structures is constrained by the on-site interaction and is favorable at fractional densities. Experimental observables are identified and discussed.

  14. Dispersal-induced synchrony, temporal stability, and clustering in a mean-field coupled Rosenzweig-MacArthur model

    NASA Astrophysics Data System (ADS)

    Arumugam, Ramesh; Dutta, Partha Sharathi; Banerjee, Tanmoy

    2015-10-01

    In spatial ecology, dispersal among a set of spatially separated habitats, named as metapopulation, preserves the diversity and persistence by interconnecting the local populations. Understanding the effects of several variants of dispersion in metapopulation dynamics and to identify the factors which promote population synchrony and population stability are important in ecology. In this paper, we consider the mean-field dispersion among the habitats in a network and study the collective dynamics of the spatially extended system. Using the Rosenzweig-MacArthur model for individual patches, we show that the population synchrony and temporal stability, which are believed to be of conflicting outcomes of dispersion, can be simultaneously achieved by oscillation quenching mechanisms. Particularly, we explore the more natural coupling configuration where the rates of dispersal of different habitats are disparate. We show that asymmetry in dispersal rate plays a crucial role in determining inhomogeneity in an otherwise homogeneous metapopulation. We further identify an unusual emergent state in the network, namely, a multi-branch clustered inhomogeneous steady state, which arises due to the intrinsic parameter mismatch among the patches. We believe that the present study will shed light on the cooperative behavior of spatially structured ecosystems.

  15. Atomic detail brownian dynamics simulations of concentrated protein solutions with a mean field treatment of hydrodynamic interactions.

    SciTech Connect

    Mereghetti, Paolo; Wade, Rebecca C.

    2012-07-26

    High macromolecular concentrations are a distinguishing feature of living organisms. Understanding how the high concentration of solutes affects the dynamic properties of biological macromolecules is fundamental for the comprehension of biological processes in living systems. In this paper, we describe the implementation of mean field models of translational and rotational hydrodynamic interactions into an atomically detailed many-protein brownian dynamics simulation method. Concentrated solutions (30-40% volume fraction) of myoglobin, hemoglobin A, and sickle cell hemoglobin S were simulated, and static structure factors, oligomer formation, and translational and rotational self-diffusion coefficients were computed. Good agreement of computed properties with available experimental data was obtained. The results show the importance of both solvent mediated interactions and weak protein-protein interactions for accurately describing the dynamics and the association properties of concentrated protein solutions. Specifically, they show a qualitative difference in the translational and rotational dynamics of the systems studied. Although the translational diffusion coefficient is controlled by macromolecular shape and hydrodynamic interactions, the rotational diffusion coefficient is affected by macromolecular shape, direct intermolecular interactions, and both translational and rotational hydrodynamic interactions.

  16. Flocking dynamics and mean-field limit in the Cucker-Smale-type model with topological interactions

    NASA Astrophysics Data System (ADS)

    Haskovec, Jan

    2013-10-01

    We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called “topological distance” in previous works), which is the number of intermediate individuals separating them. This makes the model scale-free and is motivated by recent extensive observations of starling flocks, suggesting that the interaction ruling animal collective behavior depends on topological rather than the metric distance. We study the conditions leading to asymptotic flocking in the topological model, defined as the convergence of the agents’ velocities to a common vector. The shift from metric to topological interactions requires development of new analytical methods, taking into account the graph-theoretical nature of the problem. Moreover, we provide a rigorous derivation of the mean-field limit of large populations, recovering kinetic and hydrodynamic descriptions. In particular, we introduce the novel concept of relative separation in continuum descriptions, which is applicable to a broad variety of models of collective behavior. As an example, we shortly discuss a topological modification of the attraction-repulsion model and illustrate with numerical simulations that the modified model produces interesting new pattern dynamics.

  17. Dispersal-induced synchrony, temporal stability, and clustering in a mean-field coupled Rosenzweig-MacArthur model.

    PubMed

    Arumugam, Ramesh; Dutta, Partha Sharathi; Banerjee, Tanmoy

    2015-10-01

    In spatial ecology, dispersal among a set of spatially separated habitats, named as metapopulation, preserves the diversity and persistence by interconnecting the local populations. Understanding the effects of several variants of dispersion in metapopulation dynamics and to identify the factors which promote population synchrony and population stability are important in ecology. In this paper, we consider the mean-field dispersion among the habitats in a network and study the collective dynamics of the spatially extended system. Using the Rosenzweig-MacArthur model for individual patches, we show that the population synchrony and temporal stability, which are believed to be of conflicting outcomes of dispersion, can be simultaneously achieved by oscillation quenching mechanisms. Particularly, we explore the more natural coupling configuration where the rates of dispersal of different habitats are disparate. We show that asymmetry in dispersal rate plays a crucial role in determining inhomogeneity in an otherwise homogeneous metapopulation. We further identify an unusual emergent state in the network, namely, a multi-branch clustered inhomogeneous steady state, which arises due to the intrinsic parameter mismatch among the patches. We believe that the present study will shed light on the cooperative behavior of spatially structured ecosystems. PMID:26520087

  18. Self-consistent mean-field wavefunctions of nucleon and delta for the cranked Chiral soliton bag

    NASA Astrophysics Data System (ADS)

    Post, U.; Mosel, U.

    1989-08-01

    The mean-field equations of the chiral soliton bag model are solved numerically on a full three-dimensional grid by solving the corresponding finite difference equations self-consistently. The spherical hedgehog configuration is found to be the ground state even if deformation degrees of freedom for all fields are allowed for. Individual states describing the nucleon and the delta resonance are obtained using the cranking formalism in isospace. The classical instability of the pion field, which occurs as soon as the angular frequency is larger than the pion mass, is taken into account by an explicit treatment of the asymptotic meson tails for smaller frequencies. A comparison with the perturbative approach used by other authors is given. As an alternative approach we present calculations for baryon states built up from single-quark states of sharp spin and isospin coupled to the corresponding total quantum numbers. As a consequence of the wrong spin-isospin dependence of the short-range qq interaction mediated by the chiral meson fields a negative mass splitting between nucleon and delta is found. Implications on other approaches are discussed.

  19. A Constructive Mean-Field Analysis of Multi-Population Neural Networks with Random Synaptic Weights and Stochastic Inputs

    PubMed Central

    Faugeras, Olivier; Touboul, Jonathan; Cessac, Bruno

    2008-01-01

    We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting activity, a nonlinear function of their membrane potential. At the second (mesoscopic) scale, interacting populations of neurons are described individually by similar equations. The equations describing the dynamical and the stationary mean-field behaviors are considered as functional equations on a set of stochastic processes. Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide a constructive method for effectively computing their unique solution. This method is proved to converge to the unique solution and we characterize its complexity and convergence rate. We also provide partial results for the stationary problem on infinite time intervals. These results shed some new light on such neural mass models as the one of Jansen and Rit (1995): their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis. Our numerical experiments confirm that the framework we propose and the numerical methods we derive from it provide a new and powerful tool for the exploration of neural behaviors at different scales. PMID:19255631

  20. Multidimensionally-constrained relativistic mean-field study of spontaneous fission: Coupling between shape and pairing degrees of freedom

    NASA Astrophysics Data System (ADS)

    Zhao, Jie; Lu, Bing-Nan; Nikšić, Tamara; Vretenar, Dario; Zhou, Shan-Gui

    2016-04-01

    Background: Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Purpose: The aim is to analyze the effects of particle-number fluctuation degrees of freedom on symmetric and asymmetric spontaneous fission (SF) dynamics, and to compare the findings with the results of recent studies based on the self-consistent Hartree-Fock-Bogoliubov (HFB) method. Methods: Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic-mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. Results: The dynamics of spontaneous fission of 264Fm and 250Fm are explored. Fission paths, action integrals, and corresponding half-lives computed in the three-dimensional collective space of shape and pairing coordinates, using the relativistic functional DD-PC1 and a separable pairing force of finite range, are compared with results obtained without pairing fluctuations. Results for 264Fm are also discussed in relation with those recently obtained using the HFB model. Conclusions: The inclusion of pairing correlations in the space of collective coordinates favors axially symmetric shapes along the dynamic path of the fissioning system, amplifies pairing as the path traverses the fission barriers, significantly reduces the action integral, and shortens the

  1. Global simulations of axisymmetric radiative black hole accretion discs in general relativity with a mean-field magnetic dynamo

    NASA Astrophysics Data System (ADS)

    Sądowski, Aleksander; Narayan, Ramesh; Tchekhovskoy, Alexander; Abarca, David; Zhu, Yucong; McKinney, Jonathan C.

    2015-02-01

    We present a mean-field model that emulates the magnetic dynamo operating in magnetized accretion discs. We have implemented this model in the general relativisic radiation magnetohydrodynamic (GRRMHD) code KORAL, using results from local shearing sheet simulations of the magnetorotational instability to fix the parameters of the dynamo. With the inclusion of this dynamo, we are able to run 2D axisymmetric GRRMHD simulations of accretion discs for arbitrarily long times. The simulated discs exhibit sustained turbulence, with the poloidal and toroidal magnetic field components driven towards a state similar to that seen in 3D studies. Using this dynamo code, we present a set of long-duration global simulations of super-Eddington, optically thick discs around non-spinning and spinning black holes. Super-Eddington discs around non-rotating black holes exhibit a surprisingly large efficiency, η ≈ 0.04, independent of the accretion rate, where we measure efficiency in terms of the total energy output, both radiation and mechanical, flowing out to infinity. This value significantly exceeds the efficiency predicted by slim disc models for these accretion rates. Super-Eddington discs around spinning black holes are even more efficient, and appear to extract black hole rotational energy through a process similar to the Blandford-Znajek mechanism. All the simulated models are characterized by highly super-Eddington radiative fluxes collimated along the rotation axis. We also present a set of simulations that were designed to have Eddington or slightly sub-Eddington accretion rates (dot{M} ≲ 2dot{M}_Edd). None of these models reached a steady state. Instead, the discs collapsed as a result of runaway cooling, presumably because of a thermal instability.

  2. A mean field model of the decrease of the specific surface area of dry snow during isothermal metamorphism

    NASA Astrophysics Data System (ADS)

    Legagneux, LoïC.; Domine, Florent

    2005-12-01

    The surface area of snow that is accessible to gases is an essential parameter for quantifying the exchange of trace gases between the snowpack and the atmosphere and is called the specific surface area (SSA). Snow SSA decreases during metamorphism, but this is not described in current snow models owing to the complexity of the physics and geometry of snow. In this paper, we test whether it is possible to model snow SSA changes during isothermal metamorphism without accounting for all the complexity of the three-dimensional (3-D) structure of real snow. We have developed a mean field model of snow metamorphism under isothermal conditions, grounded in the theoretical framework of transient Ostwald ripening and representing snow as a distribution of spherical particles. Analytical expressions of the growth rates of these spheres are obtained, and the evolution of two measurable parameters that characterize snow geometry, the SSA and the distribution of radii of curvature (DRC), are simulated and compared to experimental data obtained by X-ray tomography. The qualitative effects of temperature, snow density, and the condensation coefficient on the rate of SSA decrease are examined. The model predicts very well the rate of evolution of the particle size distribution, which validates our physical description of isothermal metamorphism. In particular, we find that vapor phase diffusion is rate limiting. However, the calculation of the SSA from the DRC appears delicate and evidences too crude approximations in our description of the 3-D geometry of snow. Finally, it is stressed that the initial DRC can greatly influence the rate of SSA decrease, while experimental measurements of the rate of SSA decrease suggest that all snow types evolve in a similar way. It is thus proposed that most natural fresh snows have similar DRCs.

  3. Analytical results for the statistical distribution related to a memoryless deterministic walk: dimensionality effect and mean-field models.

    PubMed

    Terçariol, César Augusto Sangaletti; Martinez, Alexandre Souto

    2005-08-01

    Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go to the nearest point which has not been visited in the preceding mu steps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial nonperiodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parametrized by the normalized incomplete beta function Id= I1/4 [1/2, (d+1) /2] . The joint distribution S(N) (mu,d) (t,p) is relevant, and the marginal distributions previously studied are particular cases. We show that, for the memory-less deterministic tourist walk in the euclidean space, this distribution is Sinfinity(1,d) (t,p) = [Gamma (1+ I(-1)(d)) (t+ I(-1)(d) ) /Gamma(t+p+ I(-1)(d)) ] delta(p,2), where t=0, 1,2, ... infinity, Gamma(z) is the gamma function and delta(i,j) is the Kronecker delta. The mean-field models are the random link models, which correspond to d-->infinity, and the random map model which, even for mu=0 , presents nontrivial cycle distribution [ S(N)(0,rm) (p) proportional to p(-1) ] : S(N)(0,rm) (t,p) =Gamma(N)/ {Gamma[N+1- (t+p) ] N( t+p)}. The fundamental quantities are the number of explored points n(e)=t+p and Id. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.

  4. Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis.

    PubMed

    Cruz, Roberto de la; Guerrero, Pilar; Spill, Fabian; Alarcón, Tomás

    2016-10-21

    We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance

  5. Mean-field modeling of the basal ganglia-thalamocortical system. I Firing rates in healthy and parkinsonian states.

    PubMed

    van Albada, S J; Robinson, P A

    2009-04-21

    Parkinsonism leads to various electrophysiological changes in the basal ganglia-thalamocortical system (BGTCS), often including elevated discharge rates of the subthalamic nucleus (STN) and the output nuclei, and reduced activity of the globus pallidus external (GPe) segment. These rate changes have been explained qualitatively in terms of the direct/indirect pathway model, involving projections of distinct striatal populations to the output nuclei and GPe. Although these populations partly overlap, evidence suggests dopamine depletion differentially affects cortico-striato-pallidal connection strengths to the two pallidal segments. Dopamine loss may also decrease the striatal signal-to-noise ratio, reducing both corticostriatal coupling and striatal firing thresholds. Additionally, nigrostriatal degeneration may cause secondary changes including weakened lateral inhibition in the GPe, and mesocortical dopamine loss may decrease intracortical excitation and especially inhibition. Here a mean-field model of the BGTCS is presented with structure and parameter estimates closely based on physiology and anatomy. Changes in model rates due to the possible effects of dopamine loss listed above are compared with experiment. Our results suggest that a stronger indirect pathway, possibly combined with a weakened direct pathway, is compatible with empirical evidence. However, altered corticostriatal connection strengths are probably not solely responsible for substantially increased STN activity often found. A lower STN firing threshold, weaker intracortical inhibition, and stronger striato-GPe inhibition help explain the relatively large increase in STN rate. Reduced GPe-GPe inhibition and a lower GPe firing threshold can account for the comparatively small decrease in GPe rate frequently observed. Changes in cortex, GPe, and STN help normalize the cortical rate, also in accord with experiments. The model integrates the basal ganglia into a unified framework along with an

  6. Extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model in an oscillating field.

    PubMed

    Robb, Daniel T; Ostrander, Aaron

    2014-02-01

    We present numerical evidence for an extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model driven by an oscillating field. The order parameter, previously taken to be the time-averaged magnetization, comprises the deviations of the Fourier components of the magnetization from their values at the critical period. The conjugate field, previously taken to be the time-averaged magnetic field, comprises the even Fourier components of the field. The scaling exponents β and δ associated with the extended order parameter and conjugate field are shown numerically to be consistent with their values in the equilibrium mean-field model.

  7. Dynamical Landau theory of the glass crossover

    NASA Astrophysics Data System (ADS)

    Rizzo, Tommaso

    2016-07-01

    I introduce a dynamical field theory to describe the glassy behavior in supercooled liquids. The mean-field approximation of the theory predicts a dynamical arrest transition, as in the ideal mode-coupling theory and mean-field discontinuous spin-glass models. Instead, beyond the mean-field approximation, the theory predicts that the transition is avoided and transformed into a crossover, as observed in experiments and simulations. To go beyond mean-field, a standard perturbative loop expansion is performed at first. Approaching the ideal critical point this expansion is divergent at all orders and I show that the leading divergent term at any given order is the same as a dynamical stochastic equation, called stochastic-beta relaxation (SBR) in Europhys. Lett. 106, 56003 (2014), 10.1209/0295-5075/106/56003. At variance with the original theory, SBR can be studied beyond mean-field directly, without the need to resort to a perturbative expansion. Thus it provides a qualitative and quantitative description of the dynamical crossover. For consistency reasons, it is important to establish the connection between the dynamical field theory and SBR beyond perturbation theory. This can be done with the help of a stronger result: the dynamical field theory is exactly equivalent to a theory with quenched disorder. Qualitatively, the nonperturbative mechanism leading to the crossover is therefore the same as the mechanism of SBR. Quantitatively, SBR is equivalent to making the mean-field approximation once the quenched disorder has been generated.

  8. Introduction to Statistical Field Theory

    NASA Astrophysics Data System (ADS)

    Brézin, Edouard

    2010-07-01

    1. A few well-known basic results; 2. Introduction: order parameters, broken symmetries; 3. Examples of physical situations modelled by the Ising model; 4. A few results about the Ising model; 5. High temperature and low temperature expansions; 6. Some geometric problems related to phase transitions; 7. Phenomenological description of the critical behaviour; 8. Mean field theory; 9. Beyond mean field theory; 10. Introduction to the renormalization group; 11. Renormalization group for the φ4 theory; 12. Renormalized theory; 13. Goldstone modes; 14. Large n; Index.

  9. Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization

    NASA Astrophysics Data System (ADS)

    Mehta, Dhagash; Hauenstein, Jonathan D.; Niemerg, Matthew; Simm, Nicholas J.; Stariolo, Daniel A.

    2015-02-01

    Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical study of the finite-size 2-spin spherical model using both numerical polynomial homotopy continuation and a reformulation via non-Hermitian matrices. The continuation approach computes all of the complex stationary points of this model while the matrix approach computes the real stationary points. Using these methods, we compute the average number of stationary points while changing the topology of the PEL as well as the variance. Histograms of these stationary points are presented along with an analysis regarding the complex stationary points. This work connects topology trivialization to two different branches of mathematics: algebraic geometry and catastrophe theory, which is fertile ground for further interdisciplinary research.

  10. Competing Orders in a Dipolar Bose - Fermi Mixture on a Square Optical Lattice: Mean-Field Perspective

    NASA Astrophysics Data System (ADS)

    Ling, Hong; Scaramaazza, Jasen; Kain, Ben

    2015-05-01

    We study superfluid pairings of two-component fermions interacting by exchanging virtual phonons of a dipolar condensate in an optical lattice that preserves the symmetry of D4. We construct, within the Hartree-Fock-Bogoliubov theory, the matrix representation of the linearized gap equation in the irreducible representations of D4. We find that each matrix element, which is a four-dimensional (4D) integral in momentum space, can be put in a separable form involving a 1D integral, which is only a function of temperature and the chemical potential, and a pairing-specific ``effective'' interaction, which is an analytical function of the parameters that characterize Fermi-Fermi interactions. We analyze the critical temperatures of various competing orders (superfluids with s-, dx2-y2-, dxy-, and g-wave symmetries and density waves) as functions of different system parameters in both the absence and presence of the dipolar interaction. We find that tuning a dipolar interaction can dramatically enhance various unconventional pairings. KITP, University of Santa Barbara; ITAMP, Harvard-Smithsonian Center for Astrophysics.

  11. Relativistic mean-field study of the properties of Z=117 nuclei and the decay chains of the {sup 293,294}117 isotopes

    SciTech Connect

    Bhuyan, M.; Patra, S. K.; Gupta, Raj K.

    2011-07-15

    We have calculated the binding energy, root-mean-square radius, and quadrupole deformation parameter for the recently synthesized superheavy element Z=117, using the axially deformed relativistic mean-field (RMF) model. The calculation is extended to various isotopes of the Z=117 element, starting from A=286 till A=310. We predict almost spherical structures in the ground state for almost all the isotopes. A shape transition appears at about A=292 from a prolate to an oblate shape structure of the Z=117 nucleus in our mean-field approach. The most stable isotope (largest binding energy per nucleon) is found to be the {sup 288}117 nucleus. Also, the Q{sub {alpha}} values and the half-life T{sub 1/2}{sup {alpha}} for the {alpha}-decay chains of {sup 293}117 and {sup 294}117 are calculated, supporting the magic numbers at N=172 and/or 184.

  12. Decoupling electrons and nuclei without the Born-Oppenheimer approximation: The electron-nucleus mean-field configuration-interaction method

    NASA Astrophysics Data System (ADS)

    Cassam-Chenaï, Patrick; Suo, Bingbing; Liu, Wenjian

    2015-07-01

    We introduce the electron-nucleus mean-field configuration-interaction (EN-MFCI) approach. It consists in building an effective Hamiltonian for the electrons taking into account a mean field due to the nuclear motion and, conversely, in building an effective Hamiltonian for the nuclear motion taking into account a mean field due to the electrons. The eigenvalue problems of these Hamiltonians are solved in basis sets giving partial eigensolutions for the active degrees of freedom (DOF's), that is to say, either for the electrons or for nuclear motion. The process can be iterated or electron and nuclear motion DOF's can be contracted in a CI calculation. In the EN-MFCI reduction of the molecular Schrödinger equation to an electronic and a nuclear problem, the electronic wave functions do not depend parametrically upon nuclear coordinates. So, it is different from traditional adiabatic methods. Furthermore, when contracting electronic and nuclear functions, a direct product basis set is built in contrast with methods which treat electrons and nuclei on the same footing, but where electron-nucleus explicitly correlated coordinates are used. Also, the EN-MFCI approach can make use of the partition of molecular DOF's into translational, rotational, and internal DOF's. As a result, there is no need to eliminate translations and rotations from the calculation, and the convergence of vibrational levels is facilitated by the use of appropriate internal coordinates. The method is illustrated on diatomic molecules.

  13. Large Deviations for Finite State Markov Jump Processes with Mean-Field Interaction Via the Comparison Principle for an Associated Hamilton-Jacobi Equation

    NASA Astrophysics Data System (ADS)

    Kraaij, Richard

    2016-07-01

    We prove the large deviation principle (LDP) for the trajectory of a broad class of finite state mean-field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well as Curie-Weiss spin flip dynamics with singular jump rates. The main step in the proof of the LDP, which is of independent interest, is the proof of the comparison principle for an associated collection of Hamilton-Jacobi equations. Additionally, we show that the LDP provides a general method to identify a Lyapunov function for the associated McKean-Vlasov equation.

  14. Present status of the theory of the high-Tc cuprates

    NASA Astrophysics Data System (ADS)

    Anderson, P. W.

    2006-04-01

    The Gutzwiller-projected mean-field theory, also called plain vanilla or renormalized mean-field theory, is explained, and its successes and possible extensions in describing the phenomenology of the cuprate superconductors are discussed. Throughout, we emphasize that while this is a Hartree-Fock-based BCS theory, it embodies fundamental differences from conventional perturbative many-body theory which may be characterized by calling it a theory of the doped Mott insulator.

  15. Anomalous diffusion in the evolution of soccer championship scores: Real data, mean-field analysis, and an agent-based model

    NASA Astrophysics Data System (ADS)

    da Silva, Roberto; Vainstein, Mendeli H.; Gonçalves, Sebastián; Paula, Felipe S. F.

    2013-08-01

    Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva , Comput. Phys. Commun.CPHCBZ0010-465510.1016/j.cpc.2012.10.030 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.

  16. Dynamics of Impurity and Valence Bands in Ga1-xMnxAs Within the Dynamical Mean-Field Approximation

    SciTech Connect

    Majidi, M. A.; Moreno, Juana; Jarrell, Mark; Fishman, Randy Scott; Aryanpour, K. A.

    2006-08-01

    We calculate the density-of-states and the spectral function of Ga1−xMnxAs within the dynamical mean-field approximation. Our model includes the competing effects of the strong spin-orbit coupling on the J=3/2 GaAs hole bands and the exchange interaction between the magnetic ions and the itinerant holes. We study the quasiparticle and impurity bands in the paramagnetic and ferromagnetic phases for different values of impurity-hole coupling Jc at a Mn doping of x=0.05. By analyzing the anisotropic angular distribution of the impurity band carriers at T=0, we conclude that the carrier polarization is optimal when the carriers move along the direction parallel to the average magnetization.

  17. A stochastically forced time delay solar dynamo model: Self-consistent recovery from a maunder-like grand minimum necessitates a mean-field alpha effect

    SciTech Connect

    Hazra, Soumitra; Nandy, Dibyendu; Passos, Dário E-mail: dariopassos@ist.utl.pt

    2014-07-01

    Fluctuations in the Sun's magnetic activity, including episodes of grand minima such as the Maunder minimum have important consequences for space and planetary environments. However, the underlying dynamics of such extreme fluctuations remain ill-understood. Here, we use a novel mathematical model based on stochastically forced, non-linear delay differential equations to study solar cycle fluctuations in which time delays capture the physics of magnetic flux transport between spatially segregated dynamo source regions in the solar interior. Using this model, we explicitly demonstrate that the Babcock-Leighton poloidal field source based on dispersal of tilted bipolar sunspot flux, alone, cannot recover the sunspot cycle from a grand minimum. We find that an additional poloidal field source effective on weak fields—e.g., the mean-field α effect driven by helical turbulence—is necessary for self-consistent recovery of the sunspot cycle from grand minima episodes.

  18. A mean field model of ligand-protein interactions: implications for the structural assessment of human immunodeficiency virus type 1 protease complexes and receptor-specific binding.

    PubMed Central

    Verkhivker, G M; Rejto, P A

    1996-01-01

    We propose a general mean field model of ligand-protein interactions to determine the thermodynamic equilibrium of a system at finite temperature. The method is employed in structural assessments of two human immuno-deficiency virus type 1 protease complexes where the gross effects of protein flexibility are incorporated by utilizing a data base of crystal structures. Analysis of the energy spectra for these complexes has revealed that structural and thermo-dynamic aspects of molecular recognition can be rationalized on the basis of the extent of frustration in the binding energy landscape. In particular, the relationship between receptor-specific binding of these ligands to human immunodeficiency virus type 1 protease and a minimal frustration principle is analyzed. Images Fig. 4 PMID:8552675

  19. A Coupled Mean Field / Gurson-Tvergaard Micromechanical Model For Ductile Fracture In Multiphase Materials With Large Volume Fraction of Voids

    NASA Astrophysics Data System (ADS)

    Van Hoof, Thibaut; Piérard, Olivier; Lani, Frédéric

    2007-04-01

    In the framework of the European project PROHIPP (New design and manufacturing processes for high pressure fluid power product — NMP 2-CT-2004-50546), CENAERO develops a library of constitutive models used to predict the mechanical response of a family of cast iron. The present contribution focuses on one particular microstructure, corresponding to a ferrite matrix containing spheroidal graphite and isolated inclusions of pearlite. An incremental mean field homogenisation scheme such as the one developed by Doghri and Ouaar is used. In the present application, the ferrite matrix is described by a Gurson type constitutive law (porous plasticity) while the pearlite inclusions are assumed to obey the classical isotropic J2 plasticity. The predictions of the micromechanical model are compared to the results of Finite Element simulations performed on three-dimensional representative volume elements (RVEs).

  20. Off-shell effects in the relativistic mean field model and their role in CC (anti)neutrino scattering at MiniBooNE kinematics

    NASA Astrophysics Data System (ADS)

    Ivanov, M. V.; González-Jiménez, R.; Caballero, J. A.; Barbaro, M. B.; Donnelly, T. W.; Udías, J. M.

    2013-11-01

    The relativistic mean field (RMF) model is used to describe nucleons in the nucleus and thereby to evaluate the effects of having dynamically off-shell spinors. Compared with free, on-shell nucleons as employed in some other models, within the RMF nucleons are described by relativistic spinors with strongly enhanced lower components. In this work it is seen that for MiniBooNE kinematics, neutrino charged-current quasielastic cross sections show some sensitivity to these off-shell effects, while for the antineutrino-nucleus case the total cross sections are seen to be essentially independent of the enhancement of the lower components. As was found to be the case when comparing the RMF results with the neutrino-nucleus data, the present impulse approximation predictions within the RMF also fall short of the MiniBooNE antineutrino-nucleus data.

  1. Configuration mixing of angular-momentum-projected triaxial relativistic mean-field wave functions. II. Microscopic analysis of low-lying states in magnesium isotopes

    SciTech Connect

    Yao, J. M.; Mei, H.; Chen, H.; Meng, J.; Ring, P.; Vretenar, D.

    2011-01-15

    The recently developed structure model that uses the generator coordinate method to perform configuration mixing of angular-momentum projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes (3DAMP+GCM), is applied in a systematic study of ground states and low-energy collective states in the even-even magnesium isotopes {sup 20-40}Mg. Results obtained using a relativistic point-coupling nucleon-nucleon effective interaction in the particle-hole channel and a density-independent {delta} interaction in the pairing channel are compared to data and with previous axial 1DAMP+GCM calculations, both with a relativistic density functional and the nonrelativistic Gogny force. The effects of the inclusion of triaxial degrees of freedom on the low-energy spectra and E2 transitions of magnesium isotopes are examined.

  2. Ab initio theory of concentration fluctuations in random alloys

    SciTech Connect

    Stocks, G.M.; Nicholson, D.M.; Gyorffy, B.L.; Wadsworth, J.S.

    1986-01-01

    This document consists of equations for the electronic mean field theory, electronic grand potential, Feynman-Pierles variational theorem, self-consistent KKR-CPa, KKR-CPA theory of direct correlation functions, first-principles Landau theory, and first-principles Cahn-Hilliard theory.

  3. Transition Helmholtz free energy, entropy, and heat capacity of free-standing smectic films in water: A mean-field treatment

    SciTech Connect

    Śliwa, Izabela; Zakharov, A. V.

    2014-11-21

    Using the extended McMillan's mean field approach with anisotropic forces a study of both the structural and thermodynamic properties of free-standing smectic film (FSSF) in water on heating to the isotropic temperature is carried out numerically. By solving the self-consistent nonlinear equations for the order parameters, we obtained that the smectic-A-isotropic (AI) transition occurs through the series of layer-thinning transitions causing the films to thin in the stepwise manner as the temperature is increased above the bulk smectic-A-isotropic temperature T{sub AI}(bulk). With enhanced pair interactions in the bounding layers, the smectic-isotropic transition corresponds to smectic melting of the central layers. The effects of surface “enhanced” pair interactions in the bounding layers and of film thickness on the orientational and translational order parameters, the Helmholtz free energy and entropy, as well as the temperature dependence of the heat capacity of FSSFs, have also been investigated. Reasonable agreement between the theoretically predicted and the experimentally obtained – by means of optical microscopy and ellipsometry techniques – data of the temperature when the thin decylcyanobiphenyl smectic film immersing in water ruptures has been obtained.

  4. Ab initio implementation of quantum trajectory mean-field approach and dynamical simulation of the N{sub 2}CO photodissociation

    SciTech Connect

    Xie, Binbin; Liu, Lihong; Cui, Ganglong; Fang, Wei-Hai; Cao, Jun; Feng, Wei; Li, Xin-qi

    2015-11-21

    In this work, the recently introduced quantum trajectory mean-field (QTMF) approach is implemented and employed to explore photodissociation dynamics of diazirinone (N{sub 2}CO), which are based on the high-level ab initio calculation. For comparison, the photodissociation process has been simulated as well with the fewest-switches surface hopping (FSSH) and the ab initio multiple spawning (AIMS) methods. Overall, the dynamical behavior predicted by the three methods is consistent. The N{sub 2}CO photodissociation at λ > 335 nm is an ultrafast process and the two C—N bonds are broken in a stepwise way, giving birth to CO and N{sub 2} as the final products in the ground state. Meanwhile, some noticeable differences were found in the QTMF, FSSH, and AIMS simulated time constants for fission of the C—N bonds, excited-state lifetime, and nonadiabatic transition ratios in different intersection regions. These have been discussed in detail. The present study provides a clear evidence that direct ab initio QTMF approach is one of the reliable tools for simulating nonadiabatic dynamics processes.

  5. Transition Helmholtz free energy, entropy, and heat capacity of free-standing smectic films in water: a mean-field treatment.

    PubMed

    Śliwa, Izabela; Zakharov, A V

    2014-11-21

    Using the extended McMillan's mean field approach with anisotropic forces a study of both the structural and thermodynamic properties of free-standing smectic film (FSSF) in water on heating to the isotropic temperature is carried out numerically. By solving the self-consistent nonlinear equations for the order parameters, we obtained that the smectic-A-isotropic (AI) transition occurs through the series of layer-thinning transitions causing the films to thin in the stepwise manner as the temperature is increased above the bulk smectic-A-isotropic temperature TAI(bulk). With enhanced pair interactions in the bounding layers, the smectic-isotropic transition corresponds to smectic melting of the central layers. The effects of surface "enhanced" pair interactions in the bounding layers and of film thickness on the orientational and translational order parameters, the Helmholtz free energy and entropy, as well as the temperature dependence of the heat capacity of FSSFs, have also been investigated. Reasonable agreement between the theoretically predicted and the experimentally obtained - by means of optical microscopy and ellipsometry techniques - data of the temperature when the thin decylcyanobiphenyl smectic film immersing in water ruptures has been obtained.

  6. Study of pK values and effective dielectric constants of ionizable residues in pentapeptides and in staphylococcal nuclease (SNase) using a mean-field approach.

    PubMed

    Bossa, Guilherme Volpe; Fahr, Alfred; Pereira de Souza, Tereza

    2014-04-17

    The determination of pK values of amino acid residues as a function of temperature and ionic concentration is crucial to understanding the dynamics of various biological processes such as adsorption of peptides and their interactions with active sites of enzymes. In this study we developed a mean-field model to calculate the position-dependent dielectric constants of ionizable groups and the mean electrostatic potential on the surface. Such potential, which takes into account the contributions exerted by neighboring groups and ions in solution, is responsible for the fine-tuning of the pK value of each residue. The proposed model was applied to the amino acids Asp, Glu, Lys, His, Tyr, and Cys, and since the results were consistent with experimentally obtained values, the model was extended and applied to computation of pK values of Gly and Ala pentapeptides and of ionizable residues of the enzyme staphylococcal nuclease (SNase). In this latter case, we used an approach similar to a first-neighbors approximation, and the results turned out to be in good agreement with previously reported data when considering only the interactions of charged groups located at distances of maximally 20 Å. These considerations and the little computational cost involved turn the suggested approach into a promising tool for the modeling of force fields in computational simulations.

  7. Finite-temperature exact diagonalization cluster dynamical mean-field study of the two-dimensional Hubbard model: Pseudogap, non-Fermi-liquid behavior, and particle-hole asymmetry

    NASA Astrophysics Data System (ADS)

    Liebsch, Ansgar; Tong, Ning-Hua

    2009-10-01

    The effect of doping in the two-dimensional Hubbard model is studied within finite-temperature exact diagonalization combined with cluster dynamical mean-field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green’s function onto 2×2 clusters, a considerably more accurate description of the low-frequency properties of the self-energy is achieved than in a pure site picture. To evaluate the phase diagram, the transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest-neighbor hopping, and temperature. The self-energy component ΣX associated with X=(π,0) is shown to develop a collective mode above EF , whose energy and strength exhibits a distinct dispersion with doping. This low-energy excitation gives rise to non-Fermi-liquid behavior as the hole doping decreases below a critical value δc , and to an increasing particle-hole asymmetry, in agreement with recent photoemission data. This behavior is consistent with the removal of spectral weight from electron states above EF and the opening of a pseudogap, which increases with decreasing doping. The phase diagram reveals that δc≈0.15…0.20 for various system parameters. For electron doping, the collective mode of ΣX(ω) and the concomitant pseudogap are located below the Fermi energy, which is consistent with the removal of spectral weight from the hole states just below EF . The critical doping, which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.

  8. Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

    NASA Astrophysics Data System (ADS)

    Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Sleigh, J. W.

    2013-04-01

    Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the

  9. Generic constraints on the relativistic mean-field and Skyrme-Hartree-Fock models from the pure neutron matter equation of state

    NASA Astrophysics Data System (ADS)

    Fattoyev, F. J.; Newton, W. G.; Xu, Jun; Li, Bao-An

    2012-08-01

    We study the nuclear symmetry energy S(ρ) and related quantities of nuclear physics and nuclear astrophysics predicted generically by relativistic mean-field (RMF) and Skyrme-Hartree-Fock (SHF) models. We establish a simple prescription for preparing equivalent RMF and SHF parametrizations starting from a minimal set of empirical constraints on symmetric nuclear matter, nuclear binding energy, and charge radii, enforcing equivalence of their Lorenz effective masses, and then using the pure neutron matter (PNM) equation of state obtained from ab initio calculations to optimize the pure isovector parameters in the RMF and SHF models. We find that the resulting RMF and SHF parametrizations give broadly consistent predictions of the symmetry energy J and its slope parameter L at saturation density within a tight range of ≲2 and ≲6 MeV, respectively, but that clear model dependence shows up in the predictions of higher-order symmetry energy parameters, leading to important differences in (a) the slope of the correlation between J and L from the confidence ellipse, (b) the isospin-dependent part of the incompressibility of nuclear matter Kτ, (c) the symmetry energy at suprasaturation densities, and (d) the predicted neutron star radii. The model dependence can lead to about 1-2 km difference in predictions of the neutron star radius given identical predicted values of J and L and symmetric nuclear matter (SNM) saturation properties. Allowing the full freedom in the effective masses in both models leads to constraints of 30≲J≲31.5 MeV, 35≲L≲60 MeV, and -330≲Kτ≲-216 MeV for the RMF model as a whole and 30≲J≲33 MeV, 28≲L≲65 MeV, and -420≲Kτ≲-325 MeV for the SHF model as a whole. Notably, given PNM constraints, these results place RMF and SHF models as a whole at odds with some constraints on Kτ inferred from giant monopole resonance and neutron skin experimental results.

  10. Utilizing satellite precipitation estimates for streamflow forecasting via adjustment of mean field bias in precipitation data and assimilation of streamflow observations

    NASA Astrophysics Data System (ADS)

    Lee, Haksu; Zhang, Yu; Seo, Dong-Jun; Xie, Pingping

    2015-10-01

    This study explores mitigating bias in satellite quantitative precipitation estimates (SQPE) and improving hydrologic predictions at ungauged locations via adjustment of the mean field bias (MFB) in SQPE and data assimilation (DA) of streamflow observations in a distributed hydrologic model. In this study, a variational procedure is used to adjust MFB in Climate Prediction Center MORPHing (CMORPH) SQPE and assimilate streamflow observations at the outlet of Elk River Basin in Missouri into the distributed Sacramento Soil Moisture Accounting (SAC-SMA) and kinematic wave routing models. The benefits of assimilation are assessed by comparing the streamflow predictions with or without DA at both the outlet and an upstream location, and by comparing the soil moisture grids forced by CMORPH SQPE against those forced by higher-quality multisensor quantitative precipitation estimates (MQPE) from National Weather Service. Special attention is given to the dependence of the efficacy of DA on the quality and latency of the SQPE, and the impact of dynamic correction of MFB in the SQPE via DA. The results show that adjusting MFB in CMORPH SQPE in addition to assimilating outlet flow reduces 66% of the bias in the CMORPH SQPE analysis and the RMSE of 12-h streamflow predictions by 81% at the outlet and 34-62% at interior locations of the catchment. Compared to applying a temporally invariant MFB for the entire storm, the DA-based, dynamic MFB correction reduces the RMSE of 6-h streamflow prediction by 63% at the outlet and 39-69% at interior locations. It is also shown that the accuracy of streamflow prediction deteriorates if the delineation of the precipitation area by CMORPH SQPE is significantly different, as measured by the Hausdorff distance, from that by MQPE. When compared with adjusting MFB in the CMORPH SQPE over the entire assimilation window, adjusting the MFB for all but the latest 18 h (i.e., the latency of CMORPH SQPE) within the assimilation window reduces the

  11. Symmetry energy of cold nucleonic matter within a relativistic mean field model encapsulating effects of high-momentum nucleons induced by short-range correlations

    NASA Astrophysics Data System (ADS)

    Cai, Bao-Jun; Li, Bao-An

    2016-01-01

    It is well known that short-range nucleon-nucleon correlations (SRC) from the tensor components and/or the repulsive core of nuclear forces lead to a high- (low-)momentum tail (depletion) in the single-nucleon momentum distribution above (below) the nucleon Fermi surface in cold nucleonic matter. Significant progress was made recently in constraining the isospin-dependent parameters characterizing the SRC-modified single-nucleon momentum distribution in neutron-rich nucleonic matter using both experimental data and microscopic model calculations. Using the constrained single-nucleon momentum distribution in a nonlinear relativistic mean field (RMF) model, we study the equation of state (EOS) of asymmetric nucleonic matter (ANM), especially the density dependence of nuclear symmetry energy Esym(ρ ) . First, as a test of the model, the average nucleon kinetic energy extracted recently from electron-nucleus scattering experiments using a neutron-proton dominance model is well reproduced by the RMF model incorporating effects of the SRC-induced high-momentum nucleons, while it is significantly under predicted by the RMF model using a step function for the single-nucleon momentum distribution as in free Fermi gas (FFG) models. Second, consistent with earlier findings within nonrelativistic models, the kinetic symmetry energy of quasinucleons is found to be Esymkin(ρ0) =-16.94 ±13.66 MeV which is dramatically different from the prediction of Esymkin(ρ0) ≈12.5 MeV by FFG models at nuclear matter saturation density ρ0=0.16 fm-3 . Third, comparing the RMF calculations with and without the high-momentum nucleons using two sets of model parameters both reproducing identically all empirical constraints on the EOS of symmetric nuclear matter (SNM) and the symmetry energy of ANM at ρ0, the SRC-modified single-nucleon momentum distribution is found to make the Esym(ρ ) more concave around ρ0 by softening it significantly at both subsaturation and suprasaturation

  12. Modeling the magnetic isotherms of (La0.56Ce0.14)Sr0.30MnO3 by a mean-field scaling method and estimation of magnetic entropy change

    NASA Astrophysics Data System (ADS)

    Yahyaoui, S.; Khalfaoui, M.; Kallel, S.; Kallel, N.; Amaral, J. S.; Ben Lamine, A.

    2015-11-01

    We report a study on the magnetic properties of the (La0.56Ce0.14)Sr0.30MnO3 perovskite, by a mean-field method. By scaling of the experimental magnetization data, the mean-field exchange parameter λ and the BS function of the equation of state BS [ (H +Hexch) / T ] are directly determined, as well as the order of the phase transition. The spin quantum number of the manganite has been also determined. The mean-field scaling has been used to estimate magnetic entropy change (- ΔSM) within the thermodynamics of the model and without using the usual numerical integration of a Maxwell relation. The maxima of the positive absolute value of (- ΔSM) upon variation of the applied magnetic field at 1 and 5 T are about 1.68 and 5.04 J kg-1 K-1, respectively. Satisfactory agreement between the mean-field model and experimental behavior has been found.

  13. Efficient perturbation theory for quantum lattice models.

    PubMed

    Hafermann, H; Li, G; Rubtsov, A N; Katsnelson, M I; Lichtenstein, A I; Monien, H

    2009-05-22

    We present a novel approach to long-range correlations beyond dynamical mean-field theory, through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Néel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte Carlo results. An illustration of how the approach captures and allows us to distinguish short- and long-range correlations is given.

  14. Application of an Extended Parabolic Equation to the Calculation of the Mean Field and the Transverse and Longitudinal Mutual Coherence Functions Within Atmospheric Turbulence

    NASA Technical Reports Server (NTRS)

    Manning, Robert M.

    2005-01-01

    Solutions are derived for the generalized mutual coherence function (MCF), i.e., the second order moment, of a random wave field propagating through a random medium within the context of the extended parabolic equation. Here, "generalized" connotes the consideration of both the transverse as well as the longitudinal second order moments (with respect to the direction of propagation). Such solutions will afford a comparison between the results of the parabolic equation within the pararaxial approximation and those of the wide-angle extended theory. To this end, a statistical operator method is developed which gives a general equation for an arbitrary spatial statistical moment of the wave field. The generality of the operator method allows one to obtain an expression for the second order field moment in the direction longitudinal to the direction of propagation. Analytical solutions to these equations are derived for the Kolmogorov and Tatarskii spectra of atmospheric permittivity fluctuations within the Markov approximation.

  15. Correlation of electronic structure and magnetic moment in Ga1-xMnxN : First-principles, mean field and high temperature series expansions calculations

    NASA Astrophysics Data System (ADS)

    Masrour, R.; Hlil, E. K.

    2016-08-01

    Self-consistent ab initio calculations based on density-functional theory and using both full potential linearized augmented plane wave and Korring-Kohn-Rostoker-coherent potential approximation methods, are performed to investigate both electronic and magnetic properties of the Ga1-xMnxN system. Magnetic moments considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters such as the magnetic phase diagram and the critical exponent. The increasing of the dilution x in this system has allowed to verify a series of HTSEs predictions on the possibility of ferromagnetism in dilute magnetic insulators and to demonstrate that the interaction changes from antiferromagnetic to ferromagnetic passing through the spins glace phase.

  16. Microscopic study of low-lying spectra of Λ hypernuclei based on a beyond-mean-field approach with a covariant energy density functional

    NASA Astrophysics Data System (ADS)

    Mei, H.; Hagino, K.; Yao, J. M.; Motoba, T.

    2015-06-01

    We present a detailed formalism of the microscopic particle-rotor model for hypernuclear low-lying states based on a covariant density functional theory. In this method, the hypernuclear states are constructed by coupling a hyperon to low-lying states of the core nucleus, which are described by the generator coordinate method (GCM) with the particle number and angular momentum projections. We apply this method to study in detail the low-lying spectrum of C13Λ and Ne21Λ hypernuclei. We also briefly discuss the structure of Sm155Λ as an example of heavy deformed hypernuclei. It is shown that the low-lying excitation spectra with positive-parity states of the hypernuclei, which are dominated by Λ hyperon in the s orbital coupled to the core states, are similar to that for the corresponding core states, while the electric quadrupole transition strength, B (E 2 ) , from the 21+ state to the ground state is reduced according to the mass number of the hypernuclei. Our study indicates that the energy splitting between the first 1 /2- and 3 /2- hypernuclear states is generally small for all the hypernuclei which we study. However, their configurations depend much on the properties of a core nucleus, in particular on the sign of deformation parameter. That is, the first 1 /2- and 3 /2- states in Λ13C are dominated by a single configuration with Λ particle in the p -wave orbits and thus provide good candidates for a study of the Λ spin-orbit splitting. On the other hand, those states in the other hypernuclei exhibit a large configuration mixing and thus their energy difference cannot be interpreted as the spin-orbit splitting for the p orbits.

  17. CONNECTING LOCAL STRUCTURE TO INTERFACE FORMATION: A Molecular Scale van der Waals Theory of Nonuniform Liquids

    NASA Astrophysics Data System (ADS)

    Weeks, John D.

    2002-10-01

    This article reviews a new and general theory of nonuniform fluids that naturally incorporates molecular scale information into the classical van der Waals theory of slowly varying interfaces. The method optimally combines two standard approximations, molecular (mean) field theory to describe interface formation and linear response (or Gaussian fluctuation) theory to describe local structure. Accurate results have been found in many different applications in nonuniform simple fluids and these ideas may have important implications for the theory of hydrophobic interactions in water.

  18. Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

    NASA Technical Reports Server (NTRS)

    Wolpert, David H.

    2005-01-01

    A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.

  19. Slave boson theories of correlated electron systems

    SciTech Connect

    Woelfle, P.

    1995-05-01

    Slave boson theories of various models of correlated fermions are critically reviewed and several new results are presented. In the example of the Anderson impurity model the limitations of slave boson mean field theory are discussed. Self-consistent conserving approximations are compared with results obtained from the numerical renormalization group. The gauge field theory of the t-J-model is considered in the quasistatic approximation. It is shown that weak localization effects can give valuable information on the existence of gauge fields. Applications of the slave-boson approach due to Kotliar and Ruckenstein to the Hubbard model are also discussed.

  20. Magnetic and antimagnetic rotation in covariant density functional theory

    SciTech Connect

    Zhao, P. W.; Liang, H. Z.; Peng, J.; Ring, P.; Zhang, S. Q.; Meng, J.

    2012-10-20

    Progress on microscopic and self-consistent description of the magnetic rotation and antimagnetic rotation phenomena in tilted axis cranking relativistic mean-field theory based on a point-coupling interaction are briefly reviewed. In particular, the microscopic pictures of the shears mechanism in {sup 60}Ni and the two shears-like mechanism in {sup 105}Cd are discussed.