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Sample records for nuclear hamiltonian ab

  1. Ab Initio Neutron Drops with Chiral Hamiltonians

    NASA Astrophysics Data System (ADS)

    Potter, Hugh; Maris, Pieter; Vary, James

    2015-04-01

    Ab initio calculations for neutron drops are of interest for insights into neutron-rich nuclei and neutron star matter, and for examining the neutron-only sector of nucleon-nucleon and 3-nucleon interactions. I present ab initio results calculated using the no-core shell model with 2- and 3-body chiral Hamiltonians for neutron drops up to 20 neutrons confined in a 10 MeV harmonic trap. I discuss ground state energies, internal energies, radii, and evidence for pairing. In addition, excitation energies can be used to investigate the spin-orbit splittings in the p-shell and sd -shell. Prior Green's Function Monte Carlo calculations using the Argonne v8' potential with added 3-nucleon forces serve as a comparison. Supported by DOE Grants DESC0008485 (SciDAC/NUCLEI), DE-FG02-87ER40371, and NSF Grant 0904782; computational resources provided by the Oak Ridge Leadership Computing Facility (DOE Office of Science Contract DE-AC05-00OR22725) under an INCITE award.

  2. Construction of diabatic Hamiltonian matrix from ab initio calculated molecular symmetry adapted nonadiabatic coupling terms and nuclear dynamics for the excited states of Na3 cluster.

    PubMed

    Mukherjee, Saikat; Bandyopadhyay, Sudip; Paul, Amit Kumar; Adhikari, Satrajit

    2013-04-25

    We present the molecular symmetry (MS) adapted treatment of nonadiabatic coupling terms (NACTs) for the excited electronic states (2(2)E' and 1(2)A1') of Na3 cluster, where the adiabatic potential energy surfaces (PESs) and the NACTs are calculated at the MRCI level by using an ab initio quantum chemistry package (MOLPRO). The signs of the NACTs at each point of the configuration space (CS) are determined by employing appropriate irreducible representations (IREPs) arising due to MS group, and such terms are incorporated into the adiabatic to diabatic transformation (ADT) equations to obtain the ADT angles. Since those sign corrected NACTs and the corresponding ADT angles demonstrate the validity of curl condition for the existence of three-state (2(2)E' and 1(2)A1') sub-Hilbert space, it becomes possible to construct the continuous, single-valued, symmetric, and smooth 3 × 3 diabatic Hamiltonian matrix. Finally, nuclear dynamics has been carried out on such diabatic surfaces to explore whether our MS-based treatment of diabatization can reproduce the pattern of the experimental spectrum for system B of Na3 cluster. PMID:23521047

  3. Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

    NASA Astrophysics Data System (ADS)

    Fang, Shiang; Kuate Defo, Rodrick; Shirodkar, Sharmila N.; Lieu, Simon; Tritsaris, Georgios A.; Kaxiras, Efthimios

    2015-11-01

    We present an accurate ab initio tight-binding Hamiltonian for the transition metal dichalcogenides, MoS2, MoSe2, WS2, WSe2, with a minimal basis (the d orbitals for the metal atoms and p orbitals for the chalcogen atoms) based on a transformation of the Kohn-Sham density functional theory Hamiltonian to a basis of maximally localized Wannier functions. The truncated tight-binding Hamiltonian, with only on-site, first, and partial second neighbor interactions, including spin-orbit coupling, provides a simple physical picture and the symmetry of the main band-structure features. Interlayer interactions between adjacent layers are modeled by transferable hopping terms between the chalcogen p orbitals. The full-range tight-binding Hamiltonian can be reduced to hybrid-orbital k .p effective Hamiltonians near the band extrema that capture important low-energy excitations. These ab initio Hamiltonians can serve as the starting point for applications to interacting many-body physics including optical transitions and Berry curvature of bands, of which we give some examples.

  4. Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory

    SciTech Connect

    Vary, J. P.; Maris, P.; Honkanen, H.; Li, J.; Shirokov, A. M.; Brodsky, S. J.; Harindranath, A.

    2009-12-17

    Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually, we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements.

  5. Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory

    SciTech Connect

    Vary, J.P.; Maris, P.; Shirokov, A.M.; Honkanen, H.; li, J.; Brodsky, S.J.; Harindranath, A.; Teramond, G.F.de; /Costa Rica U.

    2009-08-03

    Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually,we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements.

  6. Ab initio study of neutron drops with chiral Hamiltonians

    NASA Astrophysics Data System (ADS)

    Potter, H. D.; Fischer, S.; Maris, P.; Vary, J. P.; Binder, S.; Calci, A.; Langhammer, J.; Roth, R.

    2014-12-01

    We report ab initio calculations for neutron drops in a 10 MeV external harmonic-oscillator trap using chiral nucleon-nucleon plus three-nucleon interactions. We present total binding energies, internal energies, radii and odd-even energy differences for neutron numbers N = 2- 18 using the no-core shell model with and without importance truncation. Furthermore, we present total binding energies for N = 8 , 16 , 20 , 28 , 40 , 50 obtained in a coupled-cluster approach. Comparisons with quantum Monte Carlo results, where available, using Argonne v8‧ with three-nucleon interactions reveal important dependences on the chosen Hamiltonian.

  7. Ab initio nuclear structure theory

    NASA Astrophysics Data System (ADS)

    Negoita, Gianina Alina

    Ab initio no core methods have become major tools for understanding the properties of light nuclei based on realistic nucleon-nucleon (NN) and three-nucleon (NNN) interactions. A brief description is provided for the inter-nucleon interactions that fit two-body scattering and bound state data, as well as NNN interactions. Major new progress, including the goal of applying these interactions to solve for properties of nuclei, is limited by convergence issues. That is, with the goal of obtaining high precision solutions of the nuclear many-body Hamiltonian with no core methods (all nucleons treated on the same footing), one needs to proceed to very large basis spaces to achieve a convergence pattern suitable for extrapolation to the exact result. This thesis investigates (1) the similarity renormalization group (SRG) approach to soften the interaction, while preserving its phase shift properties, and (2) adoption of a realistic basis space using Woods-Saxon (WS) single-particle wavefunctions. Both have their advantages and limitations, discussed here. For (1), SRG was demonstrated by applying it to a realistic NN interaction, JISP16, in a harmonic oscillator (HO) representation. The degree of interaction softening achieved through a regulator parameter is examined. For (2), new results are obtained with the realistic JISP16 NN interaction in ab initio calculations of light nuclei 4He, 6He and 12C, using a WS basis optimized to minimize the ground-state energy within the truncated no core shell model. These are numerically-intensive many-body calculations. Finally, to gain insight into the potential for no core investigations of heavier nuclei, an initial investigation was obtained for the odd mass A = 47 - 49 region nuclei straddling 48Ca. The motivation for selecting these nuclei stems from the aim of preparing for nuclear double beta-decay studies of 48Ca. In these heavier systems, phenomenological additions to the realistic NN interaction determined by previous

  8. Ab initio calculation of excitonic Hamiltonian of light-harvesting complex LH1 of Thermochromatium tepidum

    NASA Astrophysics Data System (ADS)

    Kozlov, Maxim I.; Poddubnyy, Vladimir V.; Glebov, Ilya O.; Belov, Aleksandr S.; Khokhlov, Daniil V.

    2016-02-01

    The electronic properties of light-harvesting complexes determine the efficiency of energy transfer in photosynthetic antennae. Ab initio calculations of the electronic properties of bacteriochlorophylls (composing the LH1 complex of the purple bacteria Thermochromatium tepidum) were performed. Based on these calculations, the excitonic Hamiltonian of a native cyclic complex and the Hamiltonians of open complexes with several removed bacteriochlorophylls were constructed. Absorption spectra calculated based on these Hamiltonians agree well with the experimental data. We found that the parameters of interaction between the neighboring bacteriochlorophylls are significantly larger than the empirical parameters suggested previously.

  9. Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

    SciTech Connect

    Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K.

    2015-09-14

    We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.

  10. Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their derivation

    NASA Astrophysics Data System (ADS)

    Chibotaru, L. F.; Ungur, L.

    2012-08-01

    A methodology for the rigorous nonperturbative derivation of magnetic pseudospin Hamiltonians of mononuclear complexes and fragments based on ab initio calculations of their electronic structure is described. It is supposed that the spin-orbit coupling and other relativistic effects are already taken fully into account at the stage of quantum chemistry calculations of complexes. The methodology is based on the establishment of the correspondence between the ab initio wave functions of the chosen manifold of multielectronic states and the pseudospin eigenfunctions, which allows to define the pseudospin Hamiltonians in the unique way. Working expressions are derived for the pseudospin Zeeman and zero-field splitting Hamiltonian corresponding to arbitrary pseudospins. The proposed calculation methodology, already implemented in the SINGLE_ANISO module of the MOLCAS-7.6 quantum chemistry package, is applied for a first-principles evaluation of pseudospin Hamiltonians of several complexes exhibiting weak, moderate, and very strong spin-orbit coupling effects.

  11. Ab-Initio Hamiltonian Approach to Light Nuclei And to Quantum Field Theory

    SciTech Connect

    Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Shirokov, A.M.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Ng, E.G.; Yang, C.; Sosonkina, M.; /Ames Lab

    2012-06-22

    Nuclear structure physics is on the threshold of confronting several long-standing problems such as the origin of shell structure from basic nucleon-nucleon and three-nucleon interactions. At the same time those interactions are being developed with increasing contact to QCD, the underlying theory of the strong interactions, using effective field theory. The motivation is clear - QCD offers the promise of great predictive power spanning phenomena on multiple scales from quarks and gluons to nuclear structure. However, new tools that involve non-perturbative methods are required to build bridges from one scale to the next. We present an overview of recent theoretical and computational progress with a Hamiltonian approach to build these bridges and provide illustrative results for the nuclear structure of light nuclei and quantum field theory.

  12. Unified ab initio approaches to nuclear structure and reactions

    NASA Astrophysics Data System (ADS)

    Navrátil, Petr; Quaglioni, Sofia; Hupin, Guillaume; Romero-Redondo, Carolina; Calci, Angelo

    2016-05-01

    The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of the nuclear forces, with two-, three- and possibly higher many-nucleon components, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD-employing Hamiltonians constructed within chiral effective field theory. After a brief overview of the field, we focus on ab initio many-body approaches—built upon the no-core shell model—that are capable of simultaneously describing both bound and scattering nuclear states, and present results for resonances in light nuclei, reactions important for astrophysics and fusion research. In particular, we review recent calculations of resonances in the 6He halo nucleus, of five- and six-nucleon scattering, and an investigation of the role of chiral three-nucleon interactions in the structure of 9Be. Further, we discuss applications to the 7Be {({{p}},γ )}8{{B}} radiative capture. Finally, we highlight our efforts to describe transfer reactions including the 3H{({{d}},{{n}})}4He fusion.

  13. Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians

    NASA Astrophysics Data System (ADS)

    Stroberg, S. R.; Hergert, H.; Holt, J. D.; Bogner, S. K.; Schwenk, A.

    2016-05-01

    We present ab initio predictions for ground and excited states of doubly open-shell fluorine and neon isotopes based on chiral two- and three-nucleon interactions. We use the in-medium similarity renormalization group to derive mass-dependent s d valence-space Hamiltonians. The experimental ground-state energies are reproduced through neutron number N =14 , beyond which a new targeted normal-ordering procedure improves agreement with data and large-space multireference calculations. For spectroscopy, we focus on neutron-rich F-2623 and Ne-2624 isotopes near N =14 ,16 magic numbers. In all cases we find agreement with experiment and established phenomenology. Moreover, yrast states are well described in 20Ne and 24Mg, providing a path toward an ab initio description of deformation in the medium-mass region.

  14. Symmetry of nuclear Hamiltonian as an origin of clustering

    NASA Astrophysics Data System (ADS)

    Tchuvil'sky, Yu. M.

    2011-12-01

    It is established that the set of solutions of the Hamiltonian of the generalized Elliott SU(3) model in the space of A-fermion wave functions contains a subset of multicluster solutions Ψ{Δ/ A } which can be precisely represented in terms of solutions of the Hamiltonian of the same form acting in the reduced space of certain intercluster coordinates. The conditions imposed on a multicluster partition which exhibits such properties are determined by applying the group-theory methods.

  15. Symmetry of nuclear Hamiltonian as an origin of clustering

    SciTech Connect

    Tchuvil'sky, Yu. M.

    2011-12-15

    It is established that the set of solutions of the Hamiltonian of the generalized Elliott SU(3) model in the space of A-fermion wave functions contains a subset of multicluster solutions {Psi}{sub {Delta}}{sup A} which can be precisely represented in terms of solutions of the Hamiltonian of the same form acting in the reduced space of certain intercluster coordinates. The conditions imposed on a multicluster partition which exhibits such properties are determined by applying the group-theory methods.

  16. Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator

    SciTech Connect

    Szalay, Viktor

    2015-05-07

    A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, T-hat, is presented. It is in the Eckart frame and it is of the same form as Watson’s normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact T-hat given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.

  17. Solving the eigenvalue problem of the nuclear Yukawa-folded mean-field Hamiltonian

    NASA Astrophysics Data System (ADS)

    Dobrowolski, A.; Pomorski, K.; Bartel, J.

    2016-02-01

    The nuclear Hamiltonian with a Yukawa-folded mean-field potential is diagonalized within the basis of a deformed harmonic-oscillator in Cartesian coordinates. The nuclear shape is characterized by the equivalent sharp surface described either by the well known Funny-Hills or the Trentalange-Koonin-Sierk parametrizations. They are both able to describe a very vast variety of nuclear deformations, including necked-in shapes, left-right asymmetry and non-axiality. The only imposed limitation on the nuclear shape is the z-signature symmetry, which corresponds to a symmetry of the shape with respect to a rotation by an angle π around the z-axis. On output, the computer code produces for a given nucleus with mass number A and charge number Z the energy eigenvalues and eigenfunctions of the mean-field Hamiltonian at chosen deformation.

  18. Relativistic nuclear Hamiltonian and currents to (v/c){sub 2}.

    SciTech Connect

    R. Schiavilla

    1995-08-01

    Relativistic Hamiltonians are defines as the sum of relativistic one-body kinetic energies and many-body interactions and their boost corrections. The calculation of the latter from commutation relations of the Poincare group is reviewed. It is shown that the most important terms can be understood from classical relativistic mechanics. The constraints of relativistic covariance on the charge and current densities are examined. Nuclear charge and current operators that satisfy them up to order (1/m){sup 2} are derived.

  19. Ab initio determination of spin Hamiltonians with anisotropic exchange interactions: The case of the pyrochlore ferromagnet Lu2V2O7

    NASA Astrophysics Data System (ADS)

    Riedl, Kira; Guterding, Daniel; Jeschke, Harald O.; Gingras, Michel J. P.; Valentí, Roser

    2016-07-01

    We present a general framework for deriving effective spin Hamiltonians of correlated magnetic systems based on a combination of relativistic ab initio density functional theory calculations, exact diagonalization of a generalized Hubbard Hamiltonian on finite clusters, and spin projections onto the low-energy subspace. A key motivation is to determine anisotropic bilinear exchange couplings in materials of interest. As an example, we apply this method to the pyrochlore Lu2V2O7 where the vanadium ions form a lattice of corner-sharing spin-1/2 tetrahedra. In this compound, anisotropic Dzyaloshinskii-Moriya interactions (DMIs) play an essential role in inducing a magnon Hall effect. We obtain quantitative estimates of the nearest-neighbor Heisenberg exchange, the DMI, and the symmetric part of the anisotropic exchange tensor. Finally, we compare our results with experimental ones on the Lu2V2O7 compound.

  20. Ab Initio Nuclear Structure and Reaction Calculations for Rare Isotopes

    SciTech Connect

    Draayer, Jerry P.

    2014-09-28

    We have developed a novel ab initio symmetry-adapted no-core shell model (SA-NCSM), which has opened the intermediate-mass region for ab initio investigations, thereby providing an opportunity for first-principle symmetry-guided applications to nuclear structure and reactions for nuclear isotopes from the lightest p-shell systems to intermediate-mass nuclei. This includes short-lived proton-rich nuclei on the path of X-ray burst nucleosynthesis and rare neutron-rich isotopes to be produced by the Facility for Rare Isotope Beams (FRIB). We have provided ab initio descriptions of high accuracy for low-lying (including collectivity-driven) states of isotopes of Li, He, Be, C, O, Ne, Mg, Al, and Si, and studied related strong- and weak-interaction driven reactions that are important, in astrophysics, for further understanding stellar evolution, X-ray bursts and triggering of s, p, and rp processes, and in applied physics, for electron and neutrino-nucleus scattering experiments as well as for fusion ignition at the National Ignition Facility (NIF).

  1. Body-fixed relativistic molecular Hamiltonian and its application to nuclear spin-rotation tensor: Linear molecules

    NASA Astrophysics Data System (ADS)

    Xiao, Yunlong; Liu, Wenjian

    2013-07-01

    The relativistic molecular Hamiltonian written in the body-fixed frame of reference is the basis for high-precision calculations of spectroscopic parameters involving nuclear vibrations and/or rotations. Such a Hamiltonian that describes electrons fully relativistically and nuclei quasi-relativistically is just developed for semi-rigid nonlinear molecules [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)], 10.1063/1.4797496. Yet, the formulation should somewhat be revised for linear molecules thanks to some unusual features arising from the redundancy of the rotation around the molecular axis. Nonetheless, the resulting isomorphic Hamiltonian is rather similar to that for nonlinear molecules. Consequently, the relativistic formulation of nuclear spin-rotation (NSR) tensor for linear molecules is very much the same as that for nonlinear molecules. So is the relativistic mapping between experimental NSR and NMR.

  2. Ab initio methods for nuclear properties - a computational physics approach

    NASA Astrophysics Data System (ADS)

    Maris, Pieter

    2011-04-01

    A microscopic theory for the structure and reactions of light nuclei poses formidable challenges for high-performance computing. Several ab-initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab-initio no-core full configuration (NCFC) approach is based on basis space expansion methods and uses Slater determinants of single-nucleon basis functions to express the nuclear wave function. In this approach, the quantum many-particle problem becomes a large sparse matrix eigenvalue problem. The eigenvalues of this matrix give us the binding energies, and the corresponding eigenvectors the nuclear wave functions. These wave functions can be employed to evaluate experimental quantities. In order to reach numerical convergence for fundamental problems of interest, the matrix dimension often exceeds 1 billion, and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. I discuss different strategies for distributing and solving this large sparse matrix on current multicore computer architectures, including methods to deal with with memory bottleneck. Several of these strategies have been implemented in the code MFDn, which is a parallel fortran code for nuclear structure calculations. I will show scaling behavior and compare the performance of the pure MPI version with the hybrid MPI/OpenMP code on Cray XT4 and XT5 platforms. For large core counts (typically 5,000 and above), the hybrid version is more efficient than pure MPI. With this code, we have been able to predict properties of the unstable nucleus 14F, which have since been confirmed by experiments. I will also give an overview of other recent results for nuclei in the A = 6 to 16 range with 2- and 3-body interactions. Supported in part by US DOE Grant DE-FC02-09ER41582.

  3. Vibrational dynamics of zero-field-splitting hamiltonian in gadolinium-based MRI contrast agents from ab initio molecular dynamics.

    PubMed

    Lasoroski, Aurélie; Vuilleumier, Rodolphe; Pollet, Rodolphe

    2014-07-01

    The electronic relaxation of gadolinium complexes used as MRI contrast agents was studied theoretically by following the short time evolution of zero-field-splitting parameters. The statistical analysis of ab initio molecular dynamics trajectories provided a clear separation between static and transient contributions to the zero-field-splitting. For the latter, the correlation time was estimated at approximately 0.1 ps. The influence of the ligand was also probed by replacing one pendant arm of our reference macrocyclic complex by a bulkier phosphonate arm. In contrast to the transient contribution, the static zero-field-splitting was significantly influenced by this substitution. PMID:25005282

  4. Vibrational dynamics of zero-field-splitting hamiltonian in gadolinium-based MRI contrast agents from ab initio molecular dynamics

    SciTech Connect

    Lasoroski, Aurélie; Vuilleumier, Rodolphe; Pollet, Rodolphe

    2014-07-07

    The electronic relaxation of gadolinium complexes used as MRI contrast agents was studied theoretically by following the short time evolution of zero-field-splitting parameters. The statistical analysis of ab initio molecular dynamics trajectories provided a clear separation between static and transient contributions to the zero-field-splitting. For the latter, the correlation time was estimated at approximately 0.1 ps. The influence of the ligand was also probed by replacing one pendant arm of our reference macrocyclic complex by a bulkier phosphonate arm. In contrast to the transient contribution, the static zero-field-splitting was significantly influenced by this substitution.

  5. Isoscalar monopole resonance of the alpha particle: a prism to nuclear Hamiltonians.

    PubMed

    Bacca, Sonia; Barnea, Nir; Leidemann, Winfried; Orlandini, Giuseppina

    2013-01-25

    We present an ab initio study of the isoscalar monopole excitations of (4)He using different realistic nuclear interactions, including modern effective field theory potentials. In particular we concentrate on the transition form factor F(M) to the narrow 0(+) resonance close to threshold. F(M) exhibits a strong potential model dependence, and can serve as a kind of prism to distinguish among different nuclear force models. Compared to the measurements obtained from inelastic electron scattering off ^{4}He, one finds that the state-of-the-art theoretical transition form factors are at variance with experimental data, especially in the case of effective field theory potentials. We discuss some possible reasons for such a discrepancy, which still remains a puzzle. PMID:25166158

  6. Ab Initio and Model-Hamiltonian Study of the Torsional Variation of the Three CH Stretching Normal Modes in Methanol

    NASA Astrophysics Data System (ADS)

    Xu, Li-Hong; Lees, Ronald M.; Hougen, Jon T.

    2013-06-01

    The ν_{2}, ν_{3} and ν_{9} CH stretching modes of methanol in the 3μm region exhibit a significant amount of torsion-vibration interaction, as illustrated for ν_{9} by the facts that: (i) the three hydrogen atoms each pass through a plane of symmetry of the molecule twice during the course of one full internal rotation motion, once at a minimum and once at a maximum in the three-fold potential energy curve, (ii) the H atom in the plane of symmetry is nearly motionless for the ν_{9} mode, and therefore (iii) the property of remaining motionless must be transferred from one H to another six times during one full internal rotation motion. In this talk we examine quantitatively the general phenomenon of torsion-vibration interaction in the methyl top stretching modes in two ways. First, we present plots of normal modes produced in Gaussian projected frequency calculations that are expressed either in terms of several sets of internal coordinates, or in terms of Cartesian displacement vectors for the methyl hydrogen atoms. Some of these plots display a nearly three-fold sine or cosine behavior, where the sine or cosine behavior is dictated by group-theoretical symmetry arguments. Other plots display stunning features ranging from loss of simple three-fold oscillatory pattern to cusp-like peaks or dips. Somewhat surprisingly, none of our ab initio plots for methanol exhibit a sign change after a 2π internal rotation of the methyl top. Second, we present a relatively simple model for the three CH stretching motions, characterized by three parameters associated with: (i) a vibrational A/E energy difference, (ii) a Jahn-Teller-like torsion-vibration interaction term within the vibrational E state, and (iii) a Renner-Teller-like torsion-vibration interaction term within the E state. This model gives nearly quantitative agreement with both the regular and irregular features of the ab initio plots. The good agreement suggests that various aspects of the physics of the

  7. Vortices of polarization in BaTiO3 core-shell nanoceramics: Calculations based on ab initio derived Hamiltonian versus Landau theory

    NASA Astrophysics Data System (ADS)

    Anoufa, M.; Kiat, J. M.; Kornev, I.; Bogicevic, C.

    2013-10-01

    In this paper, we want to emphasize the fact that many experimental properties of ceramics can be explained by the existence of a core-shell structure of the grains, particularly at small sizes. In this framework, we have studied BaTiO3 (BT) ceramics constituted of core-shell nanoparticles, nanowires, or nanoplanes by using ab initio derived effective Hamiltonian calculations whose application range is for large values of shell thickness and low values of shell permittivity. Many differences and new features compared to the situation of nanodots are induced by the core-shell structure. For instance, phase sequences are different; there is also a coexistence of vortices found by Naumov, Bellaiche, and Fu [I. I. Naumov, L. Bellaiche, and H. Fu, Nature (London)10.1038/nature03107 432, 737 (2004)] in the case of isolated dots with a homogeneous polarization, a transition from cubic paraelectric phase towards nonpolar rhombohedral phase, anomalies in dielectric permittivity associated with the onset of toroidal moments, etc. Afterwards, we compare these results with those obtained by the Landau theory of core-shell ceramics we have recently published. However, the ab initio calculations fail to capture the physics at small shell thickness and/or high shell permittivity, whereas the Landau theory fails to predict the peculiar properties of the phases in which vortices exist. Therefore, in a tentative way to build a global theory, we have constructed a Landau potential using both the polarization and the toroidal moment as competing order parameters, which allows us to propose a phase diagram, whatever the thickness and permittivity of the shell are.

  8. The ab initio model potential method with the spin-free relativistic scheme by eliminating small components Hamiltonian

    NASA Astrophysics Data System (ADS)

    Motegi, Kyosuke; Nakajima, Takahito; Hirao, Kimihiko; Seijo, Luis

    2001-04-01

    A relativistic ab initio model potential (AIMP) for Pt, Au, and Hg atoms has been developed using a relativistic scheme by eliminating small components (RESC) in which the 5p, 5d, and 6s electrons are treated explicitly. The quality of new RESC-AIMP has been tested by calculating the spectroscopic properties of the hydrides of these elements using the Hartree-Fock and coupled cluster with singles and doubles (CCSD) methods. The agreement with reference all-electron RESC calculations is excellent. The RESC-AIMP method is applied successfully in the investigation of the spectroscopic constants of Au2 and Hg2 using the CCSD method with a perturbative estimate of the contributions of triples. The ground state of Pt2 is also determined by RESC-AIMP with the second-order complete active space perturbation method. The results show that scalar relativistic effects on the valence properties are well described by the RESC-AIMP method. The effect on the basis set superposition error on the spectroscopic constants is also examined.

  9. Spin-orbit decomposition of ab initio nuclear wave functions

    NASA Astrophysics Data System (ADS)

    Johnson, Calvin W.

    2015-03-01

    Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum j , leading to j -j coupling, decades ago phenomenological models suggested that a simpler picture for 0 p -shell nuclides can be realized via coupling of the total spin S and total orbital angular momentum L . I revisit this idea with large-basis, no-core shell-model calculations using modern ab initio two-body interactions and dissect the resulting wave functions into their component L - and S -components. Remarkably, there is broad agreement with calculations using the phenomenological Cohen-Kurath forces, despite a gap of nearly 50 years and six orders of magnitude in basis dimensions. I suggest that L -S decomposition may be a useful tool for analyzing ab initio wave functions of light nuclei, for example, in the case of rotational bands.

  10. Ab Initio Calculations Of Nuclear Reactions And Exotic Nuclei

    SciTech Connect

    Quaglioni, S.

    2014-05-05

    Our ultimate goal is to develop a fundamental theory and efficient computational tools to describe dynamic processes between nuclei and to use such tools toward supporting several DOE milestones by: 1) performing predictive calculations of difficult-to-measure landmark reactions for nuclear astrophysics, such as those driving the neutrino signature of our sun; 2) improving our understanding of the structure of nuclei near the neutron drip line, which will be the focus of the DOE’s Facility for Rare Isotope Beams (FRIB) being constructed at Michigan State University; but also 3) helping to reveal the true nature of the nuclear force. Furthermore, these theoretical developments will support plasma diagnostic efforts at facilities dedicated to the development of terrestrial fusion energy.

  11. Ab initio nuclear structure from lattice effective field theory

    SciTech Connect

    Lee, Dean

    2014-11-11

    This proceedings article reviews recent results by the Nuclear Lattice EFT Collaboration on an excited state of the {sup 12}C nucleus known as the Hoyle state. The Hoyle state plays a key role in the production of carbon via the triple-alpha reaction in red giant stars. We discuss the structure of low-lying states of {sup 12}C as well as the dependence of the triple-alpha reaction on the masses of the light quarks.

  12. Hamiltonian purification

    SciTech Connect

    Orsucci, Davide; Burgarth, Daniel; Facchi, Paolo; Pascazio, Saverio; Nakazato, Hiromichi; Yuasa, Kazuya; Giovannetti, Vittorio

    2015-12-15

    The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.

  13. Semi-empirical and ab initio DFT modeling of the spin-Hamiltonian parameters for Fe6+: K2MO4 (M = S, Cr, Se)

    NASA Astrophysics Data System (ADS)

    Avram, N. M.; Brik, M. G.; Andreici, E.-L.

    2014-09-01

    In this paper we calculated the spin-Hamiltonian parameters (g factors {{g}||}, {{g}\\bot } and zero field splitting parameter D) for Fe6+ ions doped in K2MO4 (M = S, Cr, Se) crystals, taking into account the actual site symmetry of the Fe6+ impurity ion. The suggested method is based on the successful application of two different approaches: the crystal field theory (CFT) and density functional based (DFT). Within the CFT model we used the cluster approach and the perturbation theory method, based on the crystal field parameters, which were calculated in the superposition model. Within the DFT approach the calculations were done at the self-consistent field (SCF) by solving the coupled perturbed SCF equations. Comparison with experimental data shows that the obtained results are quite satisfactory, which proves applicability of the suggested calculating technique.

  14. Pruning the Hamiltonian Matrix in MULTIMODE: Test for C2H4 and Application to CH3NO2 Using a New Ab Initio Potential Energy Surface.

    PubMed

    Wang, Xiaohong; Carter, Stuart; Bowman, Joel M

    2015-11-25

    We report vibrational self-consistent field/virtual state configuration interaction energies of nitromethane using the code MULTIMODE and a new full-dimensional potential energy surface (PES). The PES is a precise, permutationally invariant linear least-squares fit to 17,049 electronic energies, using the CCSD(T)-F12b method with HaDZ basis (cc-pVDZ basis for H atoms, and aug-cc-pVDZ basis for C, O, N atoms). Nitromethane has 15 vibrational degrees of freedom, including one that is a nearly free internal methyl torsion, which is accurately described by the PES. This torsional mode makes vibrational calculations very challenging and here we present the results of calculations without it. Nevertheless, 14-mode calculations are still challenging and can lead to very large Hamiltonian matrices. To address this issue, we apply a pruning scheme, suggested previously by Handy and Carter, that reduces the size of matrix without sacrificing accuracy in the eigenvalues. The method is briefly described here in the context of partitioning theory. A new and more efficient implementation of it, coded in the latest version of MULTIMODE program, is described. The accuracy and efficiency are demonstrated for 12-mode C2H4 and then applied to CH3NO2. Agreement with available experimental values of the CH3NO2 14 fundamentals is very good. Diffusion Monte Carlo calculations in full dimensionality are done for the zero-point energy and wavefuction. These indicate that the torisonal motion is nearly a free-rotor in this state. PMID:26529348

  15. Realistic collective nuclear Hamiltonian

    SciTech Connect

    Dufour, M.; Zuker, A.P.

    1996-10-01

    The residual part of the realistic forces{emdash}obtained after extracting the monopole terms responsible for bulk properties{emdash}is strongly dominated by pairing and quadrupole interactions, with important {sigma}{tau}{center_dot}{sigma}{tau}, octupole, and hexadecapole contributions. Their forms retain the simplicity of the traditional pairing plus multipole models, while eliminating their flaws through a normalization mechanism dictated by a universal {ital A}{sup {minus}1/3} scaling. Coupling strengths and effective charges are calculated and shown to agree with empirical values. Comparisons between different realistic interactions confirm the claim that they are very similar. {copyright} {ital 1996 The American Physical Society.}

  16. Symmetry-Adapted Ab Initio Shell Model for Nuclear Structure Calculations

    NASA Astrophysics Data System (ADS)

    Draayer, J. P.; Dytrych, T.; Launey, K. D.; Langr, D.

    2012-05-01

    An innovative concept, the symmetry-adapted ab initio shell model, that capitalizes on partial as well as exact symmetries that underpin the structure of nuclei, is discussed. This framework is expected to inform the leading features of nuclear structure and reaction data for light and medium mass nuclei, which are currently inaccessible by theory and experiment and for which predictions of modern phenomenological models often diverge. We use powerful computational and group-theoretical algorithms to perform ab initio CI (configuration-interaction) calculations in a model space spanned by SU(3) symmetry-adapted many-body configurations with the JISP16 nucleon-nucleon interaction. We demonstrate that the results for the ground states of light nuclei up through A = 16 exhibit a strong dominance of low-spin and high-deformation configurations together with an evident symplectic structure. This, in turn, points to the importance of using a symmetry-adapted framework, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation.

  17. Integration of ab-initio nuclear calculation with derivative free optimization technique

    SciTech Connect

    Sharda, Anurag

    2008-01-01

    Optimization techniques are finding their inroads into the field of nuclear physics calculations where the objective functions are very complex and computationally intensive. A vast space of parameters needs searching to obtain a good match between theoretical (computed) and experimental observables, such as energy levels and spectra. Manual calculation defies the scope of such complex calculation and are prone to error at the same time. This body of work attempts to formulate a design and implement it which would integrate the ab initio nuclear physics code MFDn and the VTDIRECT95 code. VTDIRECT95 is a Fortran95 suite of parallel code implementing the derivative-free optimization algorithm DIRECT. Proposed design is implemented for a serial and parallel version of the optimization technique. Experiment with the initial implementation of the design showing good matches for several single-nucleus cases are conducted. Determination and assignment of appropriate number of processors for parallel integration code is implemented to increase the efficiency and resource utilization in the case of multiple nuclei parameter search.

  18. Ab Initio Enhanced calphad Modeling of Actinide-Rich Nuclear Fuels

    SciTech Connect

    Morgan, Dane; Yang, Yong Austin

    2013-10-28

    The process of fuel recycling is central to the Advanced Fuel Cycle Initiative (AFCI), where plutonium and the minor actinides (MA) Am, Np, and Cm are extracted from spent fuel and fabricated into new fuel for a fast reactor. Metallic alloys of U-Pu-Zr-MA are leading candidates for fast reactor fuels and are the current basis for fast spectrum metal fuels in a fully recycled closed fuel cycle. Safe and optimal use of these fuels will require knowledge of their multicomponent phase stability and thermodynamics (Gibbs free energies). In additional to their use as nuclear fuels, U-Pu-Zr-MA contain elements and alloy phases that pose fundamental questions about electronic structure and energetics at the forefront of modern many-body electron theory. This project will validate state-of-the-art electronic structure approaches for these alloys and use the resulting energetics to model U-Pu-Zr-MA phase stability. In order to keep the work scope practical, researchers will focus on only U-Pu-Zr-{Np,Am}, leaving Cm for later study. The overall objectives of this project are to: Provide a thermodynamic model for U-Pu-Zr-MA for improving and controlling reactor fuels; and, Develop and validate an ab initio approach for predicting actinide alloy energetics for thermodynamic modeling.

  19. Input/Output of ab-initio nuclear structure calculations for improved performance and portability

    SciTech Connect

    Laghave, Nikhil

    2010-01-01

    Many modern scientific applications rely on highly computation intensive calculations. However, most applications do not concentrate as much on the role that input/output operations can play for improved performance and portability. Parallelizing input/output operations of large files can significantly improve the performance of parallel applications where sequential I/O is a bottleneck. A proper choice of I/O library also offers a scope for making input/output operations portable across different architectures. Thus, use of parallel I/O libraries for organizing I/O of large data files offers great scope in improving performance and portability of applications. In particular, sequential I/O has been identified as a bottleneck for the highly scalable MFDn (Many Fermion Dynamics for nuclear structure) code performing ab-initio nuclear structure calculations. We develop interfaces and parallel I/O procedures to use a well-known parallel I/O library in MFDn. As a result, we gain efficient I/O of large datasets along with their portability and ease of use in the down-stream processing. Even situations where the amount of data to be written is not huge, proper use of input/output operations can boost the performance of scientific applications. Application checkpointing offers enormous performance improvement and flexibility by doing a negligible amount of I/O to disk. Checkpointing saves and resumes application state in such a manner that in most cases the application is unaware that there has been an interruption to its execution. This helps in saving large amount of work that has been previously done and continue application execution. This small amount of I/O provides substantial time saving by offering restart/resume capability to applications. The need for checkpointing in optimization code NEWUOA has been identified and checkpoint/restart capability has been implemented in NEWUOA by using simple file I/O.

  20. Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory.

    PubMed

    Marsalek, Ondrej; Markland, Thomas E

    2016-02-01

    Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost. PMID:26851913

  1. Predictive Nuclear Many-Body Theory with Ab Initio Methods: A Brief Survey and A Look Ahead

    NASA Astrophysics Data System (ADS)

    Hergert, Heiko

    2015-10-01

    The reach of ab initio many-body techniques has increased tremendously in recent years, owing to new developments in many-body theory as well as advances in their numerical implementation. Coupled Cluster, Self-Consistent Green's Function, and In-Medium Similarity Renormalization Group (IM-SRG) calculations are routinely performed for isotopes in the A ~ 100 region. Moreover, these techniques have been extended to tackle open-shell nuclei, either directly or through the auxiliary step of deriving valence-space interactions for use with existing Shell Model technology. One of the most powerful aspects of ab initio methods is their capability to provide results for energies and other observables with systematic uncertainties. Together with new accurate nuclear forces (and operators) derived from Chiral Effective Field Theory, they provide a consistent framework--and a road map--for a predictive description of nuclei. This will have a critical impact on the search for the limits of nuclear existence, tests of fundamental symmetries (e.g., the search for neutrinoless double beta decay), our understanding of quenching and effective charges in phenomenological Shell Model calculations etc. Using the Multi-Reference IM-SRG as a representative example, I will survey the current capabilities of ab initio methods with an emphasis on uncertainty quantification, highlight successes in the description of ground-state properties and spectra, and preview upcoming developments like the construction of consistent transition operators.

  2. Operator evolution for ab initio theory of light nuclei

    NASA Astrophysics Data System (ADS)

    Schuster, Micah; Quaglioni, Sofia; Johnson, Calvin; Jurgenson, Eric; Navrátil, Petr

    2014-09-01

    The past two decades have seen a revolution in ab initio calculations of nuclear properties. One key element has been the development of a rigorous effective interaction theory, applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence as a function of the model space size. For consistency, however, one ought to apply the same transformation to other operators when calculating transitions and mean values from the eigenstates of the renormalized Hamiltonian. Working in a translationally invariant harmonic oscillator basis for the two- and three-nucleon systems, we evolve the Hamiltonian, square radius, and total dipole strength operators by the similarity renormalization group (SRG). The inclusion of up to three-body matrix elements in the 4He nucleus all but completely restores the invariance of the expectation values under the transformation. We also consider a Gaussian operator with adjustable range; short ranges have the largest absolute renormalization when including two- and three-body induced terms, while at long ranges the induced three-body contribution takes on increased relative importance. The past two decades have seen a revolution in ab initio calculations of nuclear properties. One key element has been the development of a rigorous effective interaction theory, applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence as a function of the model space size. For consistency, however, one ought to apply the same transformation to other operators when calculating transitions and mean values from the eigenstates of the renormalized Hamiltonian. Working in a translationally invariant harmonic oscillator basis for the two- and three-nucleon systems, we evolve the Hamiltonian, square radius, and total dipole strength operators by the similarity renormalization group (SRG). The inclusion of up to three-body matrix elements in the 4He nucleus all but completely restores

  3. Ab Initio Calculations Of Light-Ion Reactions

    SciTech Connect

    Navratil, P; Quaglioni, S; Roth, R; Horiuchi, W

    2012-03-12

    The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of nuclear forces, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD employing Hamiltonians constructed within chiral effective field theory. In this contribution, we present one of such promising techniques capable of describing simultaneously both bound and scattering states in light nuclei. By combining the resonating-group method (RGM) with the ab initio no-core shell model (NCSM), we complement a microscopic cluster approach with the use of realistic interactions and a microscopic and consistent description of the clusters. We discuss applications to light nuclei scattering, radiative capture and fusion reactions.

  4. Hamiltonian cosmology of bigravity

    NASA Astrophysics Data System (ADS)

    Soloviev, V. O.

    The purpose of this talk is to give an introduction both to the Hamiltonian formalism and to the cosmological equations of bigravity. In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in addressing cosmological problems.

  5. Hamiltonian Light-Front Ffield Theory in a Basis Function Approach

    SciTech Connect

    Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Sternberg, P.; Ng, E.G.; Yang, C.

    2009-05-15

    Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here, we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography. We outline our approach, present illustrative features of some non-interacting systems in a cavity and discuss the computational challenges.

  6. Kdm2a/b Lysine Demethylases Regulate Canonical Wnt Signaling by Modulating the Stability of Nuclear β-Catenin.

    PubMed

    Lu, Lei; Gao, Yan; Zhang, Zan; Cao, Qing; Zhang, Xuena; Zou, Jianghuan; Cao, Ying

    2015-06-22

    In the absence of Wnt activation, cytosolic β-catenin is degraded through GSK3/CK1-mediated phosphorylation at the N terminus. Here, we show that, upon Wnt activation, the stability of nuclear β-catenin is regulated via methylation/demethylation. The protein lysine demethylases Kdm2a and Kdm2b regulate the turnover of non-phosphorylated β-catenin specifically within the nucleus via direct interaction with the fourth and fifth armadillo repeats. The lysine residues within this region are required for the methylation of non-phosphorylated β-catenin, which is demethylated by Kdm2a/b and subsequently ubiquitylated. During Xenopus embryogenesis, kdm2a/b genes are transcribed during early embryogenesis and are required for the specification of the body axis. Kdm2a/b knockdown in Xenopus embryos leads to increases in non-phosphorylated and methylated β-catenin, concurrent with the upregulation of β-catenin target genes. This mechanism is required for controlling the output of the Wnt/β-catenin signaling pathway to maintain normal cellular functions. PMID:26004508

  7. Open-shell nuclei and excited states from multireference normal-ordered Hamiltonians

    NASA Astrophysics Data System (ADS)

    Gebrerufael, Eskendr; Calci, Angelo; Roth, Robert

    2016-03-01

    We discuss the approximate inclusion of three-nucleon (3 N ) interactions into ab initio nuclear structure calculations using a multireference formulation of normal ordering and Wick's theorem. Following the successful application of single-reference normal ordering for the study of ground states of closed-shell nuclei, e.g., in coupled-cluster theory, multireference normal ordering opens a path to open-shell nuclei and excited states. Based on different multideterminantal reference states we benchmark the truncation of the normal-ordered Hamiltonian at the two-body level in no-core shell-model calculations for p -shell nuclei, including 6Li,12C, and 10B. We find that this multireference normal-ordered two-body approximation is able to capture the effects of the 3 N interaction with sufficient accuracy, both for ground-state and excitation energies, at the computational cost of a two-body Hamiltonian. It is robust with respect to the choice of reference states and has a multitude of applications in ab initio nuclear structure calculations of open-shell nuclei and their excitations as well as in nuclear reaction studies.

  8. Dynamical supersymmetric Dirac Hamiltonians

    SciTech Connect

    Ginocchio, J.N.

    1986-01-01

    Using the language of quantum electrodynamics, the Dirac Hamiltonian of a neutral fermion interacting with a tensor field is examined. A supersymmetry found for a general Dirac Hamiltonian of this type is discussed, followed by consideration of the special case of a harmonic electric potential. The square of the Dirac Hamiltonian of a neutral fermion interacting via an anomalous magnetic moment in an electric potential is shown to be equivalent to a three-dimensional supersymmetric Schroedinger equation. It is found that for a potential that grows as a power of r, the lowest energy of the Hamiltonian equals the rest mass of the fermion, and the Dirac eigenfunction has only an upper component which is normalizable. It is also found that the higher energy states have upper and lower components which form a supersymmetric doublet. 15 refs. (LEW)

  9. Implementation of a vector potential method in an ab initio Hartree-Fock code

    NASA Astrophysics Data System (ADS)

    Tevekeliyska, Violina; Springborg, Michael; Champagne, Benoît; Kirtman, Bernard

    2012-12-01

    For extended systems exposed to an external, electrostatic field, the presence of the field leads to an extra term (E⃗. P⃗) to the Hamiltonian, where E⃗ is the field vector and P⃗ is the polarization of the system of interest. In order to find out how a polymer chain responds to an external electric perturbation, a field with a charge and a current term for the polarization is added to an ab initio Hartree-Fock Hamiltonian. The polarization expression is taken from an efficient vector potential approach (VPA) [1] for calculating electronic and nuclear responses of infinite periodic systems to finite electric fields and is implemented in the ab initio LCAO-SCF algorithm [3], which computes band structure of regular or helical polymers, taking into account the one-dimensional translational symmetry. A smoothing procedure for numerical differentiation of the orbital coefficients is used in order to calculate self-consistently the charge flow contribution to the polarization.

  10. Flexible nuclear screening approximation to the two-electron spin–orbit coupling based on ab initio parameterization

    SciTech Connect

    Chalupský, Jakub Yanai, Takeshi

    2013-11-28

    The derivation, implementation, and validation of a new approximation to the two-electron spin–orbit coupling (SOC) terms is reported. The approximation, referred to as flexible nuclear screening spin–orbit, is based on the effective one-electron spin–orbit operator and accounts for two-electron SOC effects by screening nuclear charges. A highly flexible scheme for the nuclear screening is developed, mainly using parameterization based on ab initio atomic SOC calculations. Tabulated screening parameters are provided for contracted and primitive Gaussian-type basis functions of the ANO-RCC basis set for elements from H to Cm. The strategy for their adaptation to any other Gaussian basis set is presented and validated. A model to correct for the effect of splitting of transition metal d orbitals on their SOC matrix elements is introduced. The method is applied to a representative set of molecules, and compared to exact treatment and other approximative approaches at the same level of relativistic theory. The calculated SOC matrix elements are in very good agreement with their “exact” values; deviation below 1% is observed on average. The presented approximation is considered to be generally applicable, simple to implement, highly efficient, and accurate.

  11. Flexible nuclear screening approximation to the two-electron spin-orbit coupling based on ab initio parameterization

    NASA Astrophysics Data System (ADS)

    Chalupský, Jakub; Yanai, Takeshi

    2013-11-01

    The derivation, implementation, and validation of a new approximation to the two-electron spin-orbit coupling (SOC) terms is reported. The approximation, referred to as flexible nuclear screening spin-orbit, is based on the effective one-electron spin-orbit operator and accounts for two-electron SOC effects by screening nuclear charges. A highly flexible scheme for the nuclear screening is developed, mainly using parameterization based on ab initio atomic SOC calculations. Tabulated screening parameters are provided for contracted and primitive Gaussian-type basis functions of the ANO-RCC basis set for elements from H to Cm. The strategy for their adaptation to any other Gaussian basis set is presented and validated. A model to correct for the effect of splitting of transition metal d orbitals on their SOC matrix elements is introduced. The method is applied to a representative set of molecules, and compared to exact treatment and other approximative approaches at the same level of relativistic theory. The calculated SOC matrix elements are in very good agreement with their "exact" values; deviation below 1% is observed on average. The presented approximation is considered to be generally applicable, simple to implement, highly efficient, and accurate.

  12. Precise Lifetime Measurements in Light Nuclei for Benchmarking Modern Ab-initio Nuclear Structure Models

    SciTech Connect

    Lister, C.J.; McCutchan, E.A.

    2014-06-15

    A new generation of ab-initio calculations, based on realistic two- and three-body forces, is having a profound impact on our view of how nuclei work. To improve the numerical methods, and the parameterization of 3-body forces, new precise data are needed. Electromagnetic transitions are very sensitive to the dynamics which drive mixing between configurations. We have made a series of precise (< 3%) measurements of electromagnetic transitions in the A=10 nuclei {sup 10}C and {sup 10}Be by using the Doppler Shift Attenuation method carefully. Many interesting features can be reproduced including the strong α clustering. New measurements on {sup 8}Be and {sup 12}Be highlight the interplay between the alpha clusters and their valence neutrons.

  13. Primary oocyte transcriptional activation of aqp1ab by the nuclear progestin receptor determines the pelagic egg phenotype of marine teleosts.

    PubMed

    Zapater, Cinta; Chauvigné, François; Tingaud-Sequeira, Angèle; Finn, Roderick Nigel; Cerdà, Joan

    2013-05-15

    In marine teleosts, the aqp1ab water channel plays a vital role in the development of the pelagic egg phenotype. However, the developmental control of aqp1ab activation during oogenesis remains to be established. Here, we report the isolation of the 5'-flanking region of the teleost gilthead seabream aqp1ab gene, in which we identify conserved cis-regulatory elements for the binding of the nuclear progestin receptor (Pgr) and members of the Sox family of transcription factors. Subcellular localization studies indicated that the Pgr, as well as sox3 and -8b transcripts, are co-expressed in seabream oogonia, whereas in meiosis-arrested primary growth (pre-vitellogenic) oocytes, when aqp1ab mRNA and protein are first synthesized, the Pgr appears to be completely translocated from the ooplasm into the nucleus. By contrast, sox9b is highly expressed in more advanced oocytes, coinciding with a strong depletion of aqp1ab transcripts in the oocyte. Functional characterization of wild-type and mutated aqp1ab promoter constructs, using mammalian cells and Xenopus laevis oocytes, demonstrated that aqp1ab transcription is initiated by the Pgr, which is activated by the progestin 17α,20β-dihydroxy-4-pregnen-3-one (17,20β-P), the natural ligand of the seabream Pgr. In vitro incubation of seabream primary ovarian explants with the follicle-stimulating hormone or 17,20β-P confirmed that progestin-activated Pgr enhanced Aqp1ab synthesis via the aqp1ab promoter. However, transactivation assays in heterologous systems showed that Sox transcription factors can potentially modulate this mechanism. These data uncover the existence of an endocrine pathway involved in the early activation of a water channel necessary for egg formation in marine teleosts. PMID:23499660

  14. Photoexcited Nuclear Dynamics with Ab Initio Electronic Structure Theory: Is TD-DFT Ready For the Challenge?

    NASA Astrophysics Data System (ADS)

    Subotnik, Joseph

    In this talk, I will give a broad overview of our work in nonadiabatic dynamics, i.e. the dynamics of strongly coupled nuclear-electronic motion whereby the relaxation of a photo-excited electron leads to the heating up of phonons. I will briefly discuss how to model such nuclear motion beyond mean field theory. Armed with the proper framework, I will then focus on how to calculate one flavor of electron-phonon couplings, known as derivative couplings in the chemical literature. Derivative couplings are the matrix elements that couple adiabatic electronic states within the Born-Oppenheimer treatment, and I will show that these matrix elements show spurious poles using formal (frequency-independent) time-dependent density functional theory. To correct this TD-DFT failure, a simple approximation will be proposed and evaluated. Finally, time permitting, I will show some ab initio calculations whereby one can use TD-DFT derivative couplings to study electronic relaxation through a conical intersection.

  15. Direct assessment of quantum nuclear effects on hydrogen bond strength by constrained-centroid ab initio path integral molecular dynamics.

    PubMed

    Walker, Brent; Michaelides, Angelos

    2010-11-01

    The impact of quantum nuclear effects on hydrogen (H-) bond strength has been inferred in earlier work from bond lengths obtained from path integral molecular dynamics (PIMD) simulations. To obtain a direct quantitative assessment of such effects, we use constrained-centroid PIMD simulations to calculate the free energy changes upon breaking the H-bonds in dimers of HF and water. Comparing ab initio simulations performed using PIMD and classical nucleus molecular dynamics (MD), we find smaller dissociation free energies with the PIMD method. Specifically, at 50 K, the H-bond in (HF)(2) is about 30% weaker when quantum nuclear effects are included, while that in (H(2)O)(2) is about 15% weaker. In a complementary set of simulations, we compare unconstrained PIMD and classical nucleus MD simulations to assess the influence of quantum nuclei on the structures of these systems. We find increased heavy atom distances, indicating weakening of the H-bond consistent with that observed by direct calculation of the free energies of dissociation. PMID:21054031

  16. Ab initio simulation of radiation damage in nuclear reactor pressure vessel materials

    NASA Astrophysics Data System (ADS)

    Watts, Daniel; Finkenstadt, Daniel

    2012-02-01

    Using Kinetic Monte Carlo we developed a code to study point defect hopping in BCC metallic alloys using energetics and attempt frequencies calculated using VASP, an electronic structure software package. Our code provides a way of simulating the effects of neutron radiation on potential reactor materials. Specifically we will compare the Molybdenum-Chromium alloy system to steel alloys for use in nuclear reactor pressure vessels.

  17. Microscopic plasma Hamiltonian

    NASA Technical Reports Server (NTRS)

    Peng, Y.-K. M.

    1974-01-01

    A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.

  18. Quantum ring-polymer contraction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics

    NASA Astrophysics Data System (ADS)

    John, Christopher; Spura, Thomas; Habershon, Scott; Kühne, Thomas D.

    2016-04-01

    We present a simple and accurate computational method which facilitates ab initio path-integral molecular dynamics simulations, where the quantum-mechanical nature of the nuclei is explicitly taken into account, at essentially no additional computational cost in comparison to the corresponding calculation using classical nuclei. The predictive power of the proposed quantum ring-polymer contraction method is demonstrated by computing various static and dynamic properties of liquid water at ambient conditions using density functional theory. This development will enable routine inclusion of nuclear quantum effects in ab initio molecular dynamics simulations of condensed-phase systems.

  19. Ab initio calculations of reactions with light nuclei

    NASA Astrophysics Data System (ADS)

    Quaglioni, Sofia; Hupin, Guillaume; Calci, Angelo; Navrátil, Petr; Roth, Robert

    2016-03-01

    An ab initio (i.e., from first principles) theoretical framework capable of providing a unified description of the structure and low-energy reaction properties of light nuclei is desirable to further our understanding of the fundamental interactions among nucleons, and provide accurate predictions of crucial reaction rates for nuclear astrophysics, fusion-energy research, and other applications. In this contribution we review ab initio calculations for nucleon and deuterium scattering on light nuclei starting from chiral two- and three-body Hamiltonians, obtained within the framework of the ab initio no-core shell model with continuum. This is a unified approach to nuclear bound and scattering states, in which square-integrable energy eigenstates of the A-nucleon system are coupled to (A-a)+a target-plus-projectile wave functions in the spirit of the resonating group method to obtain an efficient description of the many-body nuclear dynamics both at short and medium distances and at long ranges.

  20. Vibrational circular dichroism from ab initio molecular dynamics and nuclear velocity perturbation theory in the liquid phase.

    PubMed

    Scherrer, Arne; Vuilleumier, Rodolphe; Sebastiani, Daniel

    2016-08-28

    We report the first fully ab initio calculation of dynamical vibrational circular dichroism spectra in the liquid phase using nuclear velocity perturbation theory (NVPT) derived electronic currents. Our approach is rigorous and general and thus capable of treating weak interactions of chiral molecules as, e.g., chirality transfer from a chiral molecule to an achiral solvent. We use an implementation of the NVPT that is projected along the dynamics to obtain the current and magnetic dipole moments required for accurate intensities. The gauge problem in the liquid phase is resolved in a twofold approach. The electronic expectation values are evaluated in a distributed origin gauge, employing maximally localized Wannier orbitals. In a second step, the gauge invariant spectrum is obtained in terms of a scaled molecular moments, which allows to systematically include solvent effects while keeping a significant signal-to-noise ratio. We give a thorough analysis and discussion of this choice of gauge for the liquid phase. At low temperatures, we recover the established double harmonic approximation. The methodology is applied to chiral molecules ((S)-d2-oxirane and (R)-propylene-oxide) in the gas phase and in solution. We find an excellent agreement with the theoretical and experimental references, including the emergence of signals due to chirality transfer from the solute to the (achiral) solvent. PMID:27586898

  1. Hamiltonian spinfoam gravity

    NASA Astrophysics Data System (ADS)

    Wieland, Wolfgang M.

    2014-01-01

    This paper presents a Hamiltonian formulation of spinfoam gravity, which leads to a straightforward canonical quantization. To begin with, we derive a continuum action adapted to a simplicial decomposition of space-time. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise—in the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may still miss an additional constraint. Finally, we canonically quantize and recover the EPRL (Engle-Pereira-Rovelli-Livine) face amplitudes. Communicated by P R L V Moniz

  2. Ab initio nuclear many-body perturbation calculations in the Hartree-Fock basis

    NASA Astrophysics Data System (ADS)

    Hu, B. S.; Xu, F. R.; Sun, Z. H.; Vary, J. P.; Li, T.

    2016-07-01

    Starting from realistic nuclear forces, the chiral N3LO and JISP16, we have applied many-body perturbation theory (MBPT) to the structure of closed-shell nuclei, 4He and 16O. The two-body N3LO interaction is softened by a similarity renormalization group transformation while JISP16 is adopted without renormalization. The MBPT calculations are performed within the Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can reduce the computational task. Corrections up to the third order in energy and up to the second order in radius are evaluated. Higher-order corrections in the HF basis are small relative to the leading-order perturbative result. Using the antisymmetrized Goldstone diagram expansions of the wave function, we directly correct the one-body density for the calculation of the radius, rather than calculate corrections to the occupation probabilities of single-particle orbits as found in other treatments. We compare our results with other methods where available and find good agreement. This supports the conclusion that our methods produce reasonably converged results with these interactions. We also compare our results with experimental data.

  3. Chaotic Hamiltonian dynamics

    SciTech Connect

    Bialek, J.M.

    1988-01-01

    Chaotic behavior may be observed in deterministic Hamiltonian Systems with as few as three dimensions, i.e, X, P, and t. The amount of chaotic behavior depends on the relative influence of the integrable and non-integrable parts of the Hamiltonian. The Standard Map is such a system and the amount of chaotic behavior may be varied by adjusting a single parameter. The global phase space portrait is a complicated mixture of quiescent and chaotic regions. First a new calculational method, characterized by a Fractual Diagram, is presented. This allows the quantitative prediction of the boundaries between regular and chaotic regions in phase space. Where these barriers are located gives qualitative insight into diffusion in phase space. The method is illustrated with the Standard Map but may be applied to any Hamiltonian System. The second phenomenon is the Universal Behavior predicted to occur for all area preserving maps. As a parameter is varied causing the mapping to become more chaotic a pattern is observed in the location and stability of the fixed points of the maps. The fixed points undergo an infinite sequence of period doubling bifurcations in a finite range of the parameter. The relative locations of the fixed point bifurcation and the parameter intervals between bifurcations both asymptotically approach constants which are Universal in that the same constants keep appearing in different problems.

  4. Extensions of Natural Hamiltonians

    NASA Astrophysics Data System (ADS)

    Rastelli, G.

    2014-03-01

    Given an n-dimensional natural Hamiltonian L on a Riemannian or pseudo-Riemannian manifold, we call "extension" of L the n+1 dimensional Hamiltonian H = ½p2u + α(u)L + β(u) with new canonically conjugated coordinates (u,pu). For suitable L, the functions α and β can be chosen depending on any natural number m such that H admits an extra polynomial first integral in the momenta of degree m, explicitly determined in the form of the m-th power of a differential operator applied to a certain function of coordinates and momenta. In particular, if L is maximally superintegrable (MS) then H is MS also. Therefore, the extension procedure allows the creation of new superintegrable systems from old ones. For m=2, the extra first integral generated by the extension procedure determines a second-order symmetry operator of a Laplace-Beltrami quantization of H, modified by taking in account the curvature of the configuration manifold. The extension procedure can be applied to several Hamiltonian systems, including the three-body Calogero and Wolfes systems (without harmonic term), the Tremblay-Turbiner-Winternitz system and n-dimensional anisotropic harmonic oscillators. We propose here a short review of the known results of the theory and some previews of new ones.

  5. Quantum Hamiltonian Physics with Supercomputers

    NASA Astrophysics Data System (ADS)

    Vary, James P.

    2014-06-01

    The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark-gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.

  6. Stimulated Raman signals at conical intersections: Ab initio surface hopping simulation protocol with direct propagation of the nuclear wave function

    SciTech Connect

    Kowalewski, Markus Mukamel, Shaul

    2015-07-28

    Femtosecond Stimulated Raman Spectroscopy (FSRS) signals that monitor the excited state conical intersections dynamics of acrolein are simulated. An effective time dependent Hamiltonian for two C—H vibrational marker bands is constructed on the fly using a local mode expansion combined with a semi-classical surface hopping simulation protocol. The signals are obtained by a direct forward and backward propagation of the vibrational wave function on a numerical grid. Earlier work is extended to fully incorporate the anharmonicities and intermode couplings.

  7. Stimulated Raman signals at conical intersections: Ab initio surface hopping simulation protocol with direct propagation of the nuclear wave function

    NASA Astrophysics Data System (ADS)

    Kowalewski, Markus; Mukamel, Shaul

    2015-07-01

    Femtosecond Stimulated Raman Spectroscopy (FSRS) signals that monitor the excited state conical intersections dynamics of acrolein are simulated. An effective time dependent Hamiltonian for two C—H vibrational marker bands is constructed on the fly using a local mode expansion combined with a semi-classical surface hopping simulation protocol. The signals are obtained by a direct forward and backward propagation of the vibrational wave function on a numerical grid. Earlier work is extended to fully incorporate the anharmonicities and intermode couplings.

  8. Drift Hamiltonian in magnetic coordinates

    SciTech Connect

    White, R.B.; Boozer, A.H.; Hay, R.

    1982-02-01

    A Hamiltonian formulation of the guiding-center drift in arbitrary, steady state, magnetic and electric fields is given. The canonical variables of this formulation are simply related to the magnetic coordinates. The modifications required to treat ergodic magnetic fields using magnetic coordinates are explicitly given in the Hamiltonian formulation.

  9. Hamiltonian light-front field theory in a basis function approach

    SciTech Connect

    Vary, J. P.; Honkanen, H.; Li Jun; Maris, P.; Brodsky, S. J.; Harindranath, A.; Sternberg, P.; Ng, E. G.; Yang, C.

    2010-03-15

    Hamiltonian light-front quantum field theory constitutes a framework for the nonperturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories is obtained that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from light-front holography. We outline our approach and present illustrative features of some noninteracting systems in a cavity. We illustrate the first steps toward solving quantum electrodynamics (QED) by obtaining the mass eigenstates of an electron in a cavity in small basis spaces and discuss the computational challenges.

  10. Effective Hamiltonians for phosphorene and silicene

    DOE PAGESBeta

    Lew Yan Voon, L. C.; Lopez-Bezanilla, A.; Wang, J.; Zhang, Y.; Willatzen, M.

    2015-02-01

    We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene.We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, itmore » is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector.We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k · p parameters.« less

  11. Effective Hamiltonians for phosphorene and silicene

    SciTech Connect

    Lew Yan Voon, L. C.; Lopez-Bezanilla, A.; Wang, J.; Zhang, Y.; Willatzen, M.

    2015-02-01

    We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene.We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector.We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k · p parameters.

  12. Robust Online Hamiltonian Learning

    NASA Astrophysics Data System (ADS)

    Granade, Christopher; Ferrie, Christopher; Wiebe, Nathan; Cory, David

    2013-05-01

    In this talk, we introduce a machine-learning algorithm for the problem of inferring the dynamical parameters of a quantum system, and discuss this algorithm in the example of estimating the precession frequency of a single qubit in a static field. Our algorithm is designed with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online, during experimental data collection, or can be used as a tool for post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. Finally, we discuss the performance of the our algorithm by appeal to the Cramer-Rao bound. This work was financially supported by the Canadian government through NSERC and CERC and by the United States government through DARPA. NW would like to acknowledge funding from USARO-DTO.

  13. Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians

    NASA Astrophysics Data System (ADS)

    Subasi, Yigit; Jarzynski, Christopher

    The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary k-body interactions, their use is limited to small k because the strength of interaction is k'th order in perturbation theory. Here we develop a nonperturbative technique for obtaining effective k-body interactions using Hamiltonians consisting of at most l-body interactions with l < k . This technique works best for Hamiltonians with a few interactions with very large k and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme. We gratefully acknowledge financial support from the Lockheed Martin Corporation under Contract U12001C.

  14. Ab initio-driven nuclear energy density functional method. A proposal for safe/correlated/improvable parametrizations of the off-diagonal EDF kernels

    NASA Astrophysics Data System (ADS)

    Duguet, T.; Bender, M.; Ebran, J.-P.; Lesinski, T.; Somà, V.

    2015-12-01

    This programmatic paper lays down the possibility to reconcile the necessity to resum many-body correlations into the energy kernel with the fact that safe multi-reference energy density functional (EDF) calculations cannot be achieved whenever the Pauli principle is not enforced, as is for example the case when many-body correlations are parametrized under the form of empirical density dependencies. Our proposal is to exploit a newly developed ab initio many-body formalism to guide the construction of safe, explicitly correlated and systematically improvable parametrizations of the off-diagonal energy and norm kernels that lie at the heart of the nuclear EDF method. The many-body formalism of interest relies on the concepts of symmetry breaking and restoration that have made the fortune of the nuclear EDF method and is, as such, amenable to this guidance. After elaborating on our proposal, we briefly outline the project we plan to execute in the years to come.

  15. Determination of nuclear quadrupole moments – An example of the synergy of ab initio calculations and microwave spectroscopy

    SciTech Connect

    Kellö, Vladimir

    2015-01-22

    Highly correlated scalar relativistic calculations of electric field gradients at nuclei in diatomic molecules in combination with accurate nuclear quadrupole coupling constants obtained from microwave spectroscopy are used for determination of nuclear quadrupole moments.

  16. Time-dependent drift Hamiltonian

    SciTech Connect

    Boozer, A.H.

    1983-03-01

    The lowest-order drift equations are given in a canonical magnetic coordinate form for time-dependent magnetic and electric fields. The advantages of the canonical Hamiltonian form are also discussed.

  17. Hamiltonian analysis of interacting fluids

    NASA Astrophysics Data System (ADS)

    Banerjee, Rabin; Ghosh, Subir; Mitra, Arpan Krishna

    2015-05-01

    Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical (Noether) stress tensor and the symmetric one obtained by metric variation are discussed.

  18. Hamiltonian description of the ideal fluid

    SciTech Connect

    Morrison, P.J.

    1994-01-01

    Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.

  19. Ab Initio Simulation of the Photoelectron Spectrum for Methoxy Radical

    NASA Astrophysics Data System (ADS)

    Cheng, Lan; Weichman, Marissa L.; Kim, Jongjin B.; Ichino, Takatoshi; Neumark, Daniel; Stanton, John F.

    2015-06-01

    A theoretical simulation of the photoelectron spectrum for the ground state of methoxy radical is reported based on the quasidiabatic model Hamiltonian originally proposed by Köppel, Domcke, and Cederbaum. The parameters in the model Hamiltonian have been obtained from ab initio coupled-cluster calculations. The linear and quadratic force constants have been calculated using equation-of-motion coupled-cluster ionization potential method with the singles, doubles, and triples (EOMIP-CCSDT) truncation scheme together with atomic natural orbital basis sets of triple-zeta quality (ANO1). The cubic and quartic force constants have been obtained from EOMIP-CCSD calculations with ANO basis sets of double-zeta quality (ANO0), and the spin-orbit coupling constant has been computed at the EOMIP-CCSD/pCVTZ level. The nuclear Schroedinger equation has been solved using the Lanzcos algorithm to obtain vibronic energy levels as well as the corresponding intensities. The simulated spectrum compares favorably with the recent high-resolution slow electron velocity-map imaging experiment for vibronic levels up to 2000 cm-1.

  20. Solutions of the Bohr Hamiltonian, a compendium

    NASA Astrophysics Data System (ADS)

    Fortunato, L.

    2005-10-01

    The Bohr Hamiltonian, also called collective Hamiltonian, is one of the cornerstones of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the V(β,γ) potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussion. It is the aim of the present monograph to present in detail all the known solutions in γ-unstable and γ-stable cases, in a taxonomic and didactical way. In pursuing this task we especially stressed the mathematical side leaving the discussion of the physics to already published comprehensive material. The paper contains also a new approximate solution for the linear potential, and a new solution for prolate and oblate soft axial rotors, as well as some new formulae and comments. The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling of bands in triaxial nuclei.

  1. Hamiltonian approach to frame dragging

    NASA Astrophysics Data System (ADS)

    Epstein, Kenneth J.

    2008-07-01

    A Hamiltonian approach makes the phenomenon of frame dragging apparent “up front” from the appearance of the drag velocity in the Hamiltonian of a test particle in an arbitrary metric. Hamiltonian (1) uses the inhomogeneous force equation (4), which applies to non-geodesic motion as well as to geodesics. The Hamiltonian is not in manifestly covariant form, but is covariant because it is derived from Hamilton’s manifestly covariant scalar action principle. A distinction is made between manifest frame dragging such as that in the Kerr metric, and hidden frame dragging that can be made manifest by a coordinate transformation such as that applied to the Robertson-Walker metric in Sect. 2. In Sect. 3 a zone of repulsive gravity is found in the extreme Kerr metric. Section 4 treats frame dragging in special relativity as a manifestation of the equivalence principle in accelerated frames. It answers a question posed by Bell about how the Lorentz contraction can break a thread connecting two uniformly accelerated rocket ships. In Sect. 5 the form of the Hamiltonian facilitates the definition of gravitomagnetic and gravitoelectric potentials.

  2. Ab initio calculations on the excited states of Na3 cluster to explore beyond Born-Oppenheimer theories: adiabatic to diabatic potential energy surfaces and nuclear dynamics.

    PubMed

    Paul, Amit Kumar; Ray, Somrita; Mukhopadhyay, Debasis; Adhikari, Satrajit

    2011-07-21

    We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na(3) cluster and present the adiabatic PESs for the electronic states 2(2)E' and 1(2)A(1)', and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 2(2)E' and 1(2)A(1)' demonstrate the numerical validity of so called "Curl Condition," such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the "adiabatic-diabatic transformation (ADT)" equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na(3) cluster and thereby, to explore the numerical validity of the theoretical development on beyond Born-Oppenheimer approach for adiabatic to diabatic transformation. PMID:21786987

  3. Ab Initio Calculation of Nuclear Magnetic Resonance Chemical Shift Anisotropy Tensors 1. Influence of Basis Set on the Calculation of 31P Chemical Shifts

    SciTech Connect

    Alam, T.M.

    1998-09-01

    The influence of changes in the contracted Gaussian basis set used for ab initio calculations of nuclear magnetic resonance (NMR) phosphorous chemical shift anisotropy (CSA) tensors was investigated. The isotropic chemical shitl and chemical shift anisotropy were found to converge with increasing complexity of the basis set at the Hartree-Fock @IF) level. The addition of d polarization function on the phosphorous nucIei was found to have a major impact of the calculated chemical shi~ but diminished with increasing number of polarization fimctions. At least 2 d polarization fimctions are required for accurate calculations of the isotropic phosphorous chemical shift. The introduction of density fictional theory (DFT) techniques through tie use of hybrid B3LYP methods for the calculation of the phosphorous chemical shift tensor resulted in a poorer estimation of the NMR values, even though DFT techniques result in improved energy and force constant calculations. The convergence of the W parametem with increasing basis set complexity was also observed for the DFT calculations, but produced results with consistent large deviations from experiment. The use of a HF 6-31 l++G(242p) basis set represents a good compromise between accuracy of the simulation and the complexity of the calculation for future ab initio calculations of 31P NMR parameters in larger complexes.

  4. Variational identities and Hamiltonian structures

    SciTech Connect

    Ma Wenxiu

    2010-03-08

    This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.

  5. First principles of Hamiltonian medicine

    PubMed Central

    Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

    2014-01-01

    We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease. PMID:24686937

  6. Ab Initio No-Core Shell Model

    SciTech Connect

    Barrett, B R; Navratil, P; Vary, J P

    2011-04-11

    A long-standing goal of nuclear theory is to determine the properties of atomic nuclei based on the fundamental interactions among the protons and neutrons (i.e., nucleons). By adopting nucleon-nucleon (NN), three-nucleon (NNN) and higher-nucleon interactions determined from either meson-exchange theory or QCD, with couplings fixed by few-body systems, we preserve the predictive power of nuclear theory. This foundation enables tests of nature's fundamental symmetries and offers new vistas for the full range of complex nuclear phenomena. Basic questions that drive our quest for a microscopic predictive theory of nuclear phenomena include: (1) What controls nuclear saturation; (2) How the nuclear shell model emerges from the underlying theory; (3) What are the properties of nuclei with extreme neutron/proton ratios; (4) Can we predict useful cross sections that cannot be measured; (5) Can nuclei provide precision tests of the fundamental laws of nature; and (6) Under what conditions do we need QCD to describe nuclear structure, among others. Along with other ab initio nuclear theory groups, we have pursued these questions with meson-theoretical NN interactions, such as CD-Bonn and Argonne V18, that were tuned to provide high-quality descriptions of the NN scattering phase shifts and deuteron properties. We then add meson-theoretic NNN interactions such as the Tucson-Melbourne or Urbana IX interactions. More recently, we have adopted realistic NN and NNN interactions with ties to QCD. Chiral perturbation theory within effective field theory ({chi}EFT) provides us with a promising bridge between QCD and hadronic systems. In this approach one works consistently with systems of increasing nucleon number and makes use of the explicit and spontaneous breaking of chiral symmetry to expand the strong interaction in terms of a dimensionless constant, the ratio of a generic small momentum divided by the chiral symmetry breaking scale taken to be about 1 GeV/c. The resulting NN

  7. Lowest eigenvalues of random Hamiltonians

    SciTech Connect

    Shen, J. J.; Zhao, Y. M.; Arima, A.; Yoshinaga, N.

    2008-05-15

    In this article we study the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues is applicable to many different systems. We improve the accuracy of the formula by considering the third central moment. We show that these formulas are applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.

  8. Quasilocal Hamiltonians in general relativity

    SciTech Connect

    Anderson, Michael T.

    2010-10-15

    We analyze the definition of quasilocal energy in general relativity based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular, the Hamiltonian constraint on the timelike boundary, neglected in previous studies, is emphasized here. We argue that a consistent definition of quasilocal energy in general relativity requires, at a minimum, a framework based on the (currently unknown) geometric well-posedness of the initial boundary value problem for the Einstein equations.

  9. Nonlocal Hamiltonian gauge theories and their connection with lattice Hamiltonians

    SciTech Connect

    Ktorides, C.N.; Mavromatos, N.E.

    1985-06-15

    We introduce the concept of primitive Hamiltonian density for nonlocal Abelian gauge theories. We subsequently study the local limit both with respect to the continuum and with respect to a lattice structure introduced via hypercubic cells. The non-Abelian case is also discussed.

  10. Ab-Initio Shell Model with a Core

    SciTech Connect

    Lisetskiy, A F; Barrett, B R; Kruse, M; Navratil, P; Stetcu, I; Vary, J P

    2008-06-04

    We construct effective 2- and 3-body Hamiltonians for the p-shell by performing 12{h_bar}{Omega} ab initio no-core shell model (NCSM) calculations for A=6 and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the 0{h_bar}{Omega} space. We then separate these effective Hamiltonians into 0-, 1- and 2-body contributions (also 3-body for A=7) and analyze the systematic behavior of these different parts as a function of the mass number A and size of the NCSM basis space. The role of effective 3- and higher-body interactions for A > 6 is investigated and discussed.

  11. Remembering AB

    NASA Astrophysics Data System (ADS)

    Belyayev, S. T.

    2013-06-01

    In 1947 I became a second-year student at Moscow State University's Physics and Engineering Department, where a part of the week's classes were taught at base organizations. Our group's base was the future Kurchatov Institute, at that time known as the mysterious "Laboratory N^circ 2," and later as LIPAN. . Besides group lectures and practical work at the experimental laboratories, we also had access to the general seminars which Igor Vasilyevich Kurchatov tried to hold, with Leonid Vasilyevich Groshev filling in when he was absent. At the seminar, theorists spoke as welcome co-presenters and commentators. In 1949 I felt ready to approach A. B. Migdal to ask if I could transfer to his theoretical sector. In response, he suggested a number of simple qualitative problems, which I then successfully solved. (Incidentally, AB used the very same "introductory problems" for screening many generations of students.) So I wound up among AB's students. From 1952 on (for 10 years) I also served as an employee of the Migdal Sector. My memoirs here are mainly inspired by these years of constant communication with AB. After my departure for Novosibirsk in 1962, although our meetings still took place, they became occasional....

  12. A Note on Hamiltonian Graphs

    ERIC Educational Resources Information Center

    Skurnick, Ronald; Davi, Charles; Skurnick, Mia

    2005-01-01

    Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

  13. Nuclear Zero Point Effects as a Function of Density in Ice-like Structures and Liquid Water from vdW-DF Ab Initio Calculations

    NASA Astrophysics Data System (ADS)

    Pamuk, Betül; Allen, Philip B.; Soler, Jose M.; Fernández-Serra, Marivi

    2014-03-01

    The contributions of nuclear zero point vibrations to the structures of liquid water and ice are not negligible. Recently, we have explained the source of an anomalous isotope shift in hexagonal ice, representing itself as an increase in the lattice volume when H is replaced by D, by calculating free energy within the quasiharmonic approximation, with ab initio density functional theory. In this work, we extend our studies to analyze the zero point effect in other ice-like structures under different densities: clathrate hydrates, LDL and HDL-like amorphous ices with different densities, and a highly dense ice phase, ice VIII. We show that there is a transition from anomalous isotope effect to normal isotope effect as the density increases. We also analyze nuclear zero point effects in liquid water using different vdW-DFs and make connections to this anomalous-normal isotope effect transition in ice. This work is supported by DOE Early Career Award No. DE-SC0003871.

  14. Three-cluster dynamics within an ab initio framework

    DOE PAGESBeta

    Quaglioni, Sofia; Romero-Redondo, Carolina; Navratil, Petr

    2013-09-26

    In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to amore » 4He+n+n description of 6He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core (4He) polarization effects.« less

  15. An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH2

    NASA Astrophysics Data System (ADS)

    Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.

    We have calculated ab initio the three-dimensional potential-energy surface of the NH2 molecule at 145 nuclear geometries spanning energy ranges of about 18 000 cm-1 for the NH stretch and 12 000 cm-1 for the bend. The ab initio configuration-interaction calculations were done using the multireference MRD-CI method. The calculated equilibrium configuration has NH bond length re = 1·0207 Å and bond angle α = 103·1°. The rotational-vibrational energies for 14NH2, 14NHD and 14ND2 were calculated variationally using the Morse-oscillator rigid-bender internal-dynamics Hamiltonian. For 14NH2 we calculate that υ1 = 3267 (3219) cm-1, υ2 = 1462 (1497) cm-1 and υ3 = 3283 (3301) cm-1, where experimental values are given in parentheses.

  16. Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

    SciTech Connect

    Tronko, Natalia; Brizard, Alain J.

    2015-11-15

    A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.

  17. Constructing Dense Graphs with Unique Hamiltonian Cycles

    ERIC Educational Resources Information Center

    Lynch, Mark A. M.

    2012-01-01

    It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

  18. Geometric Hamiltonian structures and perturbation theory

    SciTech Connect

    Omohundro, S.

    1984-08-01

    We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.

  19. Hamiltonian dynamics of extended objects

    NASA Astrophysics Data System (ADS)

    Capovilla, R.; Guven, J.; Rojas, E.

    2004-12-01

    We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.

  20. Discrete Hamiltonian for general relativity

    NASA Astrophysics Data System (ADS)

    Ziprick, Jonathan; Gegenberg, Jack

    2016-02-01

    Beginning from the Ashtekar formulation of general relativity, we derive a physical Hamiltonian written in terms of (classical) loop gravity variables. This is done by defining the gravitational fields within a complex of three-dimensional cells and imposing that curvature and torsion vanish within each cell. The resulting theory is holographic, with the bulk dynamics being captured completely by degrees of freedom living on cell boundaries. Quantization is readily obtainable by existing methods.

  1. Contact symmetries and Hamiltonian thermodynamics

    SciTech Connect

    Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.

    2015-10-15

    It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.

  2. Higher-dimensional Wannier functions of multiparameter Hamiltonians

    NASA Astrophysics Data System (ADS)

    Hanke, Jan-Philipp; Freimuth, Frank; Blügel, Stefan; Mokrousov, Yuriy

    2015-05-01

    When using Wannier functions to study the electronic structure of multiparameter Hamiltonians H(k ,λ ) carrying a dependence on crystal momentum k and an additional periodic parameter λ , one usually constructs several sets of Wannier functions for a set of values of λ . We present the concept of higher-dimensional Wannier functions (HDWFs), which provide a minimal and accurate description of the electronic structure of multiparameter Hamiltonians based on a single set of HDWFs. The obstacle of nonorthogonality of Bloch functions at different λ is overcome by introducing an auxiliary real space, which is reciprocal to the parameter λ . We derive a generalized interpolation scheme and emphasize the essential conceptual and computational simplifications in using the formalism, for instance, in the evaluation of linear response coefficients. We further implement the necessary machinery to construct HDWFs from ab initio within the full potential linearized augmented plane-wave method (FLAPW). We apply our implementation to accurately interpolate the Hamiltonian of a one-dimensional magnetic chain of Mn atoms in two important cases of λ : (i) the spin-spiral vector q and (ii) the direction of the ferromagnetic magnetization m ̂. Using the generalized interpolation of the energy, we extract the corresponding values of magnetocrystalline anisotropy energy, Heisenberg exchange constants, and spin stiffness, which compare very well with the values obtained from direct first principles calculations. For toy models we demonstrate that the method of HDWFs can also be used in applications such as the virtual crystal approximation, ferroelectric polarization, and spin torques.

  3. Effect of Intermolecular Hydrogen Bonding on the Nuclear Quadrupole Interaction in Imidazole and its Derivatives as Studied by ab initio Molecular Orbital Calculations

    NASA Astrophysics Data System (ADS)

    Nakamura, Nobuo; Masui, Hirotsugo; Ueda, Takahiro

    2000-02-01

    Ab initio Hartree-Fock molecular orbital calculations were applied to the crystalline imidazole and its derivatives in order to examine systematically the effect of possible N-H---N type hydrogen bond-ing on the nuclear quadrupole interaction parameters in these materials. The nitrogen quadrupole coupling constant (QCC) and the asymmetry parameter (η) of the electric field gradient (EFG) were found to depend strongly on the size of the molecular clusters, from single molecule, to dimer, trimer and to the infinite molecular chain, i.e., crystalline state, implying that the intermolecular N-H -N hydrogen bond affects significantly the electronic structure of imidazole molecule. A certain correla-tion between the QCC of 14N and the N-H bond distance R was also found and interpreted on the basis of the molecular orbital theory. However, we found that the value of the calculated EFG at the hy-drogen position of the N-H group, or the corresponding QCC value of 2 H, increases drastically as R-3 when R is shorter than about 0.1 nm, due probably to the inapplicability of the Gaussian basis sets to the very short chemical bond as revealed in the actual imidazole derivatives. We suggested that the ob-served N-H distances in imidazole derivatives should be re-examined.

  4. Operator evolution for ab initio electric dipole transitions of 4He

    DOE PAGESBeta

    Schuster, Micah D.; Quaglioni, Sofia; Johnson, Calvin W.; Jurgenson, Eric D.; Navartil, Petr

    2015-07-24

    A goal of nuclear theory is to make quantitative predictions of low-energy nuclear observables starting from accurate microscopic internucleon forces. A major element of such an effort is applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence of ab initio calculations as a function of the model space size. The consistent simultaneous transformation of external operators, however, has been overlooked in applications of the theory, particularly for nonscalar transitions. We study the evolution of the electric dipole operator in the framework of the similarity renormalization group method and apply the renormalized matrix elements to the calculationmore » of the 4He total photoabsorption cross section and electric dipole polarizability. All observables are calculated within the ab initio no-core shell model. Furthermore, we find that, although seemingly small, the effects of evolved operators on the photoabsorption cross section are comparable in magnitude to the correction produced by including the chiral three-nucleon force and cannot be neglected.« less

  5. Operator evolution for ab initio electric dipole transitions of 4 He

    NASA Astrophysics Data System (ADS)

    Schuster, Micah; Quaglioni, Sofia; Johnson, Calvin; Jurgenson, Eric; Navratil, Petr

    2015-04-01

    A goal of nuclear theory is to make quantitative predictions of low-energy nuclear observables starting from accurate microscopicinternucleon forces. Modern effective interaction theory, applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence of ab initio calculations as a function of the model space size, is a major element of such an effort. The consistent simultaneous transformation of external operators, however, has been overlooked in applications of the theory, particularly for non-scalar transitions. We study the evolution of the electric dipole operator in the framework of the similarity-renormalization group method and apply the renormalized matrix elements to the calculation of the 4 He total photo absorption cross section and electric dipole polarizability. All observables are calculated within the ab initio no-core shell model. We find that, although seemingly small, the effects of induced operators on the photo absorption cross section are comparable in magnitude to the correction produced by including the three-nucleon force and cannot be neglected. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  6. Killing symmetries as Hamiltonian constraints

    NASA Astrophysics Data System (ADS)

    Lusanna, Luca

    2016-02-01

    The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time, while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive.

  7. Coherent states for quadratic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Contreras-Astorga, Alonso; Fernández C, David J.; Velázquez, Mercedes

    2011-01-01

    The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

  8. Extrapolation methods for obtaining low-lying eigenvalues of a large-dimensional shell model Hamiltonian matrix

    SciTech Connect

    Yoshinaga, N.; Arima, A.

    2010-04-15

    We propose some new, efficient, and practical extrapolation methods to obtain a few low-lying eigenenergies of a large-dimensional Hamiltonian matrix in the nuclear shell model. We obtain those energies at the desired accuracy by extrapolation after diagonalizing small-dimensional submatrices of the sorted Hamiltonian matrix.

  9. Chasing hamiltonian structure in gyrokinetic theory

    NASA Astrophysics Data System (ADS)

    Burby, J. W.

    Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a emph{stochastic} Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.

  10. Characterization of DNA sequences that mediate nuclear protein binding to the regulatory region of the Pisum sativum (pea) chlorophyl a/b binding protein gene AB80: identification of a repeated heptamer motif.

    PubMed

    Argüello, G; García-Hernández, E; Sánchez, M; Gariglio, P; Herrera-Estrella, L; Simpson, J

    1992-05-01

    Two protein factors binding to the regulatory region of the pea chlorophyl a/b binding protein gene AB80 have been identified. One of these factors is found only in green tissue but not in etiolated or root tissue. The second factor (denominated ABF-2) binds to a DNA sequence element that contains a direct heptamer repeat TCTCAAA. It was found that presence of both of the repeats is essential for binding. ABF-2 is present in both green and etiolated tissue and in roots and factors analogous to ABF-2 are present in several plant species. Computer analysis showed that the TCTCAAA motif is present in the regulatory region of several plant genes. PMID:1303797

  11. Computing statistics for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Tupper, P. F.

    2007-08-01

    We present the results of a set of numerical experiments designed to investigate the appropriateness of various integration schemes for molecular dynamics simulations. In particular, we wish to identify which numerical methods, when applied to an ergodic Hamiltonian system, sample the state-space in an unbiased manner. We do this by describing two Hamiltonian system for which we can analytically compute some of the important statistical features of its trajectories, and then applying various numerical integration schemes to them. We can then compare the results from the numerical simulation against the exact results for the system and see how closely they agree. The statistic we study is the empirical distribution of particle velocity over long trajectories of the systems. We apply four methods: one symplectic method (Stormer-Verlet) and three energy-conserving step-and-project methods. The symplectic method performs better on both test problems, accurately computing empirical distributions for all step-lengths consistent with stability. Depending on the test system and the method, the step-and-project methods are either no longer ergodic for any step length (thus giving the wrong empirical distribution) or give the correct distribution only in the limit of step-size going to zero.

  12. Asymptocic Freedom of Gluons in Hamiltonian Dynamics

    NASA Astrophysics Data System (ADS)

    Gómez-Rocha, María; Głazek, Stanisław D.

    2016-07-01

    We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian {β} -function coincides with the one obtained in an earlier calculation using a different generator.

  13. Effective multiband Hamiltonian for InAs in wurtzite phase

    NASA Astrophysics Data System (ADS)

    Faria Junior, Paulo E.; Campos, Tiago; Bastos, Carlos M. O.; Sipahi, Guilherme M.; Gmitra, Martin; Fabian, Jaroslav

    Recent advances in nanostructure growth techniques allowed the synthesis of new III-V compounds with wurtzite crystal structure. Although ab initio band structures for these new wurtzite materials can be found in the literature, we still lack multiband models and parameter sets that can be simply used to investigate, for instance, quantum confinement effects. In this study, we calculated the ab initio band structure of bulk InAs wurtzite and developed a multiband k.p Hamiltonian to describe the energy bands around the energy gap. In order to correctly describe the spin splitting effects we included the k-dependent spin-orbit term, often neglected in literature. We showed that our model is very robust to describe the important features of the band structure and also the spin splittings with great agreement to the ab initio values. CNPq (149904/2013­-4 and 88887.110814/2015-00), CAPES PVE (88881.068174/2014-01), DFG SFB 689 and FAPESP (2012/05618-0).

  14. Collective rotation from ab initio theory

    NASA Astrophysics Data System (ADS)

    Caprio, M. A.; Maris, P.; Vary, J. P.; Smith, R.

    2015-08-01

    Through ab initio approaches in nuclear theory, we may now seek to quantitatively understand the wealth of nuclear collective phenomena starting from the underlying internucleon interactions. No-core configuration interaction (NCCI) calculations for p-shell nuclei give rise to rotational bands, as evidenced by rotational patterns for excitation energies, electromagnetic moments and electromagnetic transitions. In this review, NCCI calculations of 7-9Be are used to illustrate and explore ab initio rotational structure, and the resulting predictions for rotational band properties are compared with experiment. We highlight the robustness of ab initio rotational predictions across different choices for the internucleon interaction.

  15. Emergent properties of nuclei from ab initio coupled-cluster calculations

    NASA Astrophysics Data System (ADS)

    Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R.; Papenbrock, T.

    2016-06-01

    Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. This endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. This paper reviews some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLO{}{{sat}} is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to 56Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon–nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. The coupling to the continuum impacts the energies of the {J}π =1/{2}-,3/{2}-,7/{2}-,3/{2}+ states in {}{17,23,25}O, and—contrary to naive shell-model expectations—the level ordering of the {J}π =3/{2}+,5/{2}+,9/{2}+ states in {}{53,55,61}Ca. ).

  16. On the approximation of finding A(nother) Hamiltonian cycle in cubic Hamiltonian graphs

    NASA Astrophysics Data System (ADS)

    Bazgan, Cristina; Santha, Miklos; Tuza, Zsolt

    It is a simple fact that cubic Hamiltonian graphs have at least two Hamiltonian cycles. Finding such a cycle is NP-hard in general, and no polynomial time algorithm is known for the problem of fording a second Hamiltonian cycle when one such cycle is given as part of the input. We investigate the complexity of approximating this problem where by a feasible solution we mean a(nother) cycle in the graph. First we prove a negative result showing that the LONGEST PATH problem is not constant approximable in cubic Hamiltonian graphs unless P = NP. No such negative result was previously known for this problem in Hamiltonian graphs. In strong opposition with this result we show that there is a polynomial time approximation scheme for fording another cycle in cubic Hamiltonian graphs if a Hamiltonian cycle is given in the input.

  17. Incomplete Dirac reduction of constrained Hamiltonian systems

    SciTech Connect

    Chandre, C.

    2015-10-15

    First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.

  18. Canonical Hamiltonians for waves in inhomogeneous media

    NASA Astrophysics Data System (ADS)

    Gershgorin, Boris; Lvov, Yuri V.; Nazarenko, Sergey

    2009-01-01

    We obtain a canonical form of a quadratic Hamiltonian for linear waves in a weakly inhomogeneous medium. This is achieved by using the Wentzel-Kramers-Brillouin representation of wave packets. The canonical form of the Hamiltonian is obtained via the series of canonical Bogolyubov-type and near-identical transformations. Various examples of the application illustrating the main features of our approach are presented. The knowledge of the Hamiltonian structure for linear wave systems provides a basis for developing a theory of weakly nonlinear random waves in inhomogeneous media generalizing the theory of homogeneous wave turbulence.

  19. Operator evolution for ab initio electric dipole transitions of 4He

    SciTech Connect

    Schuster, Micah D.; Quaglioni, Sofia; Johnson, Calvin W.; Jurgenson, Eric D.; Navartil, Petr

    2015-07-24

    A goal of nuclear theory is to make quantitative predictions of low-energy nuclear observables starting from accurate microscopic internucleon forces. A major element of such an effort is applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence of ab initio calculations as a function of the model space size. The consistent simultaneous transformation of external operators, however, has been overlooked in applications of the theory, particularly for nonscalar transitions. We study the evolution of the electric dipole operator in the framework of the similarity renormalization group method and apply the renormalized matrix elements to the calculation of the 4He total photoabsorption cross section and electric dipole polarizability. All observables are calculated within the ab initio no-core shell model. Furthermore, we find that, although seemingly small, the effects of evolved operators on the photoabsorption cross section are comparable in magnitude to the correction produced by including the chiral three-nucleon force and cannot be neglected.

  20. A Student's Guide to Lagrangians and Hamiltonians

    NASA Astrophysics Data System (ADS)

    Hamill, Patrick

    2013-11-01

    Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.

  1. Nonperturbative embedding for highly nonlocal Hamiltonians

    NASA Astrophysics Data System (ADS)

    Subaşı, Yiǧit; Jarzynski, Christopher

    2016-07-01

    The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l Hamiltonian which is more local than the original one (using an analog device), and finally reverse the unitary transformation. The net effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.

  2. Hamiltonian formulation of guiding center motion

    NASA Technical Reports Server (NTRS)

    Stern, D. P.

    1971-01-01

    The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.

  3. Hamiltonian analysis of Einstein-Chern-Simons gravity

    NASA Astrophysics Data System (ADS)

    Avilés, L.; Salgado, P.

    2016-06-01

    In this work we consider the construction of the Hamiltonian action for the transgressions field theory. The subspace separation method for Chern-Simons Hamiltonian is built and used to find the Hamiltonian for five-dimensional Einstein-Chern-Simons gravity. It is then shown that the Hamiltonian for Einstein gravity arises in the limit where the scale parameter l approaches zero.

  4. Three-cluster dynamics within an ab initio framework

    SciTech Connect

    Quaglioni, Sofia; Romero-Redondo, Carolina; Navratil, Petr

    2013-09-26

    In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to a 4He+n+n description of 6He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core (4He) polarization effects.

  5. A Surrogate Hamiltonian study of femtosecond photodesorption of CO from NiO(100)

    NASA Astrophysics Data System (ADS)

    Asplund, Erik; Klüner, Thorsten

    2013-09-01

    In this paper, the Surrogate Hamiltonian approach is employed in order to study electronic relaxation in femtosecond laser-induced desorption experiments of CO from NiO(100). The study is based on ab initio calculations and a microscopic description of the NiO(100)-surface and the relaxation mechanism developed by Koch et al. The relaxation mechanism is assumed to be of dipole-dipole interaction nature, where the transition dipole moment of the adsorbate interacts with surface electron-hole pairs. In the Surrogate Hamiltonian approach the electron-hole pairs are treated as two-level systems and are described by excitation energy and a dipole charge. The Surrogate Hamiltonian parameters and potential energy surfaces used are obtained from ab initio calculations. The desorption probability and the velocity distributions of the desorbing molecules are calculated and an excited state lifetime is predicted. Throughout this paper atomic units, i.e. ℏ︀ = m e = e = a 0 = 1, have been used unless otherwise stated.

  6. Applications of Floquet-Magnus expansion, average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence.

    PubMed

    Mananga, Eugene Stephane

    2013-01-01

    This work presents the possibility of applying the Floquet-Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented. PMID:24034855

  7. Gauge transformations in multichannel laser-interaction Hamiltonians

    NASA Astrophysics Data System (ADS)

    Armstrong, G. S. J.; Esry, B. D.

    2015-05-01

    In our previous studies of molecular photodissociation, we solved the time-dependent Schrödinger equation in full dimensionality, casting the laser-molecule interaction in a length-gauge form. The nuclear wave function is then expanded on a basis of symmetric top functions in the angular coordinates. However, a velocity gauge representation of the nuclear motion may be advantageous, and may reduce the number of partial waves required in the angular basis expansion. In molecular problems, the standard transformation between length and velocity gauge must take account of the presence of short-range non-linear radial dependence of the dipole. In problems involving a single channel, the short-range behavior is not removed by the gauge transformation, leading to a short-range mixed-gauge Hamiltonian. Having derived the form of this Hamiltonian, we extend our analysis to multichannel problems, where the gauge transformation is further complicated by off-diagonal dipole terms. We examine the impact of this transformation in full-dimensional calculations, particularly its effectiveness in reducing the required size of the angular basis. This work is supported by the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S.A.

  8. Hamiltonian quantum computer in one dimension

    NASA Astrophysics Data System (ADS)

    Wei, Tzu-Chieh; Liang, John C.

    2015-12-01

    Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach is called the Hamiltonian quantum computation and it includes, for example, the continuous-time quantum cellular automata and the universal quantum walk. We consider one spatial dimension and study the compromise between the locality k and the local Hilbert space dimension d . For geometrically 2-local (i.e., k =2 ), it is known that d =8 is already sufficient for universal quantum computation but the Hamiltonian is not translationally invariant. As the locality k increases, it is expected that the minimum required d should decrease. We provide a construction of a Hamiltonian quantum computer for k =3 with d =5 . One implication is that simulating one-dimensional chains of spin-2 particles is BQP-complete (BQP denotes "bounded error, quantum polynomial time"). Imposing translation invariance will increase the required d . For this we also construct another 3-local (k =3 ) Hamiltonian that is invariant under translation of a unit cell of two sites but that requires d to be 8.

  9. Convergence of Hamiltonian systems to billiards.

    PubMed

    Collas, Peter; Klein, David; Schwebler, Hans-Peter

    1998-06-01

    We examine in detail a physically natural and general scheme for gradually deforming a Hamiltonian to its corresponding billiard, as a certain parameter k varies from one to infinity. We apply this limiting process to a class of Hamiltonians with homogeneous potential-energy functions and further investigate the extent to which the limiting billiards inherit properties from the corresponding sequences of Hamiltonians. The results are mixed. Using theorems of Yoshida for the case of two degrees of freedom, we prove a general theorem establishing the "inheritability" of stability properties of certain orbits. This result follows naturally from the convergence of the traces of appropriate monodromy matrices to the billiard analog. However, in spite of the close analogy between the concepts of integrability for Hamiltonian systems and billiards, integrability properties of Hamiltonians in a sequence are not necessarily inherited by the limiting billiard, as we show by example. In addition to rigorous results, we include numerical examples of certain interesting cases, along with computer simulations. (c) 1998 American Institute of Physics. PMID:12779750

  10. A spinor boson AB chain

    NASA Astrophysics Data System (ADS)

    Cruz Reyes, Greis Julieth; Franco, Roberto; Silva Valencia, Jereson; Universidad Santo Tomas Collaboration; Universidad Nacional de Colombia Collaboration

    Recent research is focused on superlattices arising from optical lattices, which allow a tunable environment. Experimentally bosons present transitions from superfluid to Mott insulator by changing the energy offset in the unit cell [Nat. Commun. 5:5735 (2014)]. Many studies displayed that ground state of spinless boson systems on superlattices present superfluid, Mott insulator and an additional CDW phase created by the energy shift between the sites into the unit cell [Phys. Rev. A 83, 053621 (2011)]. The first confinement methods were magnetic traps, which freezes the spin; with optical lattices the grade of freedom of spin plays an important role. We consider bosons with spin S =1 on a superlattice made by two sites with energy offset per unit cell (AB chain). The Hamiltonian that describes the system is the Bose-Hubbard model with the superlattice potential (W) and the exchange interaction (V) parameters. This model supports CDW, Mott insulator and superfluid phases. For W near to U, with V =0, Mott phase disappears, but for V increasing, a new CDW appears due to the spin interaction, while the half-integer CDW decrease. These results are widely different from spinless boson, where the CDW phases are stables.

  11. Integrability of Hamiltonian systems with algebraic potentials

    NASA Astrophysics Data System (ADS)

    Maciejewski, Andrzej J.; Przybylska, Maria

    2016-01-01

    Problem of integrability for Hamiltonian systems with potentials that are algebraic thus multivalued functions of coordinates is discussed. Introducing potential as a new variable the original Hamiltonian system on 2n dimensional phase space is extended to 2 n + 1 dimensional system with rational right-hand sides. For extended system its non-canonical degenerated Poisson structure of constant rank 2n and rational Hamiltonian is identified. For algebraic homogeneous potentials of non-zero rational homogeneity degree necessary integrability conditions are formulated. These conditions are deduced from an analysis of the differential Galois group of variational equations around particular solutions of a straight line type. Obtained integrability obstructions are applied to the class of monomial homogeneous potentials. Some integrable potentials satisfying these conditions are found.

  12. Hamiltonian quantum dynamics with separability constraints

    NASA Astrophysics Data System (ADS)

    Burić, Nikola

    2008-01-01

    Schroedinger equation on a Hilbert space H, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space PH. Separable states of a bipartite quantum system form a special submanifold of PH. We analyze the Hamiltonian dynamics that corresponds to the quantum system constrained on the manifold of separable states, using as an important example the system of two interacting qubits. The constraints introduce nonlinearities which render the dynamics nontrivial. We show that the qualitative properties of the constrained dynamics clearly manifest the symmetry of the qubits system. In particular, if the quantum Hamilton's operator has not enough symmetry, the constrained dynamics is nonintegrable, and displays the typical features of a Hamiltonian dynamical system with mixed phase space. Possible physical realizations of the separability constraints are discussed.

  13. Memories of AB

    NASA Astrophysics Data System (ADS)

    Vaks, V. G.

    2013-06-01

    I had the good fortune to be a student of A. B. Migdal - AB, as we called him in person or in his absence - and to work in the sector he headed at the Kurchatov Institute, along with his other students and my friends, including Vitya Galitsky, Spartak Belyayev and Tolya Larkin. I was especially close with AB in the second half of the 1950s, the years most important for my formation, and AB's contribution to this formation was very great. To this day, I've often quoted AB on various occasions, as it's hard to put things better or more precisely than he did; I tell friends stories heard from AB, because these stories enhance life as AB himself enhanced it; my daughter is named Tanya after AB's wife Tatyana Lvovna, and so on. In what follows, I'll recount a few episodes in my life in which AB played an important or decisive role, and then will share some other memories of AB...

  14. Toward a Fundamental Understanding of Nuclear Reactions and Exotic Nuclei

    NASA Astrophysics Data System (ADS)

    Quaglioni, Sofia; Hupin, Guillaume; Langhammer, Joachim; Romero-Redondo, Carolina; Schuster, Micah D.; Johnson, Calvin W.; Navrátil, Petr; Roth, Robert

    Nuclear systems near the drip lines offer an exciting opportunity to advance our understanding of the interactions among nucleons, which has so far been mostly based on the study of stable nuclei. However, this is not a goal devoid of challenges. From a theoretical standpoint, it requires the capability to address within an ab initio framework not only bound, but also resonant and scattering states, all of which can be strongly coupled. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from Quantum Chromodynamics employing Hamiltonians constructed within chiral effective field theory. In this contribution, we present a brief overview of one of such methods, the ab initio no-core shell model with continuum, and its applications to nucleon and deuterium scattering on light nuclei. The first investigation of the low-lying continuum spectrum of 6He within an ab initio framework that encompasses the 4He + n + n three-cluster dynamics characterizing its lowest particle-decay channel will also be briefly presented.

  15. Hamiltonian dynamics for complex food webs.

    PubMed

    Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

    2016-03-01

    We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity. PMID:27078396

  16. Chaotic maps, Hamiltonian flows, and Holographic methods.

    SciTech Connect

    Curtright, T. L.; Zachos, C. K.; High Energy Physics; Univ. of Miami

    2010-01-01

    Holographic functional methods are introduced as probes of discrete time-stepped maps that lead to chaotic behavior. The methods provide continuous time interpolation between the time steps, thereby revealing the maps to be quasi-Hamiltonian systems underlain by novel potentials that govern the motion of a perceived point particle. Between turning points, the particle is strictly driven by Hamiltonian dynamics, but at each encounter with a turning point the potential changes abruptly, loosely analogous to the switchbacks on a mountain road. A sequence of successively deepening switchback potentials explains, in physical terms, the frequency cascade and trajectory folding that occur on the particular route to chaos revealed by the logistic map.

  17. Canonical transformations and Hamiltonian evolutionary systems

    SciTech Connect

    Al-Ashhab, Samer

    2012-06-15

    In many Lagrangian field theories, one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different cases. These three cases depend on the specific dimensions of the vector bundle of the theory and the associated Hamiltonian differential operator. We also show how a canonical transformation transforms a Hamiltonian evolutionary system and its conservation laws. Finally, we illustrate these ideas with three examples.

  18. Ostrogradski Hamiltonian approach for geodetic brane gravity

    SciTech Connect

    Cordero, Ruben; Molgado, Alberto

    2010-12-07

    We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.

  19. Hamiltonian dynamics for complex food webs

    NASA Astrophysics Data System (ADS)

    Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

    2016-03-01

    We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

  20. Fractional kinetic equation for Hamiltonian chaos

    NASA Astrophysics Data System (ADS)

    Zaslavsky, G. M.

    1994-09-01

    Hamiltonian chaotic dynamics of particles (or passive particles in fluids) can be described by a fractional generalization of the Fokker-Planck-Kolmogorov equation (FFPK) which is defined by two fractional critical exponents (α, β) responsible for the space and time derivatives of the distribution function correspondingly. A renormalization method has been proposed to determine (α, β) from the first principles (ie. from the Hamiltonian). The anomalous transport exponent μ is derived as μ = β/α or μ = β/2α for the first order mean displacement in self-similar transport.

  1. Hamiltonian Dynamics of Protein Filament Formation

    NASA Astrophysics Data System (ADS)

    Michaels, Thomas C. T.; Cohen, Samuel I. A.; Vendruscolo, Michele; Dobson, Christopher M.; Knowles, Tuomas P. J.

    2016-01-01

    We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils.

  2. Hamiltonian dynamics of the parametrized electromagnetic field

    NASA Astrophysics Data System (ADS)

    Barbero G, J. Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.

    2016-06-01

    We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.

  3. Hamiltonian mechanics and planar fishlike locomotion

    NASA Astrophysics Data System (ADS)

    Kelly, Scott; Xiong, Hailong; Burgoyne, Will

    2007-11-01

    A free deformable body interacting with a system of point vortices in the plane constitutes a Hamiltonian system. A free Joukowski foil with variable camber shedding point vortices in an ideal fluid according to a periodically applied Kutta condition provides a model for fishlike locomotion which bridges the gap between inviscid analytical models that sacrifice realism for tractability and viscous computational models inaccessible to tools from nonlinear control theory. We frame such a model in the context of Hamiltonian mechanics and describe its relevance both to the study of hydrodynamic interactions within schools of fish and to the realization of model-based control laws for biomimetic autonomous robotic vehicles.

  4. Ab initio variational calculations of the vibrational properties of Li + 3, Li2Na + , LiNa + 2, and KLiNa +

    NASA Astrophysics Data System (ADS)

    Searles, D. J.; von Nagy-Felsobuki, E. I.

    1991-07-01

    A rovibrational Hamiltonian has been derived in terms of rectilinear displacement coordinates which is based on the Watson Hamiltonian. Moreover, it is a generalization of the Carney and Porter analysis for D3h triatomic systems [J. Chem. Phys. 65, 3547 (1976)] and Carney et al. analysis for C2v triatomic systems [J. Chem. Phys. 66, 3724 (1977)]. It is therefore the most general form of the Watson Hamiltonian which is applicable to a bent triatomic system. Ab initio variational calculations using this Hamiltonian are presented for vibrational properties of Li+3, Li2Na+, LiNa+2, and KLiNa+.

  5. DNA computing the Hamiltonian path problem.

    PubMed

    Lee, C M; Kim, S W; Kim, S M; Sohn, U

    1999-10-31

    The directed Hamiltonian path (DHP) problem is one of the hard computational problems for which there is no practical algorithm on a conventional computer available. Many problems, including the traveling sales person problem and the longest path problem, can be translated into the DHP problem, which implies that an algorithm for DHP can also solve all the translated problems. To study the robustness of the laboratory protocol of the pioneering DNA computing for the DHP problem performed by Leonard Adleman (1994), we investigated how the graph size, multiplicity of the Hamiltonian paths, and the size of oligonucleotides that encode the vertices would affect the laboratory procedures. We applied Adleman's protocol with 18-mer oligonucleotide per node to a graph with 8 vertices and 14 edges containing two Hamiltonian paths (Adleman used 20-mer oligonucleotides for a graph with 7 nodes, 14 edges and one Hamiltonian path). We found that depending on the graph characteristics such as the number of short cycles, the oligonucleotide size, and the hybridization conditions that used to encode the graph, the protocol should be executed with different parameters from Adleman's. PMID:10597033

  6. Hamiltonian Framework for Short Optical Pulses

    NASA Astrophysics Data System (ADS)

    Amiranashvili, Shalva

    Physics of short optical pulses is an important and active research area in nonlinear optics. In this Chapter we theoretically consider the most extreme representatives of short pulses that contain only several oscillations of electromagnetic field. Description of such pulses is traditionally based on envelope equations and slowly varying envelope approximation, despite the fact that the envelope is not "slow" and, moreover, there is no clear definition of such a "fast" envelope. This happens due to another paradoxical feature: the standard (envelope) generalized nonlinear Schrödinger equation yields very good correspondence to numerical solutions of full Maxwell equations even for few-cycle pulses, the thing that should not be.In what follows we address ultrashort optical pulses using Hamiltonian framework for nonlinear waves. As it appears, the standard optical envelope equation is just a reformulation of general Hamiltonian equations. In a sense, no approximations are required, this is why the generalized nonlinear Schrödinger equation is so effective. Moreover, the Hamiltonian framework contributes greatly to our understanding of "fast" envelopes, ultrashort solitons, stability and radiation of optical pulses. Even the inclusion of dissipative terms is possible making the Hamiltonian approach an universal theoretical tool also in extreme nonlinear optics.

  7. Hamiltonian and phenomenological models of microemulsions

    NASA Astrophysics Data System (ADS)

    Widom, B.; Dawson, K. A.; Lipkin, M. D.

    1986-12-01

    We review briefly a phenomenological microemulsion model, its phase diagram, and its interfacial tensions. We then describe a lattice model of a microemulsion, based on a prescribed Hamiltonian equivalent to that of an Ising model with competing nearest- and further-neighbor interactions. Its phase diagram and interfacial tensions are compared with those in the phenomenological model.

  8. Hamiltonian constraint in polymer parametrized field theory

    SciTech Connect

    Laddha, Alok; Varadarajan, Madhavan

    2011-01-15

    Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.

  9. The molecular symmetry adapted non - adiabatic coupling terms and diabatic Hamiltonian matrix

    NASA Astrophysics Data System (ADS)

    Mukherjee, Saikat; Bandyopadhyay, Sudip; Paul, Amit Kumar; Adhikari, Satrajit

    2013-04-01

    We calculate the adiabatic Potential Energy Surfaces (PESs) and the Non - Adiabatic Coupling Terms (NACTs) for the excited electronic states (22 E' and 12 A'1) of Na3 cluster at the MRCI level by using ab initio quantum chemistry package (MOLPRO), where the NACTs are adapted with Molecular Symmetry (MS) by employing appropriate Irreducible Representations (IREPs). Such terms are incorporated into the Adiabatic to Diabatic Transformation (ADT) equations to obtain the ADT angles to construct the continuous, single - valued, symmetric and smooth 3 × 3 diabatic Hamiltonian matrix.

  10. Simulations of the Structure and Properties of Large Icosahedral Boron Clusters Based on a Novel Semi-Empirical Hamiltonian

    NASA Astrophysics Data System (ADS)

    Tandy, Paul; Yu, Ming; Jayanthi, C. S.; Wu, Shi-Yu; Condensed Matter Theory Group Team

    2013-03-01

    A successful development of a parameterized semi-empirical Hamiltonian (SCED-LCAO) for boron based on a LCAO framework using a sp3 basis set will be discussed. The semi-empirical Hamiltonian contains environment-dependency and electron screening effects of a many-body Hamiltonian and allows for charge self-consistency. We have optimized the parameters of the SCED-LCAO Hamiltonian for boron by fitting the properties (e.g., the binding energy, bond length, etc.) of boron sheets, small clusters and boron alpha to first-principles calculations based on DFT calculations. Although extended phases of boron alpha and beta have been studied, large clusters of boron with icosahedral structures such as those cut from boron alpha are difficult if not impossible to simulate with ab initio methods. We will demonstrate the effectiveness of the SCED-LCAO Hamiltonian in studying icosahedral boron clusters containing up to 800 atoms and will report on some novel boron clusters and computational speed. Support has been provided by the Dillion Fellowship.

  11. Numerical determination of the magnetic field line Hamiltonian

    SciTech Connect

    Kuo-Petravic, G.; Boozer, A.H.

    1986-03-01

    The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories.

  12. Algebraic aspects of Tremblay-Turbiner-Winternitz Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Calzada, J. A.; Celeghini, E.; del Olmo, M. A.; Velasco, M. A.

    2012-02-01

    Using the factorization method we find a hierarchy of Tremblay-Turbiner-Winternitz Hamiltonians labeled by discrete indices. The shift operators (those connecting eigenfunctions of different Hamiltonians of the hierarchy) as well the ladder operators (they connect eigenstates of a determined Hamiltonian) obtained in this way close different algebraic structures that are presented here.

  13. Pseudo Hermitian formulation of the quantum Black-Scholes Hamiltonian

    NASA Astrophysics Data System (ADS)

    Jana, T. K.; Roy, P.

    2012-04-01

    We show that the non-Hermitian Black-Scholes Hamiltonian and its various generalizations are η-pseudo Hermitian. The metric operator η is explicitly constructed for this class of Hamiltonians. It is also shown that the effective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system.

  14. Accurate tight-binding Hamiltonians for two-dimensional and layered materials

    NASA Astrophysics Data System (ADS)

    Agapito, Luis A.; Fornari, Marco; Ceresoli, Davide; Ferretti, Andrea; Curtarolo, Stefano; Nardelli, Marco Buongiorno

    2016-03-01

    We present a scheme to controllably improve the accuracy of tight-binding Hamiltonian matrices derived by projecting the solutions of plane-wave ab initio calculations on atomic-orbital basis sets. By systematically increasing the completeness of the basis set of atomic orbitals, we are able to optimize the quality of the band-structure interpolation over wide energy ranges including unoccupied states. This methodology is applied to the case of interlayer and image states, which appear several eV above the Fermi level in materials with large interstitial regions or surfaces such as graphite and graphene. Due to their spatial localization in the empty regions inside or outside of the system, these states have been inaccessible to traditional tight-binding models and even to ab initio calculations with atom-centered basis functions.

  15. Internal dynamics in azetidine: A microwave and ab initio study

    NASA Astrophysics Data System (ADS)

    López, Juan C.; Blanco, Susana; Lesarri, Alberto; Alonso, José L.

    2001-02-01

    The internal dynamics of interconversion between equivalent conformations due to the coupling between ring puckering and NH inversion in azetidine has been investigated by rotational spectroscopy and ab initio computations. Analysis of the rotational spectra in the 8-220 GHz region has been completed for the ground state and first four excited states of the ring-puckering vibration. Rotational transitions exhibit a characteristic doubling originated by tunneling between equivalent conformations through a C2v barrier, which is related to symmetric (A1) and antisymmetric (B1) inversion states. Additionally, nuclear quadrupole hyperfine structure arising from the N nucleus could be resolved for low-J transitions. Accurate rotational and centrifugal distortion parameters together with the energy difference between inversion states derived from μc-type inversion transitions have been derived for each ring-puckering state using a two-state Hamiltonian. An effective monodimensional reduced potential function for the ring-puckering vibration V(X)=10.82(X4+14.29X-8.93X2-0.28X3) has been found consistent with the observed experimental variation of the rotational and centrifugal distortion constants with ring-puckering. This asymmetric single minimum potential function supports the existence of only one stable equatorial form. The barrier to interconversion between equivalent equatorial conformers, related to the C2v conformation of azetidine in which the ring atoms and the NH group are coplanar, has been estimated to range between 1900 and 2600 cm-1. The strong dependence of the dipole moment and quadrupole coupling constants with ring-puckering vibrational state evidence structural changes that occur along the ring-puckering coordinate.

  16. Emergent properties of nuclei from ab initio coupled-cluster calculations

    DOE PAGESBeta

    Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R.; Papenbrock, T.

    2016-05-17

    Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. Our endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. We review some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLOmore » $${}_{{\\rm{sat}}}$$ is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to 56Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon–nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. Finally, the coupling to the continuum impacts the energies of the $${J}^{\\pi }=1/{2}^{-},3/{2}^{-},7/{2}^{-},3/{2}^{+}$$ states in $${}^{\\mathrm{17,23,25}}$$O, and—contrary to naive shell-model expectations—the level ordering of the $${J}^{\\pi }=3/{2}^{+},5/{2}^{+},9/{2}^{+}$$ states in $${}^{\\mathrm{53,55,61}}$$Ca.« less

  17. Suppressing qubit dephasing using real-time Hamiltonian estimation

    PubMed Central

    Harvey, S. P.; Nichol, J. M.; Bartlett, S. D.; Doherty, A. C.; Umansky, V.; Yacoby, A.

    2014-01-01

    Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and materials engineering, quantum error correction and dynamical decoupling can mitigate decoherence, but generally increase experimental complexity. Here we improve coherence in a qubit using real-time Hamiltonian parameter estimation. Using a rapidly converging Bayesian approach, we precisely measure the splitting in a singlet-triplet spin qubit faster than the surrounding nuclear bath fluctuates. We continuously adjust qubit control parameters based on this information, thereby improving the inhomogenously broadened coherence time from tens of nanoseconds to >2 μs. Because the technique demonstrated here is compatible with arbitrary qubit operations, it is a natural complement to quantum error correction and can be used to improve the performance of a wide variety of qubits in both meteorological and quantum information processing applications. PMID:25295674

  18. Hamiltonian mechanics and divergence-free fields

    SciTech Connect

    Boozer, A.H.

    1986-08-01

    The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space.

  19. Engineering artificial Hamiltonians with parametric superconducting circuits

    NASA Astrophysics Data System (ADS)

    Lu, Yao; Chakram, Srivatsan; Leung, Nelson; Naik, Ravi; Earnest, Nathan; Groszkowski, Peter; Koch, Jens; Kapit, Eliot; Schuster, David

    One major challenge in building a large scale quantum computer is to generate and manipulate interactions between its many qubits. One promising approach is to use parametric flux or voltage modulation to realize effective interactions between different components of superconducting circuits, generating artificial Hamiltonians that are suitable for various quantum computation tasks, which might be difficult to achieve through other means. We propose a parametric superconducting circuit where transmon qubits and resonators are coupled to a flux-modulated parametric coupler. We show that with this device, arbitrary pairs of qubits or resonators in the circuit can be selectively and simultaneously brought into resonance with each other and swap excitations at a controllable rate. This allows for the creation of various artificial circuit Hamiltonians that are suitable for a number of applications such as single qubit state stablization, parametric qubit state readout, autonomous error correction and so on.

  20. Hamiltonian Dynamics of Protein Filament Formation.

    PubMed

    Michaels, Thomas C T; Cohen, Samuel I A; Vendruscolo, Michele; Dobson, Christopher M; Knowles, Tuomas P J

    2016-01-22

    We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils. PMID:26849615

  1. Conformal killing tensors and covariant Hamiltonian dynamics

    SciTech Connect

    Cariglia, M.; Gibbons, G. W.; Holten, J.-W. van; Horvathy, P. A.; Zhang, P.-M.

    2014-12-15

    A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.

  2. Hamiltonian deformations of Gabor frames: First steps

    PubMed Central

    de Gosson, Maurice A.

    2015-01-01

    Gabor frames can advantageously be redefined using the Heisenberg–Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immediately leads to the consideration of a general deformation scheme by Hamiltonian isotopies (i.e. arbitrary paths of non-linear symplectic mappings passing through the identity). We will study in some detail an associated weak notion of Hamiltonian deformation of Gabor frames, using ideas from semiclassical physics involving coherent states and Gaussian approximations. We will thereafter discuss possible applications and extensions of our method, which can be viewed – as the title suggests – as the very first steps towards a general deformation theory for Gabor frames. PMID:25892903

  3. General formalism for singly thermostated Hamiltonian dynamics.

    PubMed

    Ramshaw, John D

    2015-11-01

    A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly discussed. PMID:26651677

  4. Hamiltonian learning and certification using quantum resources.

    PubMed

    Wiebe, Nathan; Granade, Christopher; Ferrie, Christopher; Cory, D G

    2014-05-16

    In recent years quantum simulation has made great strides, culminating in experiments that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum simulators may be able to perform computational tasks that existing computers cannot, it also introduces a major challenge: certifying that the quantum simulator is in fact simulating the correct quantum dynamics. We provide an algorithm that, under relatively weak assumptions, can be used to efficiently infer the Hamiltonian of a large but untrusted quantum simulator using a trusted quantum simulator. We illustrate the power of this approach by showing numerically that it can inexpensively learn the Hamiltonians for large frustrated Ising models, demonstrating that quantum resources can make certifying analog quantum simulators tractable. PMID:24877920

  5. Squeezed states for the Bateman Hamiltonian

    NASA Astrophysics Data System (ADS)

    Aliaga, J.; Crespo, G.; Proto, A. N.

    1991-01-01

    Recently, De Brito and Baseia [Phys. Rev. A 40, 4097 (1989)] have studied the appearance of squeezed states for the Bateman Hamiltonian. Although the final results obtained in that report are correct, it is our intention to use an alternative point of view, based on a density matrix defined according to the maximum entropy principle, which allows us to reobtain those results in a more general way.

  6. The Heun operator as a Hamiltonian

    NASA Astrophysics Data System (ADS)

    Turbiner, A. V.

    2016-07-01

    It is shown that the celebrated Heun operator {H}e=-({a}0{x}3+{a}1{x}2+{a}2x)\\tfrac{{{{d}}}2}{{{{d}}x}2} + ({b}0{x}2+{b}1x+{b}2)\\tfrac{{{d}}}{{{d}}x}+{c}0x is the Hamiltonian of the {sl}(2,R)-quantum Euler–Arnold top of spin ν in a constant magnetic field. For {a}0\

  7. The Hamiltonian Mechanics of Stochastic Acceleration

    SciTech Connect

    Burby, J. W.

    2013-07-17

    We show how to nd the physical Langevin equation describing the trajectories of particles un- dergoing collisionless stochastic acceleration. These stochastic di erential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.

  8. Hamiltonian theory of guiding-center motion

    SciTech Connect

    Littlejohn, R.G.

    1980-05-01

    A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.

  9. L2-cohomology and complete Hamiltonian manifolds

    NASA Astrophysics Data System (ADS)

    Mazzeo, Rafe; Pelayo, Álvaro; Ratiu, Tudor S.

    2015-01-01

    A classical theorem of Frankel for compact Kähler manifolds states that a Kähler S1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem still holds. Finally, we present several concrete situations in which the assumptions of the metatheorem hold.

  10. Hamiltonian anomalies of bound states in QED

    SciTech Connect

    Shilin, V. I.; Pervushin, V. N.

    2013-10-15

    The Bound State in QED is described in systematic way by means of nonlocal irreducible representations of the nonhomogeneous Poincare group and Dirac's method of quantization. As an example of application of this method we calculate triangle diagram Para-Positronium {yields} {gamma}{gamma}. We show that the Hamiltonian approach to Bound State in QED leads to anomaly-type contribution to creation of pair of parapositronium by two photon.

  11. Hamiltonian time integrators for Vlasov-Maxwell equations

    SciTech Connect

    He, Yang; Xiao, Jianyuan; Zhang, Ruili; Liu, Jian; Qin, Hong; Sun, Yajuan

    2015-12-15

    Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature.

  12. Programmable quantum simulation by dynamic Hamiltonian engineering

    NASA Astrophysics Data System (ADS)

    Hayes, David; Flammia, Steven T.; Biercuk, Michael J.

    2014-08-01

    Quantum simulation is a promising near term application for quantum information processors with the potential to solve computationally intractable problems using just a few dozen interacting qubits. A range of experimental platforms have recently demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions and relativistic quantum mechanics. However, in all cases, the physics of the underlying hardware restricts the achievable inter-particle interactions and forms a serious constraint on the versatility of the simulators. To broaden the scope of these analog devices, we develop a suite of pulse sequences that permit a user to efficiently realize average Hamiltonians that are beyond the native interactions of the system. Specifically, this approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin-1/2 XYZ chains, but generalized to include long-range couplings. Our work builds on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries. We show that determining the appropriate ‘program’ of unitary pulse sequences which implements an arbitrary Hamiltonian transformation can be formulated as a linear program over functions defined by those pulse sequences, running in polynomial time and scaling efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, representing an important and broad-based success in applying functional analysis to the field of quantum information.

  13. Hamiltonian approach to the magnetostatic equilibrium problem

    SciTech Connect

    Tessarotto, M.; Zheng, Lin Jin; Johnson, J.L.

    1995-02-01

    The purpose of this paper is to investigate the classical scalar-pressure magnetostatic equilibrium problem for non-symmetric configurations in the framework of a Hamiltonian approach. Requiring that the equilibrium admits locally, in a suitable subdomain, a family of nested toroidal magnetic surfaces, the Hamiltonian equations describing the magnetic flux lines in such a subdomain are obtained for general curvilinear coordinate systems. The properties of such Hamiltonian system are investigated. A representation of the magnetic field in terms of arbitrary general curvilinear coordinates is thus obtained. Its basic feature is that the magnetic field must fulfill suitable periodicity constraints to be imposed on arbitrary rational magnetic surfaces for general non-symmetric toroidal equilibria, i.e., it is quasi-symmetric. Implications for the existence of magnetostatic equilibria are pointed out. In particular, it is proven that a generalized equilibrium equation exists for such quasi-symmetric equilibria, which extends the Grad-Shafranov equation to fully three-dimensional configurations. As an application, the case is considered of quasi-helical equilibria, i.e., displaying a magnetic field magnitude depending on the poloidal ({chi}) and toroidal ({var_theta}) angles only in terms of {alpha}={chi}-N{theta} with N an arbitrary integer.

  14. Reinforcement learning for port-hamiltonian systems.

    PubMed

    Sprangers, Olivier; Babuška, Robert; Nageshrao, Subramanya P; Lopes, Gabriel A D

    2015-05-01

    Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without any performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning (RL) approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systems's PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust. The parameters of the control law are found by using actor-critic (AC) RL, enabling the search for near-optimal control policies satisfying a desired closed-loop energy landscape. The advantage is that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the RL perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the AC framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments. PMID:25167564

  15. Regular and Chaotic Motion in Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Varvoglis, Harry

    All laws that describe the time evolution of a continuous system are given in the form of differential equations, ordinary (if the law involves one independent variable) or partial (if the law involves two or more independent variables). Historically the first law of this type was Newton's second law of motion. Since then Dynamics, as it is customary to name the branch of Mechanics that studies the motion of a body as the result of a force acting on it, has become the “typical„ case that comes into one's mind when a system of ordinary differential equation is given, although this system might as well describe any other system, e.g. physical, chemical, biological, financial etc. In particular the study of “conservative„ dynamical systems, i.e. systems of ordinary differential equations that originate from a time-independent Hamiltonian function, has become a thoroughly developed area, because of the fact that mechanical energy is very often conserved, although many other physical phenomena, beyond motion, can be described by Hamiltonian systems as well. In what follows we will restrict ourselves exactly to the study of Hamiltonian systems, as typical dynamical systems that find applications in many scientific disciplines.

  16. Redesign of the DFT/MRCI Hamiltonian

    NASA Astrophysics Data System (ADS)

    Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M.

    2016-01-01

    The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.

  17. Redesign of the DFT/MRCI Hamiltonian.

    PubMed

    Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M

    2016-01-21

    The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion. PMID:26801017

  18. Collective rotation from ab initio theory

    NASA Astrophysics Data System (ADS)

    Caprio, Mark A.; Maris, Pieter; Vary, James P.

    2015-10-01

    The challenge of ab initio nuclear theory is to quantitatively predict the complex and highly-correlated behavior of the nuclear many-body system, starting from the underlying internucleon interactions. We may now seek to understand the wealth of nuclear collective phenomena through ab initio approaches. No-core configuration interaction (NCCI) calculations for p-shell nuclei give rise to rotational bands, as evidenced by rotational patterns for excitation energies, electromagnetic moments, and electromagnetic transitions. In this talk, the intrinsic structure of these bands is discussed, and the predicted rotational bands are compared to experiment. Supported by the US DOE under Award Nos. DE-FG02-95ER-40934, DESC0008485 (SciDAC/NUCLEI), and DE-FG02-87ER40371 and the US NSF under Award No. 0904782. Computational resources provided by NERSC (US DOE Contract No. DE-AC02-05CH11231).

  19. Model many-body Stoner Hamiltonian for binary FeCr alloys

    NASA Astrophysics Data System (ADS)

    Nguyen-Manh, D.; Dudarev, S. L.

    2009-09-01

    We derive a model tight-binding many-body d -electron Stoner Hamiltonian for FeCr binary alloys and investigate the sensitivity of its mean-field solutions to the choice of hopping integrals and the Stoner exchange parameters. By applying the local charge-neutrality condition within a self-consistent treatment we show that the negative enthalpy-of-mixing anomaly characterizing the alloy in the low chromium concentration limit is due entirely to the presence of the on-site exchange Stoner terms and that the occurrence of this anomaly is not specifically related to the choice of hopping integrals describing conventional chemical bonding between atoms in the alloy. The Bain transformation pathway computed, using the proposed model Hamiltonian, for the Fe15Cr alloy configuration is in excellent agreement with ab initio total-energy calculations. Our investigation also shows how the parameters of a tight-binding many-body model Hamiltonian for a magnetic alloy can be derived from the comparison of its mean-field solutions with other, more accurate, mean-field approximations (e.g., density-functional calculations), hence stimulating the development of large-scale computational algorithms for modeling radiation damage effects in magnetic alloys and steels.

  20. A new method for distinguishing between Al 2X 6 (X=Cl, Br) conformers based on ab initio calculated nuclear quadrupole coupling constants

    NASA Astrophysics Data System (ADS)

    Hadipour, N. L.; Elmi, F.

    2003-03-01

    Nuclear quadrupole coupling constants ( χ) of 27Al, 35Cl and 81Br in AlX 3 monomers as well as Al 2X 6 (X=Cl, Br) dimers are calculated at the RHF/6-311G* and B 3LYP/6-311G* levels, using G AUSSIAN 98 package. Correlations are made between χ and dihedral angles θ, of Al 2X 6. These θs are produced through the ring puckering motions about the hinge line which joins the two bridge halogens (X b). Nuclear quadrupole coupling constants of 35Cl, 81Br and 27Al are used as probes for monitoring the departure of the symmetry of Al 2X 6 from a high symmetry point group D 2h to a lower one. The χs of chlorine nuclei of AlCl 3 differ significantly from those of Al 2Cl 6. These differences appear negligible for AlBr 3 in comparison to Al 2Br 6. This work demonstrates the considerable sensitivity of nuclear quadrupole resonance in distinguishing between Al 2X 6 conformers. This is in comparison to the usage of energy differences which is customarily employed.

  1. AB248. Expression of EphA2 protein is positively associated with age, tumor size and Fuhrman nuclear grade in clear cell renal cell carcinomas

    PubMed Central

    Wang, Longxin; Zhou, Wenquan

    2016-01-01

    Background The receptor tyrosine kinase of EphA2 has been shown frequently overexpressed in various types of human carcinomas, but the relationship between the expression of EphA2 protein in clear cell renal cell carcinoma was not well documented. Methods In the present study, using specific anit-EphA2 polyclonal antibody and immunohistochemistry, we evaluated EphA2 protein expression levels in clear cell RCC specimens surgically resected from 90 patients. Results Our results shows that EphA2 protein was positively expressed in all normal renal tubes of 90 samples (100%, 3+), which was expressed at low levels in renal cortex but high levels in the collecting ducts of the renal medulla and papilla. EphA2 was negatively or weakly expressed in 30 out of 90 samples (33.3%, 0/1+), moderately expressed in 24 samples (26.7%, 2+) and strongly expressed in 36 samples (40%, 3+). Expression of EphA2 was positively associated with age (P=0.029), tumor diameters (P<0.001) and Fuhrman nuclear grade (P<0.001). Conclusions Our results indicate that EphA2 variably expressed in clear cell renal cell carci-nomas. High expression of EphA2 was more often found in big size and high nuclear grade tumors, which indicated EphA2 protein may be used as a new marker for the prognosis of clear cell renal cell carcinoma.

  2. A self-consistent and environment-dependent Hamiltonian for large-scale simulations of complex nanostructures

    NASA Astrophysics Data System (ADS)

    Yu, Ming; Wu, S. Y.; Jayanthi, C. S.

    2009-11-01

    This review is devoted to the development of a robust semi-empirical Hamiltonian for quantum-mechanics-based simulations. The Hamiltonian referred as self-consistent (SC) and environment-dependent (ED) Hamiltonian is developed in the framework of linear combination of atomic orbitals (LCAO) and includes multi-center electron-ion and electron-electron interactions. Furthermore, the framework allows for a self-consistent treatment of charge-redistributions. The parameterized Hamiltonian matrix elements and overlap functions are obtained by fitting them to accurate first-principles database of properties corresponding to clusters and bulk phases of materials. The total energy includes the band structure energy, the correction term from the double-counting of electrons, and ion-ion repulsions, where the band structure energy is obtained by solving a generalized eigenvalue equation. Linear scaling algorithms for large-scale simulations of materials have also been incorporated. The present approach goes beyond the traditional two-center tight-binding Hamiltonians in terms of its accuracy and transferability and allows the study of system sizes that are beyond the scope of ab-initio simulations. We have studied a wide-variety of complex materials and complex phenomena using the SCED-LCAO MD that include: (i) the structure and stability of bucky-diamond carbon clusters and their phase transformations upon annealing, (ii) the initial stage of growth of single-wall carbon nanotubes (SWCNTs), and (iii) structural and electronic properties of bucky-diamond SiC clusters and SiC nanowires (NWs). The successful outcome of these case studies is a testament to the transferability of the Hamiltonian to different types of atomic environments ( i.e., co-ordinations and bonding configurations).

  3. Hierarchical structure of noncanonical Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Yoshida, Z.; Morrison, P. J.

    2016-02-01

    Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of ‘equipartition’ may bear no specific structure. Fluid turbulence is a typical example—while turbulent mixing seems to increase entropy, a variety of sustained vortical structures can emerge. In Hamiltonian formalism, some topological constraints are represented by Casimir invariants (for example, helicities of a fluid or a plasma), and then, the effective phase space is reduced to the Casimir leaves. However, a general constraint is not necessarily integrable, which precludes the existence of an appropriate Casimir invariant; the circulation is an example of such an invariant. In this work, we formulate a systematic method to embed a Hamiltonian system in an extended phase space; we introduce phantom fields and extend the Poisson algebra. A phantom field defines a new Casimir invariant, a cross helicity, which represents a topological constraint that is not integrable in the original phase space. Changing the perspective, a singularity of the extended system may be viewed as a subsystem on which the phantom fields (though they are actual fields, when viewed from the extended system) vanish, i.e., the original system. This hierarchical relation of degenerate Poisson manifolds enables us to see the ‘interior’ of a singularity as a sub Poisson manifold. The theory can be applied to describe bifurcations and instabilities in a wide class of general Hamiltonian systems (Yoshida and Morrison 2014 Fluid Dyn. Res. 46 031412).

  4. Building A Universal Nuclear Energy Density Functional (UNEDF)

    SciTech Connect

    Joe Carlson; Dick Furnstahl; Mihai Horoi; Rusty Lusk; Witek Nazarewicz; Esmond Ng; Ian Thompson; James Vary

    2012-09-30

    During the period of Dec. 1 2006 - Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: first, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory. The main physics areas of UNEDF, defined at the beginning of the project, were: ab initio structure; ab initio functionals; DFT applications; DFT extensions; reactions.

  5. Gapless topological superconductors: Model Hamiltonian and realization

    NASA Astrophysics Data System (ADS)

    Baum, Yuval; Posske, Thore; Fulga, Ion Cosma; Trauzettel, Björn; Stern, Ady

    2015-07-01

    The existence of an excitation gap in the bulk spectrum is one of the most prominent fingerprints of topological phases of matter. In this paper, we propose a family of two-dimensional Hamiltonians that yield an unusual class D topological superconductor with a gapless bulk spectrum but well-localized Majorana edge states. We perform a numerical analysis for a representative model of this phase and suggest a concrete physical realization by analyzing the effect of magnetic impurities on the surface of a strong topological insulator.

  6. Hamiltonian Description of Convective-cell Generation

    SciTech Connect

    J.A. Krommes and R.A. Kolesnikov

    2004-03-11

    The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted.

  7. Timelike singularities and Hamiltonian cosmological billiards

    NASA Astrophysics Data System (ADS)

    Klinger, Paul

    2016-06-01

    We construct a large class of vacuum solutions of the Einstein equations without any symmetries and with controlled asymptotics near a timelike singularity. The solutions are obtained by a Fuchs analysis of the equations which evolve the metric in a spacelike direction. We further observe that the change of sign of some of the terms (walls) in the associated Hamiltonian invalidate the ‘cosmological billards’ heuristic arguments for the existence of singularities of the mixmaster type in the current context. UWThPh-2015-33

  8. Quantum Hamiltonian identification from measurement time traces.

    PubMed

    Zhang, Jun; Sarovar, Mohan

    2014-08-22

    Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings. PMID:25192077

  9. Statistical mechanics of Hamiltonian adaptive resolution simulations.

    PubMed

    Español, P; Delgado-Buscalioni, R; Everaers, R; Potestio, R; Donadio, D; Kremer, K

    2015-02-14

    The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea (H-AdResS) allows one to formulate the usual tools of ensembles and statistical mechanics. We present a number of exact and approximate results that provide a statistical mechanics foundation for this simulation method. We also present simulation results that illustrate the theory. PMID:25681895

  10. Hamiltonian formalism of weakly nonlinear hydrodynamic systems

    SciTech Connect

    Pavlov, M.V.

    1988-05-01

    A study is made of systems of quasilinear equations that are diagonalizable and Hamiltonian and have the condition /delta//sub i/v/sub i/ /triple bond/ 0, where u/sub t//sup i/ /equal/ v/sup i/(u)u/sub x//sup i/, i = 1, ..., N. The conservation laws of such systems are found, together with the metric and Poisson bracket. For definite examples it is shown how solutions are found. The conditions for the existence of solutions and continuity of commuting flows are found.

  11. Hamiltonian Paths Through Two- and Three-Dimensional Grids

    PubMed Central

    Mitchell, William F.

    2005-01-01

    This paper addresses the existence of Hamiltonian paths and cycles in two-dimensional grids consisting of triangles or quadrilaterals, and three-dimensional grids consisting of tetrahedra or hexahedra. The paths and cycles may be constrained to pass from one element to the next through an edge, through a vertex, or be unconstrained and pass through either. It was previously known that an unconstrained Hamiltonian path exists in a triangular grid under very mild conditions, and that there are triangular grids for which there is no through-edge Hamiltonian path. In this paper we prove that a through-vertex Hamiltonian cycle exists in any triangular or tetrahedral grid under very mild conditions, and that there exist quadrilateral and hexahedral grids for which no unconstrained Hamiltonian path exists. The existence proofs are constructive, and lead to an efficient algorithm for finding a through-vertex Hamiltonian cycle.

  12. Perturbation Theory for Parent Hamiltonians of Matrix Product States

    NASA Astrophysics Data System (ADS)

    Szehr, Oleg; Wolf, Michael M.

    2015-05-01

    This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).

  13. Wigner quantization of some one-dimensional Hamiltonians

    SciTech Connect

    Regniers, G.; Van der Jeugt, J.

    2010-12-15

    Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have been shown. Among those we have the ubiquitous relation with Lie superalgebras and their representations. In this paper, we study two one-dimensional Hamiltonians for which the Wigner quantization is related with the orthosymplectic Lie superalgebra osp(1|2). One of them, the Hamiltonian H=xp, is popular due to its connection with the Riemann zeros, discovered by Berry and Keating on the one hand and Connes on the other. The Hamiltonian of the free particle, H{sub f}=p{sup 2}/2, is the second Hamiltonian we will examine. Wigner quantization introduces an extra representation parameter for both of these Hamiltonians. Canonical quantization is recovered by restricting to a specific representation of the Lie superalgebra osp(1|2).

  14. Accurate Effective Hamiltonians via Unitary Flow in Floquet Space

    NASA Astrophysics Data System (ADS)

    Verdeny, Albert; Mielke, Andreas; Mintert, Florian

    2013-10-01

    We present a systematic construction of effective Hamiltonians of periodically driven quantum systems. Because of an equivalence between the time dependence of a Hamiltonian and an interaction in its Floquet operator, flow equations, that permit us to decouple interacting quantum systems, allow us to identify time-independent Hamiltonians for driven systems. With this approach, we explain the experimentally observed deviation of expected suppression of tunneling in ultracold atoms.

  15. Precise Electromagnetic Tests of Ab Initio Calculations of Light Nuclei: States in {sup 10}Be

    SciTech Connect

    McCutchan, E. A.; Lister, C. J.; Wiringa, R. B.; Pieper, Steven C.; Seweryniak, D.; Greene, J. P.; Carpenter, M. P.; Janssens, R. V. F.; Khoo, T. L.; Lauritsen, T.; Zhu, S.; Chiara, C. J.; Stefanescu, I.

    2009-11-06

    In order to test ab initio calculations of light nuclei, we have remeasured lifetimes in {sup 10}Be using the Doppler shift attenuation method (DSAM) following the {sup 7}Li({sup 7}Li,alpha){sup 10}Be reaction at 8 and 10 MeV. The new experiments significantly reduce systematic uncertainties in the DSAM technique. The J{sup p}i=2{sub 1}{sup +} state at 3.37 MeV has tau=205+-(5){sub stat}+-(7){sub sys} fs corresponding to a B(E2arrow down) of 9.2(3)e{sup 2} fm{sup 4} in broad agreement with many calculations. The J{sup p}i=2{sub 2}{sup +} state at 5.96 MeV was found to have a B(E2arrow down) of 0.11(2)e{sup 2} fm{sup 4} and provides a more discriminating test of nuclear models. New Green's function Monte Carlo calculations for these states and transitions with a number of Hamiltonians are also reported and compared to experiment.

  16. Ab initio approach to effective single-particle energies in doubly closed shell nuclei

    NASA Astrophysics Data System (ADS)

    Duguet, T.; Hagen, G.

    2012-03-01

    The present work discusses, from an ab initio standpoint, the definition, the meaning, and the usefulness of effective single-particle energies (ESPEs) in doubly closed shell nuclei. We perform coupled-cluster calculations to quantify to what extent selected closed-shell nuclei in the oxygen and calcium isotopic chains can effectively be mapped onto an effective independent-particle picture. To do so, we revisit in detail the notion of ESPEs in the context of strongly correlated many-nucleon systems and illustrate the necessity of extracting ESPEs through the diagonalization of the centroid matrix, as originally argued by Baranger. For the purpose of illustration, we analyze the impact of correlations on observable one-nucleon separation energies and nonobservable ESPEs in selected closed-shell oxygen and calcium isotopes. We then state and illustrate the nonobservability of ESPEs. Similarly to spectroscopic factors, ESPEs can indeed be modified by a redefinition of inaccessible quantities while leaving actual observables unchanged. This leads to the absolute necessity of employing consistent structure and reaction models based on the same nuclear Hamiltonian to extract the shell structure in a meaningful fashion from experimental data.

  17. Omega-AB

    Energy Science and Technology Software Center (ESTSC)

    2007-05-01

    A hierarchical, modular modeling environment for hybrid simulations of sequential-modular, systems dynamics, discrete-event, and agent-based paradigms Omega-AB models contain a hierarchically-defined module tree that specifies the execution logic for the simulation, and a multi-network graph that defines the environment within which the simulation occurs. Modules are the fundamental buildinig blocks of an Omega-AB model and can define anything from a basic mathematical operation to a complex behavioral response model. Modules rely on the "plug-in" conceptmore » which allows developers to build independent module libraries that are gathered, linked, and instantiated by the Omega-AB engine at run time. Inter-module communication occurs through two complimentary systems: pull-based "ports" for general computation patterns and push-based "plugs" for event processing. The simulation environment is an abstract graph of nodes and links. Agents (module sub-trees headed up by an Agent module) reside at nodes and relate to their neighbors through typed links. To facilitate the construction and visualization of complex, interacting networks with dramatically different structure, Omega-AB provides a system for organizing the nodes into hierarchica trees that describe "slices" of the overall network.« less

  18. A Hamiltonian Five-Field Gyrofluid Model

    NASA Astrophysics Data System (ADS)

    Keramidas Charidakos, Ioannis; Waelbroeck, Francois; Morrison, Philip

    2015-11-01

    Reduced fluid models constitute versatile tools for the study of multi-scale phenomena. Examples include magnetic islands, edge localized modes, resonant magnetic perturbations, and fishbone and Alfven modes. Gyrofluid models improve over Braginskii-type models by accounting for the nonlocal response due to particle orbits. A desirable property for all models is that they not only have a conserved energy, but also that they be Hamiltonian in the ideal limit. Here, a Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of electron and ion densities, the parallel component of ion and electron velocities and ion temperature. Quasineutrality and Ampere's law determine respectively the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated to five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models. This work was funded by U.S. DOE Contract No. DE-FG02-04ER-54742.

  19. Spinor-Like Hamiltonian for Maxwellian Optics

    NASA Astrophysics Data System (ADS)

    Kulyabov, D. S.

    2016-02-01

    Background. Spinors are more special objects than tensors. Therefore spinors possess more properties than the more generic objects such as tensors. The group of Lorentz two-spinors is the covering group of the Lorentz group. Purpose. Since the Lorentz group is the symmetry group of Maxwell equations, it is reasonable to use Lorentz two-spinors and not tensors when writing the Maxwell equations. Method. We write the Maxwell equations using Lorentz two-spinors. Also a convenient representation of Lorentz two-spinors in terms of the Riemann-Silberstein complex vectors is used. Results: In the spinor formalism (in the representation of the Lorentz spinors and Riemann-Silberstein vectors) we have constructed the Hamiltonian of Maxwellian optics. With the use of spinors, the Maxwell equations take a form similar to the Dirac equation. Conclusions: For Maxwell equations in the Dirac-like form we can expand research methods by means of quantum field theory. In this form, the connection between the Hamiltonians of geometric, beam and Maxwellian optics is clearly visible.

  20. Hamiltonian theory of fractionally filled Chern bands

    NASA Astrophysics Data System (ADS)

    Murthy, Ganpathy; Shankar, R.

    2012-11-01

    There is convincing numerical evidence that fractional quantum-Hall-like ground states arise in fractionally filled Chern bands. Here, we show that the Hamiltonian theory of composite fermions (CF) can be as useful in describing these states as it was in describing the fractional quantum Hall effect (FQHE) in the continuum. We are able to introduce CFs into the fractionally filled Chern-band problem in two stages. First, we construct an algebraically exact mapping which expresses the electron density projected to the Chern band ρFCB as a sum of Girvin-MacDonald-Platzman density operators ρGMP that obey the magnetic translation algebra. Next, following our Hamiltonian treatment of the FQH problem, we rewrite the operators ρGMP in terms of CF variables which reproduce the same algebra. This naturally produces a unique Hartree-Fock ground state for the CFs, which can be used as a springboard for computing gaps, response functions, temperature-dependent phenomena, and the influence of disorder. We give two concrete examples, one of which has no analog in the continuum FQHE with ν=(1)/(5) and σxy=(2)/(5). Our approach can be easily extended to fractionally filled, strongly interacting two-dimensional time-reversal-invariant topological insulators.

  1. Ab initio infrared and Raman spectra

    NASA Technical Reports Server (NTRS)

    Fredkin, D. R.; White, S. R.; Wilson, K. R.; Komornicki, A.

    1983-01-01

    It is pointed out that with increased computer power and improved computational techniques, such as the gradients developed in recent years, it is becoming practical to compute spectra ab initio, from the fundamental constants of nature, for systems of increasing complexity. The present investigation has the objective to explore several possible ab initio approaches to spectra, giving particular attention to infrared and nonresonance Raman. Two approaches are discussed. The sequential approach, in which first the electronic part and then later the nuclear part of the Born-Oppenheimer approximation is solved, is appropriate for small systems. The simultaneous approach, in which the electronic and nuclear parts are solved at the same time, is more appropriate for many-atom systems. A review of the newer quantum gradient techniques is provided, and the infrared and Raman spectral band contours for the water molecule are computed.

  2. Order-selective multiple-quantum excitation in magic-angle spinning NMR: creating triple-quantum coherences with a trilinear Hamiltonian

    NASA Astrophysics Data System (ADS)

    Edén, Mattias

    2002-12-01

    Order-selective multiple-quantum excitation in magic-angle spinning nuclear magnetic resonance is explored using a class of symmetry-based pulse sequences, denoted S Mχ. Simple rules are presented that aid the design of S Mχ schemes with certain desirable effective Hamiltonians. They are applied to construct sequences generating trilinear effective dipolar Hamiltonians, suitable for efficient excitation of triple-quantum coherences in rotating solids. The new sequences are investigated numerically and demonstrated by 1H experiments on adamantane.

  3. Fractional Hamiltonian monodromy from a Gauss-Manin monodromy

    SciTech Connect

    Sugny, D.; Jauslin, H. R.; Mardesic, P.; Pelletier, M.; Jebrane, A.

    2008-04-15

    Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by [Nekhoroshev, Sadovskii, and Zhilinskii, C. R. Acad. Sci. Paris, Ser. 1 335, 985 (2002); and Ann. Henri Poincare 7, 1099 (2006)] for energy-momentum maps whose image has a particular type of nonisolated singularities. In this paper, we analyze the notion of fractional Hamiltonian monodromy in terms of the Gauss-Manin monodromy of a Riemann surface constructed from the energy-momentum map and associated with a loop in complex space which bypasses the line of singularities. We also prove some propositions on fractional Hamiltonian monodromy for 1:-n and m:-n resonant systems.

  4. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

    NASA Astrophysics Data System (ADS)

    Fernández, Francisco M.

    2016-06-01

    We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.

  5. Position-dependent mass quantum Hamiltonians: general approach and duality

    NASA Astrophysics Data System (ADS)

    Rego-Monteiro, M. A.; Rodrigues, Ligia M. C. S.; Curado, E. M. F.

    2016-03-01

    We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of self-adjoint Hamiltonians which are quantum mechanically equivalent to the non-self-adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of self-adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrödinger equations generated by the non-self-adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual self-adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-self-adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have self-adjoint Hamiltonians that correspond to the non-self-adjoint ones found in Harrison’s article.

  6. A method for Hamiltonian truncation: a four-wave example

    NASA Astrophysics Data System (ADS)

    Viscondi, Thiago F.; Caldas, Iberê L.; Morrison, Philip J.

    2016-04-01

    A method for extracting finite-dimensional Hamiltonian systems from a class of 2 + 1 Hamiltonian mean field theories is presented. These theories possess noncanonical Poisson brackets, which normally resist Hamiltonian truncation, but a process of beatification by coordinate transformation near a reference state is described in order to perturbatively overcome this difficulty. Two examples of four-wave truncation of Euler’s equation for scalar vortex dynamics are given and compared: one a direct non-Hamiltonian truncation of the equations of motion, the other obtained by beatifying the Poisson bracket and then truncating.

  7. Hamiltonian description of closed configurations of the vacuum magnetic field

    NASA Astrophysics Data System (ADS)

    Skovoroda, A. A.

    2015-05-01

    Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov'ev, and V.D. Shafranov.

  8. Action with Acceleration i: Euclidean Hamiltonian and Path Integral

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2013-10-01

    An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated.

  9. How is Lorentz invariance encoded in the Hamiltonian?

    NASA Astrophysics Data System (ADS)

    Kajuri, Nirmalya

    2016-07-01

    One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.

  10. Hamiltonian description of closed configurations of the vacuum magnetic field

    SciTech Connect

    Skovoroda, A. A.

    2015-05-15

    Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov’ev, and V.D. Shafranov.

  11. AB072. Novel mutation in the hepatocyte nuclear factor 1b/maturity-onset diabetes of the young type 5 gene—unreported Vietnamese case

    PubMed Central

    Dung, Vu Chi; Thao, Bui Phuong; Ngoc, Can Thi Bich; Khanh, Nguyen Ngoc; Ellard, Sian

    2015-01-01

    Maturity-onset diabetes of the young type 5 (MODY5), a type of dominantly inherited diabetes mellitus and nephropathy, has been associated with mutations of the hepatocyte nuclear factor-1 (HNF-1β) gene, mostly generating truncated protein. Various phenotypes are related to HNF-1β mutations. Our aim to describe clinical and genetic findings in the unreported Vietnamese case identified with HNF-1β mutations. The proband with kidney failure from 7.5 years of age and diabetes diagnosed at 13.5 years of age who were described. Case report included information: characteristics of diabetes, renal function and structure, pancreas structure. Genomic DNA was extracted from WBC of whole blood and HNF-1β mutation was performed using PCR and direct sequencing. The proband is heterozygous for a novel HNF-1β missense mutation (c.505T > C; p.Y169H). This mutation results in the substitution of the amino acid histidine (charged polar) for tyrosine (uncharged polar) at codon 169. The tyrosine residue is conserved across species and it is therefore likely that the p.Y169H mutation is pathogenic. This result is consistent with a diagnosis of renal cysts and diabetes syndrome (RCAD). Testing was done for proband’s parents and no mutation was found in HNF-1β. It is therefore likely that the p.Y169H mutation has arisen de novo. Kidney MRI showed right kidney atrophy and pancreas MRI showed only tissue of head of pancreas. Investigations at 14.5 years of age—diagnosed diabetes showed: plasma urea 10.1 mmol/L; creatinine 250 micrommol/L; HbA1C 13.6%. He was given insulin of 0.8 UI/kg/day and HbA1C was 6.8% after 1 year of treatment with insulin injection. Maturity-onset diabetes of the young type 5 encompasses a wide clinical spectrum. Analysis for mutations of HNF-1β is warranted, even without a family history of diabetes, in nonobese patients with diabetes and slowly progressive non diabetic nephropathy, particularly when pancreatic atrophy.

  12. Ab initio infrared and Raman spectra

    NASA Astrophysics Data System (ADS)

    Fredkin, Donald R.; Komornicki, Andrew; White, Steven R.; Wilson, Kent R.

    1983-06-01

    We discuss several ways in which molecular absorption and scattering spectra can be computed ab initio, from the fundamental constants of nature. These methods can be divided into two general categories. In the first, or sequential, type of approach, one first solves the electronic part of the Schrödinger equation in the Born-Oppenheimer approximation, mapping out the potential energy, dipole moment vector (for infrared absorption) and polarizability tensor (for Raman scattering) as functions of nuclear coordinates. Having completed the electronic part of the calculation, one then solves the nuclear part of the problem either classically or quantum mechanically. As an example of the sequential ab initio approach, the infrared and Raman rotational and vibrational-rotational spectral band contours for the water molecule are computed in the simplest rigid rotor, normal mode approximation. Quantum techniques are used to calculate the necessary potential energy, dipole moment, and polarizability information at the equilibrium geometry. A new quick, accurate, and easy to program classical technique involving no reference to Euler angles or special functions is developed to compute the infrared and Raman band contours for any rigid rotor, including asymmetric tops. A second, or simultaneous, type of ab initio approach is suggested for large systems, particularly those for which normal mode analysis is inappropriate, such as liquids, clusters, or floppy molecules. Then the curse of dimensionality prevents mapping out in advance the complete potential, dipole moment, and polarizability functions over the whole space of nuclear positions of all atoms, and a solution in which the electronic and nuclear parts of the Born-Oppenheimer approximation are simultaneously solved is needed. A quantum force classical trajectory (QFCT) molecular dynamic method, based on linear response theory, is described, in which the forces, dipole moment, and polarizability are computed quantum

  13. Formalisms for Electron Exchange Kinetics in Aqueous Solution, and the Role of Ab Initio Techniques in Their Implementation

    SciTech Connect

    Newton, M.D.

    1980-01-01

    Formalisms suitable for calculating the rate of electron exchange between transition metal complexes in aqueous solution are reviewed and implemented in conjunction with ab initio quantum chemical calculations which provide crucial off-diagonal Hamiltonian matrix elements as well as other relevant electronic structural data. Rate constants and activation parameters are calculated for the hex-aquo Fe2 +-Fe3+ system, using a simple activated complex theory, a non-adiabatic semi-classical model which includes nuclear tunnelling, and a more detailed quantum mechanical method based on the Golden Rule. Comparisons are made between calculated results and those obtained by extrapolating experimental data to zero ionic strength. All methods yield similar values for the overall rate constant (∾ 0.1 L/(mol-sec)). The experimental activation parameters (δH and δS) are in somewhat better agreement with the semi classical and quantum mechanical results than with those from the simple activated complex theory, thereby providing some indication that non-adiabaticity and nuclear tunnelling may be important in the Fe2+/3+ exchange reaction. It is concluded that a model based on direct metal-metal overlap can account for the observed reaction kinetics provided the reactants are allowed to approach well within the traditional contact distance of 6.9 Å. 6 figures, 7 tables.

  14. Ab initio effective interactions for s d -shell valence nucleons

    NASA Astrophysics Data System (ADS)

    Dikmen, E.; Lisetskiy, A. F.; Barrett, B. R.; Maris, P.; Shirokov, A. M.; Vary, J. P.

    2015-06-01

    We perform ab initio no-core shell-model calculations for A =18 and 19 nuclei in a 4 ℏ Ω , or Nmax=4 , model space by using the effective JISP16 and chiral N3LO nucleon-nucleon potentials and transform the many-body effective Hamiltonians into the 0 ℏ Ω model space to construct the A -body effective Hamiltonians in the s d shell. We separate the A -body effective Hamiltonians with A =18 and A =19 into inert core, one-, and two-body components. Then we use these core, one-, and two-body components to perform standard shell-model calculations for the A =18 and A =19 systems with valence nucleons restricted to the s d shell. Finally, we compare the standard shell-model results in the 0 ℏ Ω model space with the exact no-core shell-model results in the 4 ℏ Ω model space for the A =18 and A =19 systems and find good agreement.

  15. Multiple time step integrators in ab initio molecular dynamics

    SciTech Connect

    Luehr, Nathan; Martínez, Todd J.; Markland, Thomas E.

    2014-02-28

    Multiple time-scale algorithms exploit the natural separation of time-scales in chemical systems to greatly accelerate the efficiency of molecular dynamics simulations. Although the utility of these methods in systems where the interactions are described by empirical potentials is now well established, their application to ab initio molecular dynamics calculations has been limited by difficulties associated with splitting the ab initio potential into fast and slowly varying components. Here we present two schemes that enable efficient time-scale separation in ab initio calculations: one based on fragment decomposition and the other on range separation of the Coulomb operator in the electronic Hamiltonian. We demonstrate for both water clusters and a solvated hydroxide ion that multiple time-scale molecular dynamics allows for outer time steps of 2.5 fs, which are as large as those obtained when such schemes are applied to empirical potentials, while still allowing for bonds to be broken and reformed throughout the dynamics. This permits computational speedups of up to 4.4x, compared to standard Born-Oppenheimer ab initio molecular dynamics with a 0.5 fs time step, while maintaining the same energy conservation and accuracy.

  16. Vibrational analysis of HOCl up to 98{percent} of the dissociation energy with a Fermi resonance Hamiltonian

    SciTech Connect

    Jost, R.; Joyeux, M.; Skokov, S.; Bowman, J.

    1999-10-01

    We have analyzed the vibrational energies and wave functions of HOCl obtained from previous {ital ab initio} calculations [J. Chem. Phys. {bold 109}, 2662 (1998); {bold 109}, 10273 (1998)]. Up to approximately 13&hthinsp;000 cm{sup {minus}1}, the normal modes are nearly decoupled, so that the analysis is straightforward with a Dunham model. In contrast, above 13&hthinsp;000 cm{sup {minus}1} the Dunham model is no longer valid for the levels with no quanta in the OH stretch (v{sub 1}=0). In addition to v{sub 1}, these levels can only be assigned a so-called polyad quantum number P=2v{sub 2}+v{sub 3}, where 2 and 3 denote, respectively, the bending and OCl stretching normal modes. In contrast, the levels with v{sub 1}{ge}2 remain assignable with three v{sub i} quantum numbers up to the dissociation (D{sub 0}=19&hthinsp;290&hthinsp;cm{sup {minus}1}). The interaction between the bending and the OCl stretch ({omega}{sub 2}{congruent}2{omega}{sub 3}) is well described with a simple, fitted Fermi resonance Hamiltonian. The energies and wave functions of this model Hamiltonian are compared with those obtained from {ital ab initio} calculations, which in turn enables the assignment of many additional {ital ab initio} vibrational levels. Globally, among the 809 bound levels calculated below dissociation, 790 have been assigned, the lowest unassigned level, No. 736, being located at 18&hthinsp;885 cm{sup {minus}1} above the (0,0,0) ground level, that is, at about 98{percent} of D{sub 0}. In addition, 84 {open_quotes}resonances{close_quotes} located above D{sub 0} have also been assigned. Our best Fermi resonance Hamiltonian has 29 parameters fitted with 725 {ital ab initio} levels, the rms deviation being of 5.3 cm{sup {minus}1}. This set of 725 fitted levels includes the full set of levels up to No. 702 at 18&hthinsp;650 cm{sup {minus}1}. The {ital ab initio} levels, which are assigned but not included in the fit, are reasonably predicted by the model Hamiltonian, but with a

  17. A Hamiltonian five-field gyrofluid model

    SciTech Connect

    Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J.

    2015-11-15

    A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.

  18. Jarzynski equality for non-Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    Mandal, Dibyendu; Deweese, Michael R.

    Recent years have witnessed major advances in our understanding of nonequilibrium processes. The Jarzynski equality, for example, provides a link between equilibrium free energy differences and finite-time, nonequilibrium dynamics. We propose a generalization of this relation to non-Hamiltonian dynamics, relevant for active matter systems, continuous feedback, and computer simulation. Surprisingly, this relation allows us to calculate the free energy difference between the desired initial and final states using arbitrary dynamics. As a practical matter, this dissociation between the dynamics and the initial and final states promises to facilitate a range of techniques for free energy estimation in a single, universal expression. This material is based upon work supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under Contract Number W911NF-13-1-0390.

  19. A Hamiltonian five-field gyrofluid model

    NASA Astrophysics Data System (ADS)

    Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J.

    2015-11-01

    A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.

  20. Equivalent Hamiltonian for the Lee model

    SciTech Connect

    Jones, H. F.

    2008-03-15

    Using the techniques of quasi-Hermitian quantum mechanics and quantum field theory we use a similarity transformation to construct an equivalent Hermitian Hamiltonian for the Lee model. In the field theory confined to the V/N{theta} sector it effectively decouples V, replacing the three-point interaction of the original Lee model by an additional mass term for the V particle and a four-point interaction between N and {theta}. While the construction is originally motivated by the regime where the bare coupling becomes imaginary, leading to a ghost, it applies equally to the standard Hermitian regime where the bare coupling is real. In that case the similarity transformation becomes a unitary transformation.

  1. Geometric solitons of Hamiltonian flows on manifolds

    SciTech Connect

    Song, Chong; Sun, Xiaowei; Wang, Youde

    2013-12-15

    It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.

  2. Hamiltonian formalism and path entropy maximization

    NASA Astrophysics Data System (ADS)

    Davis, Sergio; González, Diego

    2015-10-01

    Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the second law of thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the second law is a fundamental property of plausible inference.

  3. Hamiltonian formulations and symmetries in rod mechanics

    SciTech Connect

    Dichmann, D.J.; Li, Yiwei; Maddocks, J.H.

    1996-12-31

    This article provides a survey of contemporary rod mechanics, including both dynamic and static theories. Much of what we discuss is regarded as classic material within the mechanics community, but the objective here is to provide a self-contained account accessible to workers interested in modelling DNA. We also describe a number of recent results and computations involving rod mechanics that have been obtained by our group at the University of Maryland. This work was largely motivated by applications to modelling DNA, but our approach reflects a background of research in continuum mechanics. In particular, we emphasize the role that Hamiltonian formulations and symmetries play in the effective computation of special solutions, conservation laws of dynamics and integrals of statics. 41 refs., 10 figs.

  4. Geometric solitons of Hamiltonian flows on manifolds

    NASA Astrophysics Data System (ADS)

    Song, Chong; Sun, Xiaowei; Wang, Youde

    2013-12-01

    It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.

  5. Critical Hamiltonians with long range hopping

    NASA Astrophysics Data System (ADS)

    Levitov, L. S.

    1999-11-01

    Critical states are studied by a real space RG in the problem with strong diagonal disorder and long range power law hopping. The RG ow of the distribution of coupling parameters is characterized by a family of non-trivial fix points. We consider the RG flow of the distribution of participation ratios of eigenstates. Scaling of participation ratios is sensitive to the nature of the RG fix point. For some fix points, scaling of participation ratios is characterized by a distribution of exponents, rather than by a single exponent.The RG method can be generalized to treat certain fermionic Hamiltonians with disorder and long range hopping. We derive the RG for a model of interacting two-level systems. Besides couplings, in this problem the RG includes the density of states. The density of states is renormalized so that it develops a singularity near zero energy.

  6. Optimized spatial matrix representations of quantum Hamiltonians

    NASA Astrophysics Data System (ADS)

    Lv, Q. Z.; Jennings, D. J.; Betke, J.; Su, Q.; Grobe, R.

    2016-01-01

    We examine the accuracy of several approaches to represent the quantum mechanical Schrödinger, Klein-Gordon and Dirac Hamilton operators by optimized spatial matrices. Two of the approaches are based on periodic and reflecting boundaries and have an error scaling with the number of spatial grid points that is significantly better than the ones based on the usual approaches where the momentum operator is approximated by finite-difference schemes. These N × N matrices are optimum in the sense that their eigenvalues and eigenvectors are exact representations on the spatial grid for the continuous solutions of the corresponding force-free Hamiltonian. As an example, we apply these techniques to compute the vacuum's polarization charge density from the Dirac and Foldy-Wouthuysen theory.

  7. Engineering Floquet Hamiltonians in Cold Atom Systems

    NASA Astrophysics Data System (ADS)

    Polkovnikov, Anatoli

    2016-05-01

    In this talk I will first give a brief overview of the Floquet theory, describing periodically driven systems. Then I will introduce the concept of the high-frequency expansion and will show how it generalizes the celebrated Schrieffer-Wolff transformation to driven systems. Using these tools I will illustrate how one can engineer non-trivial interacting Hamiltonians mostly in the context of cold atom systems and discuss some experimental examples. In the end I will talk about issues of heating and adiabaticity and show that there are very strong parallels between Floquet systems and disordered systems. In particular, I will argue that the heating transition is closely analogous to the many-body localization transition. AFOSR, ARO, NSF.

  8. Comments on 'Hamiltonian adaptive control of spacecraft'

    NASA Astrophysics Data System (ADS)

    Fossen, Thor I.

    1993-04-01

    In the adaptive scheme presented by Slotine and Benedetto (1990) for attitude tracking control of rigid spacecraft, the spacecraft is parameterized in terms of the inertial frame. This note shows how a parameterization in body coordinates considerably simplifies the representation of the adaptation scheme. The new symbolic expression for the regressor matrix is easy to find even for 6-degrees of freedom (DOF) Hamiltonian systems with a large number of unknown parameters. If the symbolic expression for the regressor matrix is known in advance, the computational complexity is approximately equal for both representations. In the scheme presented by Slotine and Benedetto this is not trivial because the transformation matrix between the inertial frame and the body coordinates is included in the expression for the regressor matrix. Hence, implementation for higher DOF systems is strongly complicated. An example illustrates the advantage of the new representation when modeling a simple three-DOF model of the lateral motion of a space shuttle.

  9. Friction in a Model of Hamiltonian Dynamics

    NASA Astrophysics Data System (ADS)

    Fröhlich, Jürg; Gang, Zhou; Soffer, Avy

    2012-10-01

    We study the motion of a heavy tracer particle weakly coupled to a dense ideal Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations describing a process of emission of Cerenkov radiation of sound waves into the Bose-Einstein condensate along the particle's trajectory. The emission of Cerenkov radiation results in a friction force with memory acting on the tracer particle and causing it to decelerate until it comes to rest. "A moving body will come to rest as soon as the force pushing it no longer acts on it in the manner necessary for its propulsion."—— Aristotle

  10. Hamiltonian inclusive fitness: a fitter fitness concept

    PubMed Central

    Costa, James T.

    2013-01-01

    In 1963–1964 W. D. Hamilton introduced the concept of inclusive fitness, the only significant elaboration of Darwinian fitness since the nineteenth century. I discuss the origin of the modern fitness concept, providing context for Hamilton's discovery of inclusive fitness in relation to the puzzle of altruism. While fitness conceptually originates with Darwin, the term itself stems from Spencer and crystallized quantitatively in the early twentieth century. Hamiltonian inclusive fitness, with Price's reformulation, provided the solution to Darwin's ‘special difficulty’—the evolution of caste polymorphism and sterility in social insects. Hamilton further explored the roles of inclusive fitness and reciprocation to tackle Darwin's other difficulty, the evolution of human altruism. The heuristically powerful inclusive fitness concept ramified over the past 50 years: the number and diversity of ‘offspring ideas’ that it has engendered render it a fitter fitness concept, one that Darwin would have appreciated. PMID:24132089

  11. Nonperturbative light-front Hamiltonian methods

    NASA Astrophysics Data System (ADS)

    Hiller, J. R.

    2016-09-01

    We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

  12. Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians

    SciTech Connect

    Buljubasich, Lisandro; Dente, Axel D.; Levstein, Patricia R.; Chattah, Ana K.; Pastawski, Horacio M.; Sánchez, Claudia M.

    2015-10-28

    We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.

  13. Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians

    NASA Astrophysics Data System (ADS)

    Buljubasich, Lisandro; Sánchez, Claudia M.; Dente, Axel D.; Levstein, Patricia R.; Chattah, Ana K.; Pastawski, Horacio M.

    2015-10-01

    We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates that correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.

  14. Unconstrained Hamiltonian formulation of low energy QCD

    NASA Astrophysics Data System (ADS)

    Pavel, Hans-Peter

    2014-04-01

    Using a generalized polar decomposition of the gauge fields into gaugerotation and gauge-invariant parts, which Abelianises the Non-Abelian Gauss-law constraints to be implemented, a Hamiltonian formulation of QCD in terms of gauge invariant dynamical variables can be achieved. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian naturally admits a systematic strongcoupling expansion in powers of λ = g-2/3, equivalent to an expansion in the number of spatial derivatives. The leading-order term corresponds to non-interacting hybridglueballs, whose low-lying spectrum can be calculated with high accuracy by solving the Schrödinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant fields (at the moment only for the 2-color case). The discrete glueball excitation spectrum shows a universal string-like behaviour with practically all excitation energy going in to the increase of the strengths of merely two fields, the "constant Abelian fields" corresponding to the zero-energy valleys of the chromomagnetic potential. Inclusion of the fermionic degrees of freedom significantly lowers the spectrum and allows for the study of the sigma meson. Higher-order terms in λ lead to interactions between the hybridglueballs and can be taken into account systematically using perturbation theory in λ, allowing for the study of IR-renormalisation and Lorentz invarianz. The existence of the generalized polar decomposition used, the position of the zeros of the corresponding Jacobian (Gribov horizons), and the ranges of the physical variables can be investigated by solving a system of algebraic equations. Its exact solution for the case of one spatial dimension and first numerical solutions for two and three spatial dimensions indicate that there is a finite

  15. Higher-order Hamiltonian fluid reduction of Vlasov equation

    SciTech Connect

    Perin, M.; Chandre, C.; Morrison, P.J.; Tassi, E.

    2014-09-15

    From the Hamiltonian structure of the Vlasov equation, we build a Hamiltonian model for the first three moments of the Vlasov distribution function, namely, the density, the momentum density and the specific internal energy. We derive the Poisson bracket of this model from the Poisson bracket of the Vlasov equation, and we discuss the associated Casimir invariants.

  16. On the physical applications of hyper-Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    Gaeta, Giuseppe; Rodríguez, Miguel A.

    2008-05-01

    An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate—in suitable limits—the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin.

  17. Foldy-Wouthuysen transformation for a non-Hermitian Hamiltonian

    NASA Astrophysics Data System (ADS)

    Alexandre, Jean

    2015-07-01

    The free Dirac Lagrangian is extended with a non-Hermitian mass term. It is shown that the model has real energies and a conserved current in a given region of parameter space, and the Hamiltonian is mapped on a Hermitian Hamiltonian, using a (non-unitary) Foldy-Wouthuysen transformation.

  18. Hamiltonian structures for the Ostrovsky-Vakhnenko equation

    NASA Astrophysics Data System (ADS)

    Brunelli, J. C.; Sakovich, S.

    2013-01-01

    We obtain a bi-Hamiltonian formulation for the Ostrovsky-Vakhnenko (OV) equation using its higher order symmetry and a new transformation to the Caudrey-Dodd-Gibbon-Sawada-Kotera equation. Central to this derivation is the relation between Hamiltonian structures when dependent and independent variables are transformed.

  19. Ab initio derivation of model energy density functionals

    NASA Astrophysics Data System (ADS)

    Dobaczewski, Jacek

    2016-08-01

    I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results.

  20. Hamiltonian formulation of the D-brane action and the light-cone Hamiltonian

    NASA Astrophysics Data System (ADS)

    Lee, Julian

    1998-04-01

    We present the Hamiltonian formulation of the bosonic Dirichlet p-brane action. We rewrite the recently proposed quadratic D-brane action in terms of generalized shift vector and lapse function. The first class and the second class constraints are explicitly separated for the bosonic case. We then impose the gauge conditions in such a way that only time-independent gauge transformations are left. In this gauge we obtain the light-cone Hamiltonian which is quadratic in the field momenta of scalar and vector fields. The constraints are explicitly solved to eliminate part of the canonical variables. The Dirac brackets between the remaining variables are computed and shown to be equal to simple Poisson brackets.

  1. Simulating typical entanglement with many-body Hamiltonian dynamics

    SciTech Connect

    Nakata, Yoshifumi; Murao, Mio

    2011-11-15

    We study the time evolution of the amount of entanglement generated by one-dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians.

  2. Investigation of non-Hermitian Hamiltonians in the Heisenberg picture

    NASA Astrophysics Data System (ADS)

    Miao, Yan-Gang; Xu, Zhen-Ming

    2016-05-01

    The Heisenberg picture for non-Hermitian but η-pseudo-Hermitian Hamiltonian systems is suggested. If a non-Hermitian but η-pseudo-Hermitian Hamiltonian leads to real second order equations of motion, though their first order Heisenberg equations of motion are complex, we can construct a Hermitian counterpart that gives the same second order equations of motion. In terms of a similarity transformation we verify the iso-spectral property of the Hermitian and non-Hermitian Hamiltonians and obtain the related eigenfunctions. This feature can be used to determine real eigenvalues for such non-Hermitian Hamiltonian systems. As an application, two new non-Hermitian Hamiltonians are constructed and investigated, where one is non-Hermitian and non-PT-symmetric and the other is non-Hermitian but PT-symmetric. Moreover, the complementarity and compatibility between our treatment and the PT symmetry are discussed.

  3. Hamiltonian analysis of higher derivative scalar-tensor theories

    NASA Astrophysics Data System (ADS)

    Langlois, David; Noui, Karim

    2016-07-01

    We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.

  4. Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2013-10-01

    The Euclidean action with acceleration has been analyzed in Ref. 1, and referred to henceforth as Paper I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation and destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.

  5. Quantum control by means of hamiltonian structure manipulation.

    PubMed

    Donovan, A; Beltrani, V; Rabitz, H

    2011-04-28

    A traditional quantum optimal control experiment begins with a specific physical system and seeks an optimal time-dependent field to steer the evolution towards a target observable value. In a more general framework, the Hamiltonian structure may also be manipulated when the material or molecular 'stockroom' is accessible as a part of the controls. The current work takes a step in this direction by considering the converse of the normal perspective to now start with a specific fixed field and employ the system's time-independent Hamiltonian structure as the control to identify an optimal form. The Hamiltonian structure control variables are taken as the system energies and transition dipole matrix elements. An analysis is presented of the Hamiltonian structure control landscape, defined by the observable as a function of the Hamiltonian structure. A proof of system controllability is provided, showing the existence of a Hamiltonian structure that yields an arbitrary unitary transformation when working with virtually any field. The landscape analysis shows that there are no suboptimal traps (i.e., local extrema) for controllable quantum systems when unconstrained structural controls are utilized to optimize a state-to-state transition probability. This analysis is corroborated by numerical simulations on model multilevel systems. The search effort to reach the top of the Hamiltonian structure landscape is found to be nearly invariant to system dimension. A control mechanism analysis is performed, showing a wide variety of behavior for different systems at the top of the Hamiltonian structure landscape. It is also shown that reducing the number of available Hamiltonian structure controls, thus constraining the system, does not always prevent reaching the landscape top. The results from this work lay a foundation for considering the laboratory implementation of optimal Hamiltonian structure manipulation for seeking the best control performance, especially with limited

  6. Ab initio Bogoliubov coupled cluster theory

    NASA Astrophysics Data System (ADS)

    Signoracci, Angelo; Hagen, Gaute; Duguet, Thomas

    2014-09-01

    Coupled cluster (CC) theory has become a standard method in nuclear theory for realistic ab initio calculations of medium mass nuclei, but remains limited by its requirement of a Slater determinant reference state which reasonably approximates the nuclear system of interest. Extensions of the method, such as equation-of-motion CC, permit the calculation of nuclei with one or two nucleons added or removed from a doubly magic core, yet still only a few dozen nuclei are accessible with modern computational restrictions. In order to extend the applicability of ab initio methods to open-shell systems, the superfluid nature of nuclei must be taken into account. By utilizing Bogoliubov algebra and employing spontaneous symmetry breaking with respect to particle number conservation, superfluid systems can be treated by a single reference state. An ab initio theory to include correlations on top of a Bogoliubov reference state has been developed in the guise of standard CC theory. The formalism and first results of this Bogoliubov coupled cluster theory will be presented to demonstrate the applicability of the method.

  7. Ab initio alpha-alpha scattering

    NASA Astrophysics Data System (ADS)

    Elhatisari, Serdar; Lee, Dean; Rupak, Gautam; Epelbaum, Evgeny; Krebs, Hermann; Lähde, Timo A.; Luu, Thomas; Meißner, Ulf-G.

    2015-12-01

    Processes such as the scattering of alpha particles (4He), the triple-alpha reaction, and alpha capture play a major role in stellar nucleosynthesis. In particular, alpha capture on carbon determines the ratio of carbon to oxygen during helium burning, and affects subsequent carbon, neon, oxygen, and silicon burning stages. It also substantially affects models of thermonuclear type Ia supernovae, owing to carbon detonation in accreting carbon-oxygen white-dwarf stars. In these reactions, the accurate calculation of the elastic scattering of alpha particles and alpha-like nuclei—nuclei with even and equal numbers of protons and neutrons—is important for understanding background and resonant scattering contributions. First-principles calculations of processes involving alpha particles and alpha-like nuclei have so far been impractical, owing to the exponential growth of the number of computational operations with the number of particles. Here we describe an ab initio calculation of alpha-alpha scattering that uses lattice Monte Carlo simulations. We use lattice effective field theory to describe the low-energy interactions of protons and neutrons, and apply a technique called the ‘adiabatic projection method’ to reduce the eight-body system to a two-cluster system. We take advantage of the computational efficiency and the more favourable scaling with system size of auxiliary-field Monte Carlo simulations to compute an ab initio effective Hamiltonian for the two clusters. We find promising agreement between lattice results and experimental phase shifts for s-wave and d-wave scattering. The approximately quadratic scaling of computational operations with particle number suggests that it should be possible to compute alpha scattering and capture on carbon and oxygen in the near future. The methods described here can be applied to ultracold atomic few-body systems as well as to hadronic systems using lattice quantum chromodynamics to describe the interactions of

  8. Ab initio alpha-alpha scattering.

    PubMed

    Elhatisari, Serdar; Lee, Dean; Rupak, Gautam; Epelbaum, Evgeny; Krebs, Hermann; Lähde, Timo A; Luu, Thomas; Meißner, Ulf-G

    2015-12-01

    Processes such as the scattering of alpha particles ((4)He), the triple-alpha reaction, and alpha capture play a major role in stellar nucleosynthesis. In particular, alpha capture on carbon determines the ratio of carbon to oxygen during helium burning, and affects subsequent carbon, neon, oxygen, and silicon burning stages. It also substantially affects models of thermonuclear type Ia supernovae, owing to carbon detonation in accreting carbon-oxygen white-dwarf stars. In these reactions, the accurate calculation of the elastic scattering of alpha particles and alpha-like nuclei--nuclei with even and equal numbers of protons and neutrons--is important for understanding background and resonant scattering contributions. First-principles calculations of processes involving alpha particles and alpha-like nuclei have so far been impractical, owing to the exponential growth of the number of computational operations with the number of particles. Here we describe an ab initio calculation of alpha-alpha scattering that uses lattice Monte Carlo simulations. We use lattice effective field theory to describe the low-energy interactions of protons and neutrons, and apply a technique called the 'adiabatic projection method' to reduce the eight-body system to a two-cluster system. We take advantage of the computational efficiency and the more favourable scaling with system size of auxiliary-field Monte Carlo simulations to compute an ab initio effective Hamiltonian for the two clusters. We find promising agreement between lattice results and experimental phase shifts for s-wave and d-wave scattering. The approximately quadratic scaling of computational operations with particle number suggests that it should be possible to compute alpha scattering and capture on carbon and oxygen in the near future. The methods described here can be applied to ultracold atomic few-body systems as well as to hadronic systems using lattice quantum chromodynamics to describe the interactions of

  9. Novel Exciton States in Monolayer MoS2: Unconventional Effective Hamiltonian

    NASA Astrophysics Data System (ADS)

    da Jornada, Felipe; Qiu, Diana; Louie, Steven

    2014-03-01

    Recent well-converged ab inito GW-BSE calculations show that monolayer MoS2 has a large number of strongly bound excitons with varying characters. We show that these excitonic states cannot be even qualitatively described by an effective mass hydrogenic model without a detailed understanding of the 2D screening. Additionally, we identify and analyze one exciton series having an unusually high binding energy, which originates around the Γ point of the Brillouin zone. We show that this excitonic series arises from a fundamentally different effective Hamiltonian with a kinetic energy term resembling a Mexican hat in momentum space, which is responsible for the unusual ordering of the energy levels and distribution of oscillator strength. This work was supported by NSF grant No. DMR10-1006184 and the U.S. DOE under Contract No. DE-AC02-05CH11231.

  10. ABS plastic RPCs

    SciTech Connect

    Ables, E.; Bionta, R.; Olson, H.; Ott, L.; Parker, E.; Wright, D.; Wuest, C

    1996-02-01

    After investigating a number of materials, we discovered that an ABS plastic doped with a conducting polymer performs well as the resistive electrode in a narrow gap RPC (resistive plate chamber). Operating in the streamer mode, we find efficiencies of 90-96% with low noise and low strip multiplicities. We have also studied a variety of operating gases and found that a mixture containing SF{sub 6}, a non-ozone depleting gas, argon and isobutane gives good streamer mode performance, even with isobutane concentrations of 20% or less.

  11. Hamiltonian of a spinning test particle in curved spacetime

    SciTech Connect

    Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra

    2009-11-15

    Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase space algebra in the Newton-Wigner spin supplementary condition, suitably generalized to curved spacetime, and find that the phase space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner canonical Hamiltonian computed in PN theory in the test particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type S{sub Kerr}S (and S{sub Kerr}{sup 2}) through 3PN order, S{sub Kerr} being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order.

  12. Spontaneously broken Lorentz symmetry for Hamiltonian gravity

    NASA Astrophysics Data System (ADS)

    Gielen, Steffen; Wise, Derek K.

    2012-05-01

    In Ashtekar’s Hamiltonian formulation of general relativity, and in loop quantum gravity, Lorentz covariance is a subtle issue that has been strongly debated. Maintaining manifest Lorentz covariance seems to require introducing either complex-valued fields, presenting a significant obstacle to quantization, or additional (usually second class) constraints whose solution renders the resulting phase space variables harder to interpret in a spacetime picture. After reviewing the sources of difficulty, we present a Lorentz covariant, real formulation in which second class constraints never arise. Rather than a foliation of spacetime, we use a gauge field y, interpreted as a field of observers, to break the SO(3, 1) symmetry down to a subgroup SO(3)y. This symmetry breaking plays a role analogous to that in MacDowell-Mansouri gravity, which is based on Cartan geometry, leading us to a picture of gravity as “Cartan geometrodynamics.” We study both Lorentz gauge transformations and transformations of the observer field to show that the apparent breaking of SO(3, 1) to SO(3) is not in conflict with Lorentz covariance.

  13. Similar Hamiltonian Between Avalanche-effect & Sociophysics

    NASA Astrophysics Data System (ADS)

    Maksoed, Ssi, Wh-

    2016-05-01

    Of similar Hamiltonian concerned in ``sociophysics'', there were RandomFieldIsingModel/RFIM in external field retrieved in S. Sabhapandit:``Hysteresis & Avalanche in RandomFieldIsingModel'',2002:'' ..in earthquake, it is an energy release and in case of ferromagnet, it is the size of the domain flips''. Following the extremes & compromises curve in Serge Galam: ``Sociophysics: a Review of Galam Model'', 2008 fig. 12, h 9 whereas it seems similar with ``heating curve''-Prof. Ir. Abdul Kadir: ``Mesin Arus Searah'', h 192 when the heat sources are continuous denote continuous opinion dynamics. Further, hysteresis as duties in ``Kajian Analisis Model Mikromagnetik dari Struktur Magnet Nanokomposit'', 2007 [ UI file no. S29286 ] also sought:'' calculate the probability that `one more site became unstable' causes an avalanche of the spin flips...'' usually found in Per Bak sand-pile fractal characters experiment exhibits. Great acknowledgment to HE. Mr. LieutGen-TNI[rtd]. H. TUK SETYOHADI, +62-21-7220385, Jl. Sriwijaya Raya 3, Kebayoran Baru, South-Jakarta.

  14. Origin of diffusion in Hamiltonian dynamics

    SciTech Connect

    Benisti, D.; Escande, D.F.

    1997-05-01

    Without invoking any kind of {open_quotes}loss of memory{close_quotes} hypothesis, a diffusion equation is derived for the Hamiltonian dynamics defined by H=p{sup 2}/2+(K/4{pi}{sup 2}){summation}{sub m={minus}M}{sup M}cos(q{minus}mt+{var_phi}{sub m}), where the {var_phi}{sub m}s are fixed random phases. The key point of the derivation is a property of locality for the waves inducing transport. Using perturbation theory, it is shown that only waves whose phase velocities satisfy {vert_bar}m{minus}p(t){vert_bar}{le}{alpha}(K/4{pi}{sup 2}){sup 2/3}, where {alpha} is a constant, approximately 5, play a relevant role for the statistical properties of the dynamics. This implies scaling properties for the dynamics, and leads to the understanding of the origin of force decorrelation and of diffusion, and to the prediction of their occurrence in time. Moreover, the convergence of the diffusion coefficient to its quasilinear value when K{r_arrow}{infinity} is shown, and is interpreted as the consequence of the crossover between two regimes of decorrelation that are of different natures. {copyright} {ital 1997 American Institute of Physics.}

  15. Scaling of Hamiltonian walks on fractal lattices.

    PubMed

    Elezović-Hadzić, Suncica; Marcetić, Dusanka; Maletić, Slobodan

    2007-07-01

    We investigate asymptotical behavior of numbers of long Hamiltonian walks (HWs), i.e., self-avoiding random walks that visit every site of a lattice, on various fractal lattices. By applying an exact recursive technique we obtain scaling forms for open HWs on three-simplex lattice, Sierpinski gasket, and their generalizations: Given-Mandelbrot (GM), modified Sierpinski gasket (MSG), and n -simplex fractal families. For GM, MSG and n -simplex lattices with odd values of n , the number of open HWs Z(N), for the lattice with N>1 sites, varies as omega(N)}N(gamma). We explicitly calculate the exponent gamma for several members of GM and MSG families, as well as for n-simplices with n=3, 5, and 7. For n-simplex fractals with even n we find different scaling form: Z(N) approximately omega(N)mu(N1/d(f), where d(f) is the fractal dimension of the lattice, which also differs from the formula expected for homogeneous lattices. We discuss possible implications of our results on studies of real compact polymers. PMID:17677410

  16. Dirac operators on quasi-Hamiltonian G-spaces

    NASA Astrophysics Data System (ADS)

    Song, Yanli

    2016-08-01

    We construct twisted spinor bundles as well as twisted pre-quantum bundles on quasi-Hamiltonian G-spaces, using the spin representation of loop group and the Hilbert space of Wess-Zumino-Witten model. We then define a Hilbert space together with a Dirac operator acting on it. The main result of this paper is that we show the Dirac operator has a well-defined index given by positive energy representation of the loop group. This generalizes the geometric quantization of Hamiltonian G-spaces to quasi-Hamiltonian G-spaces.

  17. New Hamiltonian constraint operator for loop quantum gravity

    NASA Astrophysics Data System (ADS)

    Yang, Jinsong; Ma, Yongge

    2015-12-01

    A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

  18. Stability of Gabor Frames Under Small Time Hamiltonian Evolutions

    NASA Astrophysics Data System (ADS)

    de Gosson, Maurice A.; Gröchenig, Karlheinz; Romero, José Luis

    2016-05-01

    We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schrödinger propagator and the phase-space nodes evolve according to the corresponding Hamiltonian flow. We prove the stability of the frame property for small times and Hamiltonians consisting of a quadratic polynomial plus a potential in the Sjöstrand class with bounded second-order derivatives. This answers a question raised in de Gosson (Appl Comput Harmonic Anal 38(2):196-221, 2015)

  19. Rosenfeld, Bergmann, Dirac and the Invention of Constrained Hamiltonian Dynamics

    NASA Astrophysics Data System (ADS)

    Salisbury, D. C.

    2008-09-01

    In a paper appearing in Annalen der Physik in 1930 Leon Rosenfeld invented the first procedure for producing Hamiltonian constraints. He displayed and correctly distinguished the vanishing Hamiltonian generator of time evolution, and the vanishing generator of gauge transformations for general relativity with Dirac electron and electrodynamic field sources. Though he did not do so, had he chosen one of his tetrad fields to be normal to his spacetime foliation, he would have anticipated by almost thirty years the general relativisitic Hamiltonian first published by Paul Dirac.

  20. Uncertainty relation for non-Hamiltonian quantum systems

    SciTech Connect

    Tarasov, Vasily E.

    2013-01-15

    General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.

  1. The Tremblay-Turbiner-Winternitz system as extended Hamiltonian

    NASA Astrophysics Data System (ADS)

    Chanu, Claudia Maria; Degiovanni, Luca; Rastelli, Giovanni

    2014-12-01

    We generalize the idea of "extension of Hamiltonian systems"—developed in a series of previous articles—which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of arbitrarily high degree, as well as the determination of new superintegrable systems from old ones. The present generalization, that we call "modified extension of Hamiltonian systems," produces the third independent first integral for the (complete) Tremblay-Turbiner-Winternitz system, as well as for the caged anisotropic oscillator in dimension two.

  2. An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator

    NASA Astrophysics Data System (ADS)

    Masterov, Ivan

    2016-01-01

    Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem in quantum theory. In order to avoid this nasty feature, the technique previously developed in [7] is used to construct an alternative Hamiltonian formulation for the multidimensional Pais-Uhlenbeck oscillator of arbitrary even order with distinct frequencies of oscillation. This construction is also generalized to the case of an N = 2 supersymmetric Pais-Uhlenbeck oscillator.

  3. Stability of Gabor Frames Under Small Time Hamiltonian Evolutions

    NASA Astrophysics Data System (ADS)

    de Gosson, Maurice A.; Gröchenig, Karlheinz; Romero, José Luis

    2016-06-01

    We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schrödinger propagator and the phase-space nodes evolve according to the corresponding Hamiltonian flow. We prove the stability of the frame property for small times and Hamiltonians consisting of a quadratic polynomial plus a potential in the Sjöstrand class with bounded second-order derivatives. This answers a question raised in de Gosson (Appl Comput Harmonic Anal 38(2):196-221, 2015)

  4. Solvable model for many-quark systems in QCD Hamiltonians

    SciTech Connect

    Yepez-Martinez, Tochtli; Hess, P. O.; Civitarese, O.

    2010-04-15

    Motivated by a canonical QCD Hamiltonian, we propose an effective Hamiltonian to represent an arbitrary number of quarks in hadronic bags. The structure of the effective Hamiltonian is discussed and the BCS-type solutions that may represent constituent quarks are presented. The single-particle orbitals are chosen as three-dimensional harmonic oscillators, and we discuss a class of exact solutions that can be obtained when a subset of single-particle basis states is restricted to include a certain number of orbital excitations. The general problem, which includes all possible orbital states, can also be solved by combining analytical and numerical methods.

  5. Remarks on Hamiltonian structures in G{sub 2}-geometry

    SciTech Connect

    Cho, Hyunjoo Salur, Sema; Todd, A. J.

    2013-12-15

    In this article, we treat G{sub 2}-geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G{sub 2}-structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G{sub 2}-structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry.

  6. Two time physics and Hamiltonian Noether theorem for gauge systems

    SciTech Connect

    Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M.

    2006-09-25

    Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints.

  7. Fractional Hamiltonian monodromy from a Gauss-Manin monodromy

    NASA Astrophysics Data System (ADS)

    Sugny, D.; Mardešić, P.; Pelletier, M.; Jebrane, A.; Jauslin, H. R.

    2008-04-01

    Fractional Hamiltonian monodromy is a generalization of the notion of Hamiltonian monodromy, recently introduced by [Nekhoroshev, Sadovskií, and Zhilinskií, C. R. Acad. Sci. Paris, Ser. 1 335, 985 (2002); Nekhoroshev, Sadovskií, and Zhilinskií, Ann. Henri Poincare 7, 1099 (2006)] for energy-momentum maps whose image has a particular type of nonisolated singularities. In this paper, we analyze the notion of fractional Hamiltonian monodromy in terms of the Gauss-Manin monodromy of a Riemann surface constructed from the energy-momentum map and associated with a loop in complex space which bypasses the line of singularities. We also prove some propositions on fractional Hamiltonian monodromy for 1:-n and m :-n resonant systems.

  8. Hamiltonian formulation of the modified Hasegawa-Mima equation

    NASA Astrophysics Data System (ADS)

    Chandre, C.; Morrison, P. J.; Tassi, E.

    2014-02-01

    We derive the Hamiltonian structure of the modified Hasegawa-Mima equation from the ion fluid equations applying Dirac's theory of constraints. We discuss the Casimirs obtained from the corresponding Poisson structure.

  9. Hermiticity of the Dirac Hamiltonian in curved spacetime

    SciTech Connect

    Huang Xing; Parker, Leonard

    2009-01-15

    In previous work on the quantum mechanics of an atom freely falling in a general curved background spacetime, the metric was taken to be sufficiently slowly varying on time scales relevant to atomic transitions that time derivatives of the metric in the vicinity of the atom could be neglected. However, when the time dependence of the metric cannot be neglected, it was shown that the Hamiltonian used there was not Hermitian with respect to the conserved scalar product. This Hamiltonian was obtained directly from the Dirac equation in curved spacetime. This raises the paradox of how it is possible for this Hamiltonian to be non-Hermitian. Here, we show that this non-Hermiticity results from a time dependence of the position eigenstates that enter into the Schroedinger wave function, and we write the expression for the Hamiltonian that is Hermitian for a general metric when the time dependence of the metric is not neglected.

  10. The Hamiltonian property of the flow of singular trajectories

    NASA Astrophysics Data System (ADS)

    Lokutsievskiy, L. V.

    2014-03-01

    Pontryagin's maximum principle reduces optimal control problems to the investigation of Hamiltonian systems of ordinary differential equations with discontinuous right-hand side. An optimal synthesis is the totality of solutions to this system with a fixed terminal (or initial) condition, which fill a region in the phase space one-to-one. In the construction of optimal synthesis, singular trajectories that go along the discontinuity surface N of the right-hand side of the Hamiltonian system of ordinary differential equations, are crucial. The aim of the paper is to prove that the system of singular trajectories makes up a Hamiltonian flow on a submanifold of N. In particular, it is proved that the flow of singular trajectories in the problem of control of the magnetized Lagrange top in a variable magnetic field is completely Liouville integrable and can be embedded in the flow of a smooth superintegrable Hamiltonian system in the ambient space. Bibliography: 17 titles.

  11. Linear transformation and oscillation criteria for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Zheng, Zhaowen

    2007-08-01

    Using a linear transformation similar to the Kummer transformation, some new oscillation criteria for linear Hamiltonian systems are established. These results generalize and improve the oscillation criteria due to I.S. Kumari and S. Umanaheswaram [I. Sowjaya Kumari, S. Umanaheswaram, Oscillation criteria for linear matrix Hamiltonian systems, J. Differential Equations 165 (2000) 174-198], Q. Yang et al. [Q. Yang, R. Mathsen, S. Zhu, Oscillation theorems for self-adjoint matrix Hamiltonian systems, J. Differential Equations 190 (2003) 306-329], and S. Chen and Z. Zheng [Shaozhu Chen, Zhaowen Zheng, Oscillation criteria of Yan type for linear Hamiltonian systems, Comput. Math. Appl. 46 (2003) 855-862]. These criteria also unify many of known criteria in literature and simplify the proofs.

  12. Construction of Lagrangians and Hamiltonians from the Equation of Motion

    ERIC Educational Resources Information Center

    Yan, C. C.

    1978-01-01

    Demonstrates that infinitely many Lagrangians and Hamiltonians can be constructed from a given equation of motion. Points out the lack of an established criterion for making a proper selection. (Author/GA)

  13. On a 'Mysterious' Case of a Quadratic Hamiltonian

    NASA Astrophysics Data System (ADS)

    Sakovich, Sergei

    2006-07-01

    We show that one of the five cases of a quadratic Hamiltonian, which were recently selected by Sokolov and Wolf who used the Kovalevskaya-Lyapunov test, fails to pass the Painlevé test for integrability.

  14. Modelling spin Hamiltonian parameters of molecular nanomagnets.

    PubMed

    Gupta, Tulika; Rajaraman, Gopalan

    2016-07-12

    Molecular nanomagnets encompass a wide range of coordination complexes possessing several potential applications. A formidable challenge in realizing these potential applications lies in controlling the magnetic properties of these clusters. Microscopic spin Hamiltonian (SH) parameters describe the magnetic properties of these clusters, and viable ways to control these SH parameters are highly desirable. Computational tools play a proactive role in this area, where SH parameters such as isotropic exchange interaction (J), anisotropic exchange interaction (Jx, Jy, Jz), double exchange interaction (B), zero-field splitting parameters (D, E) and g-tensors can be computed reliably using X-ray structures. In this feature article, we have attempted to provide a holistic view of the modelling of these SH parameters of molecular magnets. The determination of J includes various class of molecules, from di- and polynuclear Mn complexes to the {3d-Gd}, {Gd-Gd} and {Gd-2p} class of complexes. The estimation of anisotropic exchange coupling includes the exchange between an isotropic metal ion and an orbitally degenerate 3d/4d/5d metal ion. The double-exchange section contains some illustrative examples of mixed valance systems, and the section on the estimation of zfs parameters covers some mononuclear transition metal complexes possessing very large axial zfs parameters. The section on the computation of g-anisotropy exclusively covers studies on mononuclear Dy(III) and Er(III) single-ion magnets. The examples depicted in this article clearly illustrate that computational tools not only aid in interpreting and rationalizing the observed magnetic properties but possess the potential to predict new generation MNMs. PMID:27366794

  15. Trinucleon Electromagnetic Form Factors and the Light-Front Hamiltonian Dynamics

    SciTech Connect

    Baroncini, F.; Kievsky, A.; Pace, E.; Salme, G.

    2008-10-13

    This contribution briefly illustrates preliminary calculations of the electromagnetic form factors of {sup 3}He and {sup 3}H, obtained within the Light-front Relativistic Hamiltonian Dynamics, adopting i) a Poincare covariant current operator, without dynamical two-body currents, and ii) realistic nuclear bound states with S, P and D waves. The kinematical region of few (GeV/c){sup 2}, relevant for forthcoming TJLAB experiments, has been investigated, obtaining possible signatures of relativistic effects for Q{sup 2}>2.5(GeV/c){sup 2}.

  16. Five-dimensional collective Hamiltonian with the Gogny force: An ongoing saga

    NASA Astrophysics Data System (ADS)

    Libert, J.; Delaroche, J.-P.; Girod, M.

    2016-07-01

    We provide a sample of analyses for nuclear spectroscopic properties based on the five-dimensional collective Hamiltonian (5DCH) implemented with the Gogny force. The very first illustration is dating back to the late 70's. It is next followed by others, focusing on shape coexistence, shape isomerism, superdeformation, and systematics over the periodic table. Finally, the inclusion of Thouless-Valatin dynamical contributions to vibrational mass parameters is briefly discussed as a mean of strengthening the basis of the 5DCH theory.

  17. The Lagrangian-Hamiltonian formalism for higher order field theories

    NASA Astrophysics Data System (ADS)

    Vitagliano, Luca

    2010-06-01

    We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.

  18. Time and a physical Hamiltonian for quantum gravity.

    PubMed

    Husain, Viqar; Pawłowski, Tomasz

    2012-04-01

    We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. PMID:22540782

  19. Quantum and classical probability distributions for arbitrary Hamiltonians

    NASA Astrophysics Data System (ADS)

    Semay, Claude; Ducobu, Ludovic

    2016-07-01

    In the limit of large quantum excitations, the classical and quantum probability distributions for a Schrödinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is extended for one-dimensional Hamiltonians with a non-usual kinetic part. The validity of the approach is tested with a Hamiltonian containing a relativistic kinetic energy operator.

  20. Applications of Noether conservation theorem to Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Mouchet, Amaury

    2016-09-01

    The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.

  1. Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD

    SciTech Connect

    Morrison, P.J.; Greene, J.M.

    1980-04-01

    A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables.

  2. Effective Dirac Hamiltonian for anisotropic honeycomb lattices: Optical properties

    NASA Astrophysics Data System (ADS)

    Oliva-Leyva, M.; Naumis, Gerardo G.

    2016-01-01

    We derive the low-energy Hamiltonian for a honeycomb lattice with anisotropy in the hopping parameters. Taking the reported Dirac Hamiltonian for the anisotropic honeycomb lattice, we obtain its optical conductivity tensor and its transmittance for normal incidence of linearly polarized light. Also, we characterize its dichroic character due to the anisotropic optical absorption. As an application of our general findings, which reproduce the previous case of uniformly strained graphene, we study the optical properties of graphene under a nonmechanical distortion.

  3. Global Calculations Using Potential Functions and Effective Hamiltonian Models for Vibration-Rotation Spectroscopy and Dynamics of Small Polyatomic Molecules

    NASA Astrophysics Data System (ADS)

    Tuyterev, Vladimir

    2010-06-01

    It has become increasingly common to use accurate potential energy surfaces and dipole moment surfaces for predictions and assignment of high-resolution vibration-rotation molecular spectra. These surfaces are obtained either from high-level ab initio electronic structure calculations or from a direct fit to experimental spectroscopic data. The talk will continue a discussion of some recent advances in the domain of the "potentiology". The role of basis extrapolations, of the Born-Oppenheimer breakdown corrections , in particular for very highly excited vibration states will be considered. As effective polyad Hamiltonians and band transition moment operators are still widely used for data reductions in high-resolutions molecular spectroscopy, experimental spectra analyses invoke a need for accurate methods of building physically meaningful effective models from ab initio surfaces. This involves predictions for various spectroscopic constants, including vibration dependence of rotational and centrifugal distortion and resonance coupling parameters. Topics planned for discussion include: high-order Contact Transformations of rovibrational Hamiltonians and of the dipole moment for small polyatomic molecules; convergence issues; the role of the anharmonicity in a potential energy function and of resonance couplings on the normal mode mixing and on vib-rot assignments with application to high energy vibration levels of SO_2 and to ozone near the dissociation limit; intensity anomalies in H_2S / HDS / D_2S spectra, relation of the shape of ab initio dipole moment surfaces with a "mystery" of nearly vanishing symmetry allowed bands. A full account for symmetry properties requires efficient theoretical tools for transformations of molecular Hamiltonians such as irreducible tensor formalism, applications using phosphine and methane potentials will be discussed. Both potential functions and effective polyad Hamiltonians allow studying changes in quasi-classical vibration

  4. Explicit methods in extended phase space for inseparable Hamiltonian problems

    NASA Astrophysics Data System (ADS)

    Pihajoki, Pauli

    2015-03-01

    We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.

  5. MARKOV CHAIN MONTE CARLO POSTERIOR SAMPLING WITH THE HAMILTONIAN METHOD

    SciTech Connect

    K. HANSON

    2001-02-01

    The Markov Chain Monte Carlo technique provides a means for drawing random samples from a target probability density function (pdf). MCMC allows one to assess the uncertainties in a Bayesian analysis described by a numerically calculated posterior distribution. This paper describes the Hamiltonian MCMC technique in which a momentum variable is introduced for each parameter of the target pdf. In analogy to a physical system, a Hamiltonian H is defined as a kinetic energy involving the momenta plus a potential energy {var_phi}, where {var_phi} is minus the logarithm of the target pdf. Hamiltonian dynamics allows one to move along trajectories of constant H, taking large jumps in the parameter space with relatively few evaluations of {var_phi} and its gradient. The Hamiltonian algorithm alternates between picking a new momentum vector and following such trajectories. The efficiency of the Hamiltonian method for multidimensional isotropic Gaussian pdfs is shown to remain constant at around 7% for up to several hundred dimensions. The Hamiltonian method handles correlations among the variables much better than the standard Metropolis algorithm. A new test, based on the gradient of {var_phi}, is proposed to measure the convergence of the MCMC sequence.

  6. Precise electromagnetic tests of ab-initio calculations of light nucle i: states in {sup10}Be.

    SciTech Connect

    McCutchan, E. A.; Lister, C. J.; Wiringa, R. B.; Pieper, S. C.; Seweryniak, D.; Greene, J. P.; Carpenter, M. P.; Chiara, C. J.; Janssens, R. V. F.; Khoo, T. L.; Lauritsen, T.; Stefanescu, I.; Zhu, S.; Physics; Univ. of Maryland

    2009-01-01

    In order to test ab initio calculations of light nuclei, we have remeasured lifetimes in {sup 10}Be using the Doppler shift attenuation method (DSAM) following the {sup 7}Li({sup 7}Li,{alpha}){sup 10}Be reaction at 8 and 10 MeV. The new experiments significantly reduce systematic uncertainties in the DSAM technique. The J{sup TT} = 2{sub 1}{sup +} state at 3.37 MeV has T = 205 {+-} (5){sub stat}{+-}(7){sub sys} fs corresponding to a B(E2{down_arrow}) of 9.2(3)e{sup 2}fm{sup 4} in broad agreement with many calculations. The J{sup TT} = 2{sub 2}{sup +} state at 5.96 MeV was found to have a B(E2{down_arrow}) of 0.11(2)e{sup 2}fm{sup 4} and provides a more discriminating test of nuclear models. New Green's function Monte Carlo calculations for these states and transitions with a number of Hamiltonians are also reported and compared to experiment.

  7. PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics

    NASA Astrophysics Data System (ADS)

    Fring, Andreas; Jones, Hugh; Znojil, Miloslav

    2008-06-01

    Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the

  8. XMVB: a program for ab initio nonorthogonal valence bond computations.

    PubMed

    Song, Lingchun; Mo, Yirong; Zhang, Qianer; Wu, Wei

    2005-04-15

    An ab initio nonorthogonal valence bond program, called XMVB, is described in this article. The XMVB package uses Heitler-London-Slater-Pauling (HLSP) functions as state functions, and calculations can be performed with either all independent state functions for a molecule or preferably a few selected important state functions. Both our proposed paired-permanent-determinant approach and conventional Slater determinant expansion algorithm are implemented for the evaluation of the Hamiltonian and overlap matrix elements among VB functions. XMVB contains the capabilities of valence bond self-consistent field (VBSCF), breathing orbital valence bond (BOVB), and valence bond configuration interaction (VBCI) computations. The VB orbitals, used to construct VB functions, can be defined flexibly in the calculations depending on particular applications and focused problems, and they may be strictly localized, delocalized, or bonded-distorted (semidelocalized). The parallel version of XMVB based on MPI (Message Passing Interface) is also available. PMID:15704237

  9. Toward spectroscopically accurate global ab initio potential energy surface for the acetylene-vinylidene isomerization

    SciTech Connect

    Han, Huixian; Li, Anyang; Guo, Hua

    2014-12-28

    A new full-dimensional global potential energy surface (PES) for the acetylene-vinylidene isomerization on the ground (S{sub 0}) electronic state has been constructed by fitting ∼37 000 high-level ab initio points using the permutation invariant polynomial-neural network method with a root mean square error of 9.54 cm{sup −1}. The geometries and harmonic vibrational frequencies of acetylene, vinylidene, and all other stationary points (two distinct transition states and one secondary minimum in between) have been determined on this PES. Furthermore, acetylene vibrational energy levels have been calculated using the Lanczos algorithm with an exact (J = 0) Hamiltonian. The vibrational energies up to 12 700 cm{sup −1} above the zero-point energy are in excellent agreement with the experimentally derived effective Hamiltonians, suggesting that the PES is approaching spectroscopic accuracy. In addition, analyses of the wavefunctions confirm the experimentally observed emergence of the local bending and counter-rotational modes in the highly excited bending vibrational states. The reproduction of the experimentally derived effective Hamiltonians for highly excited bending states signals the coming of age for the ab initio based PES, which can now be trusted for studying the isomerization reaction.

  10. Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach.

    PubMed

    Liu, Yang; Fan, Xiaoli; Jin, Yingdi; Hu, Xiangqian; Hu, Hao

    2013-09-10

    Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantum mechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantum mechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data. PMID:26592414

  11. New construction for a QMA complete three-local Hamiltonian

    NASA Astrophysics Data System (ADS)

    Nagaj, Daniel; Mozes, Shay

    2007-07-01

    We present a new way of encoding a quantum computation into a three-local Hamiltonian. Our construction is novel in that it does not include any terms that induce legal-illegal clock transitions. Therefore, the weights of the terms in the Hamiltonian do not scale with the size of the problem as in previous constructions. This improves the construction by Kempe and Regev [Quantum Inf. Comput. 3, 258-264 (2003); e-print quant-ph/0302079] who were the first to prove that three-local Hamiltonian is complete for the complexity class QMA, the quantum analog of NP. Quantum k-SAT, a restricted version of the local Hamiltonian problem using only projector terms, was introduced by Bravyi (e-print quant-ph/0602108) as an analog of the classical k-SAT problem. Bravyi proved that quantum 4-SAT is complete for the class QMA with one-sided error (QMA1) and that quantum 2-SAT is in P. We give an encoding of a quantum circuit into a quantum 4-SAT Hamiltonian using only three-local terms. As an intermediate step to this three-local construction, we show that quantum 3-SAT for particles with dimensions 3×2×2 (a qutrit and two qubits) is QMA1 complete. The complexity of quantum 3-SAT with qubits remains an open question.

  12. Magnetic Coupling Constants in Three Electrons Three Centers Problems from Effective Hamiltonian Theory and Validation of Broken Symmetry-Based Approaches.

    PubMed

    Reta, Daniel; Moreira, Ibério de P R; Illas, Francesc

    2016-07-12

    In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical. PMID:27231983

  13. Hamiltonian Light-front Field Theory Within an AdS/QCD Basis

    SciTech Connect

    Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Sternberg, P.; Ng, E.G.; Yang, C.; /LBL, Berkeley

    2009-12-16

    Non-perturbative Hamiltonian light-front quantum field theory presents opportunities and challenges that bridge particle physics and nuclear physics. Fundamental theories, such as Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) offer the promise of great predictive power spanning phenomena on all scales from the microscopic to cosmic scales, but new tools that do not rely exclusively on perturbation theory are required to make connection from one scale to the next. We outline recent theoretical and computational progress to build these bridges and provide illustrative results for nuclear structure and quantum field theory. As our framework we choose light-front gauge and a basis function representation with two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography.

  14. Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

    NASA Astrophysics Data System (ADS)

    Xin-Lei, Kong; Hui-Bin, Wu; Feng-Xiang, Mei

    2016-01-01

    In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities. Project supported by the National Natural Science Foundation of China (Grant No. 11272050), the Excellent Young Teachers Program of North China University of Technology (Grant No. XN132), and the Construction Plan for Innovative Research Team of North China University of Technology (Grant No. XN129).

  15. The gravitational Hamiltonian, action, entropy and surface terms

    NASA Astrophysics Data System (ADS)

    Hawking, S. W.; Horowitz, Gary T.

    1996-06-01

    We give a derivation of the gravitational Hamiltonian starting from the Einstein - Hilbert action, keeping track of all surface terms. This derivation can be applied to any spacetime that asymptotically approaches a static background solution. The surface term that arises in the Hamiltonian can be taken as the definition of the `total energy', even for spacetimes that are not asymptotically flat. (In the asymptotically flat case, it agrees with the usual ADM energy.) We also discuss the relation between the Euclidean action and the Hamiltonian when there are horizons of infinite area (e.g. acceleration horizons) as well as the usual finite area black hole horizons. Acceleration horizons seem to be more analogous to extreme than nonextreme black holes, since we find evidence that their horizon area is not related to the total entropy.

  16. Cloning in nonlinear Hamiltonian quantum and hybrid mechanics

    NASA Astrophysics Data System (ADS)

    Arsenović, D.; Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

    2014-10-01

    The possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at superluminal speed, but at the same time it is impossible to clone quantum pure states.

  17. Reverse engineering of a Hamiltonian by designing the evolution operators

    NASA Astrophysics Data System (ADS)

    Kang, Yi-Hao; Chen, Ye-Hong; Wu, Qi-Cheng; Huang, Bi-Hua; Xia, Yan; Song, Jie

    2016-07-01

    We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments.

  18. Normal-ordered second-quantized Hamiltonian for molecular vibrations

    SciTech Connect

    Hirata, So; Hermes, Matthew R.

    2014-11-14

    A normal-ordered second-quantized form of the Hamiltonian is derived for quantum dynamics in a bound potential energy surface expressed as a Taylor series in an arbitrary set of orthogonal, delocalized coordinates centered at an arbitrary geometry. The constant, first-, and second-order excitation amplitudes of this Hamiltonian are identified as the ground-state energy, gradients, and frequencies, respectively, of the size-extensive vibrational self-consistent field (XVSCF) method or the self-consistent phonon method. They display the well-defined size dependence of V{sup 1−n/2}, where V is the volume and n is the number of coordinates associated with the amplitudes. It is used to rapidly derive the equations of XVSCF and vibrational many-body perturbation methods with the Møller–Plesset partitioning of the Hamiltonian.

  19. Limit of small exits in open Hamiltonian systems.

    PubMed

    Aguirre, Jacobo; Sanjuán, Miguel A F

    2003-05-01

    The nature of open Hamiltonian systems is analyzed, when the size of the exits decreases and tends to zero. Fractal basins appear typically in open Hamiltonian systems, but we claim that in the limit of small exits, the invariant sets tend to fill up the whole phase space with the strong consequence that a new kind of basin appears, where the unpredictability grows indefinitely. This means that for finite, arbitrarily small accuracy, we can find uncertain basins, where any information about the future of the system is lost. This total indeterminism had only been reported in dissipative systems, in particular in the so-called intermingled riddled basins, as well as in the riddledlike basins. We show that this peculiar, behavior is a general feature of open Hamiltonian systems. PMID:12786244

  20. Information Geometry of Complex Hamiltonians and Exceptional Points

    NASA Astrophysics Data System (ADS)

    Brody, Dorje; Graefe, Eva-Maria

    2013-08-01

    Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian, then there can be phase transitions where dynamical properties of the system change abruptly. In the vicinities of the transition points, the state of the system becomes highly sensitive to the changes of the parameters in the Hamiltonian. The parameter sensitivity can then be measured in terms of the Fisher-Rao metric and the associated curvature of the parameter-space manifold. A general scheme for the geometric study of parameter-space manifolds of eigenstates of complex Hamiltonians is outlined here, leading to generic expressions for the metric.

  1. Non-Hermitian Hamiltonians and stability of pure states

    NASA Astrophysics Data System (ADS)

    Zloshchastiev, Konstantin G.

    2015-11-01

    We demonstrate that quantum fluctuations can cause, under certain conditions, the dynamical instability of pure states that can result in their evolution into mixed states. It is shown that the degree and type of such an instability are controlled by the environment-induced anti-Hermitian terms in Hamiltonians. Using the quantum-statistical approach for non-Hermitian Hamiltonians and related non-linear master equation, we derive the equations that are necessary to study the stability properties of any model described by a non-Hermitian Hamiltonian. It turns out that the instability of pure states is not preassigned in the evolution equation but arises as the emergent phenomenon in its solutions. In order to illustrate the general formalism and different types of instability that may occur, we perform the local stability analysis of some exactly solvable two-state models, which are being used in the theories of open quantum-optical and spin systems.

  2. Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians

    NASA Astrophysics Data System (ADS)

    Ma, Fengjie; Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry

    2015-06-01

    We present a combination of a downfolding many-body approach with auxiliary-field quantum Monte Carlo (AFQMC) calculations for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using frozen orbitals constructed adaptively from the solid environment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We apply the method to calculate the equation of state of cubic BN under ultrahigh pressure, and determine the spin gap in NiO, a challenging prototypical material with strong electron correlation effects.

  3. Versal unfolding of planar Hamiltonian systems at fully degenerate equilibrium

    NASA Astrophysics Data System (ADS)

    Tang, Yilei; Zhang, Weinian

    2016-07-01

    In this paper we study bifurcations of a planar Hamiltonian system at a fully degenerate equilibrium, which has a zero linearization. Since the Poincaré normal form theory is not applicable to such a degenerate system, we investigate its restrictive normal forms in the class of Hamiltonian fields and prove that such a degenerate system is of codimension 3 degeneracy in the class, so that we introduce three parameters to versally unfold the degenerate system in the class. In order to discuss further the qualitative properties of the versal unfolding, we use the Poincaré index to determine the number and distribution of hyperbolic sectors near the degenerate equilibrium. We display its all bifurcations such as pitchfork bifurcation, saddle-center bifurcation and the Bogdanov-Takens bifurcation within Hamiltonian systems.

  4. Cluster expansion for ground states of local Hamiltonians

    NASA Astrophysics Data System (ADS)

    Bastianello, Alvise; Sotiriadis, Spyros

    2016-08-01

    A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.

  5. Reverse engineering of a Hamiltonian by designing the evolution operators.

    PubMed

    Kang, Yi-Hao; Chen, Ye-Hong; Wu, Qi-Cheng; Huang, Bi-Hua; Xia, Yan; Song, Jie

    2016-01-01

    We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments. PMID:27444137

  6. Reverse engineering of a Hamiltonian by designing the evolution operators

    PubMed Central

    Kang, Yi-Hao; Chen, Ye-Hong; Wu, Qi-Cheng; Huang, Bi-Hua; Xia, Yan; Song, Jie

    2016-01-01

    We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments. PMID:27444137

  7. Intertwined Hamiltonians in two-dimensional curved spaces

    SciTech Connect

    Aghababaei Samani, Keivan . E-mail: samani@cc.iut.ac.ir; Zarei, Mina

    2005-04-01

    The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS{sub 2}), de Sitter plane (dS{sub 2}), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle.

  8. Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

    NASA Astrophysics Data System (ADS)

    Román-Roy, Narciso

    2009-11-01

    This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.

  9. Universality for the breakup of invariant tori in Hamiltonian flows

    NASA Astrophysics Data System (ADS)

    Chandre, C.; Govin, M.; Jauslin, H. R.; Koch, H.

    1998-06-01

    In this article, we describe a new renormalization-group scheme for analyzing the breakup of invariant tori for Hamiltonian systems with two degrees of freedom. The transformation, which acts on Hamiltonians that are quadratic in the action variables, combines a rescaling of phase space and a partial elimination of irrelevant (nonresonant) frequencies. It is implemented numerically for the case applying to golden invariant tori. We find a nontrivial fixed point and compute the corresponding scaling and critical indices. If one compares flows to maps in the canonical way, our results are consistent with existing data on the breakup of golden invariant circles for area-preserving maps.

  10. Characterizing Ground and Thermal States of Few-Body Hamiltonians.

    PubMed

    Huber, Felix; Gühne, Otfried

    2016-07-01

    The question whether a given quantum state is a ground or thermal state of a few-body Hamiltonian can be used to characterize the complexity of the state and is important for possible experimental implementations. We provide methods to characterize the states generated by two- and, more generally, k-body Hamiltonians as well as the convex hull of these sets. This leads to new insights into the question of which states are uniquely determined by their marginals and to a generalization of the concept of entanglement. Finally, certification methods for quantum simulation can be derived. PMID:27419547

  11. Identifying the Hamiltonian structure in linear response theory

    NASA Astrophysics Data System (ADS)

    List, Nanna Holmgaard; Coriani, Sonia; Christiansen, Ove; Kongsted, Jacob

    2014-06-01

    We present a unifying framework for linear response eigenvalue equations that encompasses both variational Hartree-Fock and Kohn-Sham density functional theory as well as non-variational coupled-cluster theory. The joint description is rooted in the so-called Hamiltonian structure of the response kernel matrices, whose properties permit an immediate identification of the well-known paired eigenvalue spectrum describing a molecule in the isolated state. Recognizing the Hamiltonian structure underlying the equations further enables a generalization to the case of a polarizable-embedded molecule treated in variational and, in particular, in non-variational theories.

  12. Extensions of Hamiltonian systems dependent on a rational parameter

    NASA Astrophysics Data System (ADS)

    Chanu, Claudia Maria; Degiovanni, Luca; Rastelli, Giovanni

    2014-12-01

    The technique of "extension" allows to build (d + 2)-dimensional Hamiltonian systems with a non-trivial polynomial in the momenta first integral of any given degree starting from a suitable d-dimensional Hamiltonian. Until now, the application of the technique was restricted to integer values of a certain fundamental parameter determining the degree of the additional first integral. In this article, we show how the technique of extension can be generalized to any rational value of the same parameter. Several examples are given, among them the two uncoupled oscillators and a special case of the Tremblay-Turbiner-Winternitz system.

  13. A novel strong coupling expansion of the QCD Hamiltonian

    SciTech Connect

    Pavel, H.-P.

    2012-06-15

    Introducing an infinite spatial lattice with box length a, a systematic expansion of the physical QCD Hamiltonian in {lambda} = g{sup -2/3} can be obtained, with the free part being the sum of the Hamiltonians of the quantum mechanics of spatially constant fields for each box, and interaction terms proportional to {lambda}{sup n} with n spatial derivatives connecting different boxes. As an example, the energy of the vacuum and the lowest scalar glueball is calculated up to order {lambda}{sup 2} for the case of SU(2) Yang-Mills theory.

  14. Floquet Green function formalism for harmonically driven Hamiltonians

    NASA Astrophysics Data System (ADS)

    Martinez, D. F.

    2003-09-01

    A method is proposed for the calculation of the Floquet-Green function of a general Hamiltonian with harmonic time dependence. We use matrix continued fractions to derive an expression for the 'dynamical effective potential' that can be used to calculate the Floquet-Green function of the system. We demonstrate the formalism for the simple case of a space-periodic (in the tight-binding approximation) Hamiltonian with a defect whose on-site energy changes harmonically with time. We study the local density of states for this system and the behaviour of the localized states as a function of the different parameters that characterize the system.

  15. Nonclassical degrees of freedom in the Riemann Hamiltonian.

    PubMed

    Srednicki, Mark

    2011-09-01

    The Hilbert-Pólya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum Hamiltonian. If so, conjectures by Katz and Sarnak put this Hamiltonian in the Altland-Zirnbauer universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros. PMID:21981482

  16. Characterizing Ground and Thermal States of Few-Body Hamiltonians

    NASA Astrophysics Data System (ADS)

    Huber, Felix; Gühne, Otfried

    2016-07-01

    The question whether a given quantum state is a ground or thermal state of a few-body Hamiltonian can be used to characterize the complexity of the state and is important for possible experimental implementations. We provide methods to characterize the states generated by two- and, more generally, k -body Hamiltonians as well as the convex hull of these sets. This leads to new insights into the question of which states are uniquely determined by their marginals and to a generalization of the concept of entanglement. Finally, certification methods for quantum simulation can be derived.

  17. A parity breaking Ising chain Hamiltonian as a Brownian motor

    NASA Astrophysics Data System (ADS)

    Cornu, F.; Hilhorst, H. J.

    2014-10-01

    We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian {\\cal H} =-{U_2}\\sumk sksk+1 - {U_3}\\sumk sksk+1sk+3 and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio {U_3}/{U_2} and of the conserved magnetization M=\\sum_ksk . The symmetry of the U3 term in the Hamiltonian is discussed.

  18. GAUGE INVARIANCE IN A Z2 HAMILTONIAN LATTICE GUAGE THEORY.

    SciTech Connect

    SUGIHARA, T.

    2005-07-25

    We propose an efficient variational method for Z{sub 2} lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian. On the square lattice, the second order phase transition is well reproduced.

  19. Bohr Hamiltonian with Eckart potential for triaxial nuclei

    NASA Astrophysics Data System (ADS)

    Naderi, L.; Hassanabadi, H.

    2016-05-01

    In this paper, the Bohr Hamiltonian has been solved using the Eckart potential for the β-part and a harmonic oscillator for the γ-part of the Hamiltonian. The approximate separation of the variables has been possible by choosing the convenient form for the potential V(β,γ). Using the Nikiforov-Uvarov method the eigenvalues and eigenfunctions of the eigenequation for the β-part have been derived. An expression for the total energy of the levels has been represented.

  20. Time step and shadow Hamiltonian in molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Kim, Sangrak

    2015-08-01

    We examine the time step and the shadow Hamiltonian of symplectic algorithms for a bound system of a simple harmonic oscillator as a specific example. The phase space trajectory moves on the hyperplane of a constant shadow Hamiltonian. We find a stationary condition for the time step τ n with which the motion repeats itself on the phase space with a period n. Interestingly, that the time steps satisfying the stationary condition turn out to be independent of the symplectic algorithms chosen. Furthermore, the phase volume enclosed by the phase trajectory is given by n τ n Ẽ n , where Ẽ n is the initial shadow energy of the corresponding symplectic algorithm.

  1. Comments on variational ground states for lattice hamiltonians

    NASA Astrophysics Data System (ADS)

    Anishetty, Ramesh; Bovier, Anton

    1984-02-01

    We find that the nearest neighbour Jastrow type ground state cannot yield a Lorentz invariant vacuum in the continuum. This is explicitly demonstrated for the chiral model in 1+1 dimensions. The Jastrow ground state is found to be an exact ground state of a new hamiltonian which differs from the original by seemingly ``irrelevant terms'' at the continuum. However these terms prevent the restoration of Lorentz invariance. Finally we speculate that the new hamiltonian can be a non-relativistic approximation with galilean invariance.

  2. Nuclear binding near a quantum phase transition

    NASA Astrophysics Data System (ADS)

    Lee, Dean

    2016-03-01

    I review recent ab initio results by the Nuclear Lattice Effective Field Theory Collaboration showing that nature lies close to a quantum phase transition between an alpha-particle gas and nuclear liquid. I discuss the control parameter of this transition and the implications for clustering in nuclei and improving ab initio nuclear structure calculations.

  3. Probing the Symmetries of the Dirac Hamiltonian with Axially Deformed Scalar and Vector Potentials by Similarity Renormalization Group

    NASA Astrophysics Data System (ADS)

    Guo, Jian-You; Chen, Shou-Wan; Niu, Zhong-Ming; Li, Dong-Peng; Liu, Quan

    2014-02-01

    Symmetry is an important and basic topic in physics. The similarity renormalization group theory provides a novel view to study the symmetries hidden in the Dirac Hamiltonian, especially for the deformed system. Based on the similarity renormalization group theory, the contributions from the nonrelativistic term, the spin-orbit term, the dynamical term, the relativistic modification of kinetic energy, and the Darwin term are self-consistently extracted from a general Dirac Hamiltonian and, hence, we get an accurate description for their dependence on the deformation. Taking an axially deformed nucleus as an example, we find that the self-consistent description of the nonrelativistic term, spin-orbit term, and dynamical term is crucial for understanding the relativistic symmetries and their breaking in a deformed nuclear system.

  4. Hamiltonian flow in Coulomb gauge Yang-Mills theory

    SciTech Connect

    Leder, Markus; Reinhardt, Hugo; Pawlowski, Jan M.; Weber, Axel

    2011-01-15

    We derive a new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and ghost propagators are solved under the assumption of ghost dominance within different diagrammatic approximations. The results are compared to those obtained in the variational approach and the reliability of the approximations is discussed.

  5. Interatomic force constants and effective Hamiltonians for structural phase transitions

    NASA Astrophysics Data System (ADS)

    Kumar, Anil; Rabe, Karin M.

    2011-03-01

    Expansion of the total energy of a crystal around a high-symmetry reference structure provides information about material properties including the phonon dispersion, responses to applied fields, magnetostructural coupling, and structural transitions. For complex oxides, parameterization of the structural energetics by real-space interatomic force constants (IFCs) provides a computationally convenient and physically transparent way of analyzing these properties. By projection into a subspace containing the relevant degrees of freedom, one can construct an effective Hamiltonian to study properties that are not readily accessible with DFT based calculations, including properties at finite temperature or long length scales. It is well known that first-principles density-functional-theory (DFT) based-calculations can be systematically used to determine real-space IFCs of materials; this is part of several first-principles packages including ABINIT and Quantum Espresso. Here, we discuss a simple and efficient approach for construction of first-principles effective Hamiltonians which uses this computational capability to generate and compute the quadratic inter-cell parameters in a single step. We illustrate the method through the application to systems for which effective Hamiltonians have previously been constructed, and show how this approach facilitates the construction of effective Hamiltonians for new classes of crystal structures.

  6. Near strongly resonant periodic orbits in a Hamiltonian system

    PubMed Central

    Gelfreich, Vassili

    2002-01-01

    We study an analytic Hamiltonian system near a strongly resonant periodic orbit. We introduce a modulus of local analytic classification. We provide asymptotic formulae for the exponentially small splitting of separatrices for bifurcating hyperbolic periodic orbits. These formulae confirm a conjecture formulated by V. I. Arnold in the early 1970s. PMID:12391324

  7. Exponential energy growth in adiabatically changing Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Pereira, Tiago; Turaev, Dmitry

    2015-01-01

    We show that the mixed phase space dynamics of a typical smooth Hamiltonian system universally leads to a sustained exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of geometric Brownian motion with a positive drift, and relate it to the steady entropy increase after each period of the parameters variation.

  8. Hamiltonian General Relativity in Finite Space and Cosmological Potential Perturbations

    NASA Astrophysics Data System (ADS)

    Barbashov, B. M.; Pervushin, V. N.; Zakharov, A. F.; Zinchuk, V. A.

    The Hamiltonian formulation of general relativity is considered in finite space-time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac-ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x0) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution. The astrophysical application of this approach to general relativity is considered under supposition that the Dirac-ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.

  9. Integrable Hamiltonian systems on low-dimensional Lie algebras

    SciTech Connect

    Korotkevich, Aleksandr A

    2009-12-31

    For any real Lie algebra of dimension 3, 4 or 5 and any nilpotent algebra of dimension 6 an integrable Hamiltonian system with polynomial coefficients is found on its coalgebra. These systems are constructed using Sadetov's method for constructing complete commutative families of polynomials on a Lie coalgebra. Bibliography: 17 titles.

  10. The Calculation of Rotational Energy Levels Using Tunneling Hamiltonians

    NASA Astrophysics Data System (ADS)

    Hougen, Jon T.

    2009-06-01

    The present talk will present a pedagogical introduction and review of 25 years of using tunneling Hamiltonians to parameterize and fit rotationally resolved spectra of small polyatomic molecules with one or more large-amplitude motions (LAMs). This tunneling formalism does not require a quantitative knowledge of the potential surface, but instead makes use only of its symmetry properties. Topics planned for discussion include: the user communities for such Hamiltonians; the range of applicability and achievable accuracy; a representative list of molecules treated to date and their various combinations of internal-rotation, inversion, hydrogen-bond-exchange, and H-atom-transfer LAMs; a way of organizing the LAMs of these molecules in the mind using the piston-and-crankshaft vocabulary of the reciprocating engine; how the theoretical tools of point-groups, permutation-inversion groups, extended groups, and time reversal are used in the tunneling-Hamiltonian formalism; and finally a brief report on the present status of two unfinished applications of the tunneling-Hamiltonian formalism, namely cis/trans bent acetylene (HCCH) and protonated acetylene (C_2H_3^+).

  11. The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach

    ERIC Educational Resources Information Center

    Likar, A.; Razpet, N.

    2009-01-01

    The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…

  12. The Hamiltonian property of the flow of singular trajectories

    SciTech Connect

    Lokutsievskiy, L V

    2014-03-31

    Pontryagin's maximum principle reduces optimal control problems to the investigation of Hamiltonian systems of ordinary differential equations with discontinuous right-hand side. An optimal synthesis is the totality of solutions to this system with a fixed terminal (or initial) condition, which fill a region in the phase space one-to-one. In the construction of optimal synthesis, singular trajectories that go along the discontinuity surface N of the right-hand side of the Hamiltonian system of ordinary differential equations, are crucial. The aim of the paper is to prove that the system of singular trajectories makes up a Hamiltonian flow on a submanifold of N. In particular, it is proved that the flow of singular trajectories in the problem of control of the magnetized Lagrange top in a variable magnetic field is completely Liouville integrable and can be embedded in the flow of a smooth superintegrable Hamiltonian system in the ambient space. Bibliography: 17 titles.

  13. Goldfish Geodesics and Hamiltonian Reduction of Matrix Dynamics

    NASA Astrophysics Data System (ADS)

    Arnlind, Joakim; Bordemann, Martin; Hoppe, Jens; Lee, Choonkyu

    2008-04-01

    We describe the Hamiltonian reduction of a time-dependent real-symmetric N× N matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.

  14. Davidson potential and SUSYQM in the Bohr Hamiltonian

    SciTech Connect

    Georgoudis, P. E.

    2013-06-10

    The Bohr Hamiltonian is modified through the Shape Invariance principle of SUper-SYmmetric Quantum Mechanics for the Davidson potential. The modification is equivalent to a conformal transformation of Bohr's metric, generating a different {beta}-dependence of the moments of inertia.

  15. Linear Hamiltonian systems - The Riccati group and its invariants

    NASA Technical Reports Server (NTRS)

    Garzia, M. R.; Martin, C. F.; Loparo, K. A.

    1982-01-01

    The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of Hamiltonian matrices. Within this framework canonical forms are developed for the matrix coefficients of the Riccati differential equation.

  16. Infrared limit of Horava's gravity with the global Hamiltonian constraint

    SciTech Connect

    Kobakhidze, Archil

    2010-09-15

    We show that Horava's theory of gravitation with the global Hamiltonian constraint does not reproduce general relativity in the infrared domain. There is one extra propagating degree of freedom, besides those two associated with the massless graviton, which does not decouple.

  17. Note on Hamiltonian format of Lotka-Volterra dynamics

    NASA Astrophysics Data System (ADS)

    Kerner, E. H.

    1990-12-01

    It is pointed out that the Hamiltonian form of Lotka-Volterra dynamics, recently observed by Nutku, was worked out many years ago; also that Volterra's many-spicies dynamics had been Hamiltonized, including a novel path to its statistical mechanics.

  18. Maxwell-Vlasov equations as a continuous Hamiltonian system

    SciTech Connect

    Morrison, P.J.

    1980-11-01

    The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B, and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion.

  19. Maxwell-Vlasov equations as a continuous Hamiltonian system

    SciTech Connect

    Morrison, P.J.

    1980-09-01

    The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion.

  20. Non-Hermitian Hamiltonians with unitary and antiunitary symmetries

    SciTech Connect

    Fernández, Francisco M. Garcia, Javier

    2014-03-15

    We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C{sub 2v} exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •PT-symmetric multidimensional oscillators appear to show PT phase transitions. •This transition was conjectured to be a high-energy phenomenon. •We show that point group symmetry is useful for predicting broken PT symmetry in multidimensional oscillators. •PT-symmetric oscillators with C{sub 2v} symmetry exhibit phase transitions at the trivial Hermitian limit.

  1. Simulating Hamiltonian Dynamics with a Truncated Taylor Series

    NASA Astrophysics Data System (ADS)

    Somma, Rolando

    2015-03-01

    One of the main motivations for quantum computers is their ability to efficiently simulate the dynamics of quantum systems. Since the mid-1990s, many algorithms have been developed to simulate Hamiltonian dynamics on a quantum computer, with applications to problems such as simulating spin models and quantum chemistry. While it is now well known that quantum computers can efficiently simulate Hamiltonian dynamics, ongoing work has improved the performance and expanded the scope of such simulations. In this talk, I will describe a very simple and efficient algorithm for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. This algorithm can simulate the time evolution of a wide variety of physical systems. The cost of this algorithm depends only logarithmically on the inverse of the desired precision, and can be shown to be optimal. Such a cost also represents an exponential improvement over known methods for Hamiltonian simulation based on, e.g., Trotter-Suzuki approximations. Roughly speaking, doubling the number of digits of accuracy of the simulation only doubles the complexity. The new algorithm and its analysis are highly simplified due to a technique for implementing linear combinations of unitary operations to directly apply the truncated Taylor series. This is joint work with Dominic Berry, Andrew Childs, Richard Cleve, and Robin Kothari.

  2. A separable shadow Hamiltonian hybrid Monte Carlo method

    NASA Astrophysics Data System (ADS)

    Sweet, Christopher R.; Hampton, Scott S.; Skeel, Robert D.; Izaguirre, Jesús A.

    2009-11-01

    Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC's performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog/Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a second-order integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http://mdlab.sourceforge.net/s2hmc).

  3. Evolutionary approach for determining first-principles hamiltonians

    NASA Astrophysics Data System (ADS)

    Hart, Gus L. W.; Blum, Volker; Walorski, Michael J.; Zunger, Alex

    2005-05-01

    Modern condensed-matter theory from first principles is highly successful when applied to materials of given structure-type or restricted unit-cell size. But this approach is limited where large cells or searches over millions of structure types become necessary. To treat these with first-principles accuracy, one 'coarse-grains' the many-particle Schrödinger equation into 'model hamiltonians' whose variables are configurational order parameters (atomic positions, spin and so on), connected by a few 'interaction parameters' obtained from a microscopic theory. But to construct a truly quantitative model hamiltonian, one must know just which types of interaction parameters to use, from possibly 106-108 alternative selections. Here we show how genetic algorithms, mimicking biological evolution ('survival of the fittest'), can be used to distil reliable model hamiltonian parameters from a database of first-principles calculations. We demonstrate this for a classic dilemma in solid-state physics, structural inorganic chemistry and metallurgy: how to predict the stable crystal structure of a compound given only its composition. The selection of leading parameters based on a genetic algorithm is general and easily applied to construct any other type of complex model hamiltonian from direct quantum-mechanical results.

  4. Evolutionary approach for determining first-principles hamiltonians.

    PubMed

    Hart, Gus L W; Blum, Volker; Walorski, Michael J; Zunger, Alex

    2005-05-01

    Modern condensed-matter theory from first principles is highly successful when applied to materials of given structure-type or restricted unit-cell size. But this approach is limited where large cells or searches over millions of structure types become necessary. To treat these with first-principles accuracy, one 'coarse-grains' the many-particle Schrodinger equation into 'model hamiltonians' whose variables are configurational order parameters (atomic positions, spin and so on), connected by a few 'interaction parameters' obtained from a microscopic theory. But to construct a truly quantitative model hamiltonian, one must know just which types of interaction parameters to use, from possibly 10(6)-10(8) alternative selections. Here we show how genetic algorithms, mimicking biological evolution ('survival of the fittest'), can be used to distil reliable model hamiltonian parameters from a database of first-principles calculations. We demonstrate this for a classic dilemma in solid-state physics, structural inorganic chemistry and metallurgy: how to predict the stable crystal structure of a compound given only its composition. The selection of leading parameters based on a genetic algorithm is general and easily applied to construct any other type of complex model hamiltonian from direct quantum-mechanical results. PMID:15834412

  5. Quantum finance Hamiltonian for coupon bond European and barrier options

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2008-03-01

    Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is “knocked out” (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates’ Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can—to a good approximation—be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

  6. When a local Hamiltonian must be frustration-free.

    PubMed

    Sattath, Or; Morampudi, Siddhardh C; Laumann, Chris R; Moessner, Roderich

    2016-06-01

    A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory. PMID:27199483

  7. Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes

    SciTech Connect

    Dias, Goncalo A. S.; Lemos, Jose P. S.

    2008-10-15

    The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free {omega} parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{+-}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3), all with a Maxwell term. The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P{sub M};Q,P{sub Q}), where M is the mass parameter, which for {omega}<-(3/2) and for {omega}={+-}{infinity} needs a careful renormalization, P{sub M} is the conjugate momenta of M, Q is the charge parameter, and P{sub Q} is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field {phi}. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the

  8. Hamiltonian formalism for perfect fluids in general relativity

    SciTech Connect

    Demaret, J.; Moncrief, V.

    1980-05-15

    Schutz's Hamiltonian theory of a relativistic perfect fluid, based on the velocity-potential version of classical perfect fluid hydrodynamics as formulated by Seliger and Whitham, is used to derive, in the framework of the Arnowitt, Deser, and Misner (ADM) method, a general partially reduced Hamiltonian for relativistic systems filled with a perfect fluid. The time coordinate is chosen, as in Lund's treatment of collapsing balls of dust, as minus the only velocity potential different from zero in the case of an irrotational and isentropic fluid. A ''semi-Dirac'' method can be applied to quantize astrophysical and cosmological models in the framework of this partially reduced formalism. If one chooses Taub's adapted comoving coordinate system, it is possible to derive a fully reduced ADM Hamiltonian, which is equal to minus the total baryon number of the fluid, generalizing a result previously obtained by Moncrief in the more particular framework of Taub's variational principle, valid for self-gravitating barotropic relativistic perfect fluids. An unconstrained Hamiltonian density is then explicitly derived for a fluid obeying the equation of state p=(gamma-1)rho (1 < or = ..gamma.. < or = 2), which can adequately describe the phases of very high density attained in a catastrophic collapse or during the early stages of the Universe. This Hamiltonian density, shown to be equivalent to Moncrief's in the particular case of an isentropic fluid, can be simplified for fluid-filled class-A diagonal Bianchi-type cosmological models and appears as a suitable starting point for the study of the canonical quantization of these models.

  9. Simple Hamiltonians which exhibit drastic failures by variational determination of the two-particle reduced density matrix with some well known N-representability conditions.

    PubMed

    Nakata, Maho; Braams, Bastiaan J; Fukuda, Mituhiro; Percus, Jerome K; Yamashita, Makoto; Zhao, Zhengji

    2006-12-28

    Calculations on small molecular systems indicate that the variational approach employing the two-particle reduced density matrix (2-RDM) as the basic unknown and applying the P, Q, G, T1, and T2 representability conditions provides an accuracy that is competitive with the best standard ab initio methods of quantum chemistry. However, in this paper we consider a simple class of Hamiltonians for which an exact ground state wave function can be written as a single Slater determinant and yet the same 2-RDM approach gives a drastically nonrepresentable result. This shows the need for stronger representability conditions than the mentioned ones. PMID:17199342

  10. Lagrangian and Hamiltonian structure of magnetofluid models with gyroviscous-like contributions

    NASA Astrophysics Data System (ADS)

    Wurm, Alexander; Morrison, P. J.

    2012-03-01

    Many magnetofluid theories, like ideal MHD and various reduced models, exhibit a noncanonical Hamiltonian structure when expressed in Eulerian variables [1]. Of particular interest are magnetofluid models that systematically include contributions due to finite ion gyro-radii. Building on the work of Ref. [2] we generalize the so-called gyro-map to three dimensional magnetofluid theories. Starting with the 3D ideal MHD noncanonical Poisson bracket [1] and a Hamiltonian including general gyroviscous terms, we derive equations of motions and compare them to, e.g., Braginskii [3] in the collisionless limit. In addition we explore the Lagrangian version of these theories which use Hamilton's principle to derive the equations of motion [4]. [4pt] [1] P.J. Morrison and J.M. Greene, Phys. Rev. A 45,790 (1980).[0pt] [2] P.J. Morrison, I.L. Caldas, and H. Tasso, Z. Naturforsch. 39a, 1023 (1984).[0pt] [3] S.I. Braginskii, in Review of Plasma Physics, ed. M.A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 205.[0pt] [4] W.A. Newcomb, Nuclear Fusion: 1962 Suppl. Part 2, p. 451.

  11. A Hamiltonian theory of adaptive resolution simulations of classical and quantum models of nuclei

    NASA Astrophysics Data System (ADS)

    Kreis, Karsten; Donadio, Davide; Kremer, Kurt; Potestio, Raffaello

    2015-03-01

    Quantum delocalization of atomic nuclei strongly affects the physical properties of low temperature systems, such as superfluid helium. However, also at room temperature nuclear quantum effects can play an important role for molecules composed by light atoms. An accurate modeling of these effects is possible making use of the Path Integral formulation of Quantum Mechanics. In simulations, this numerically expensive description can be restricted to a small region of space, while modeling the remaining atoms as classical particles. In this way the computational resources required can be significantly reduced. In the present talk we demonstrate the derivation of a Hamiltonian formulation for a bottom-up, theoretically solid coupling between a classical model and a Path Integral description of the same system. The coupling between the two models is established with the so-called Hamiltonian Adaptive Resolution Scheme, resulting in a fully adaptive setup in which molecules can freely diffuse across the classical and the Path Integral regions by smoothly switching their description on the fly. Finally, we show the validation of the approach by means of adaptive resolution simulations of low temperature parahydrogen. Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany.

  12. A generalised 17-state vibronic-coupling Hamiltonian model for ethylene

    NASA Astrophysics Data System (ADS)

    Jornet-Somoza, Joaquim; Lasorne, Benjamin; Robb, Michael A.; Meyer, Hans-Dieter; Lauvergnat, David; Gatti, Fabien

    2012-08-01

    In a previous work [B. Lasorne, M. A. Robb, H.-D. Meyer, and F. Gatti, "The electronic excited states of ethylene with large-amplitude deformations: A dynamical symmetry group investigation," Chem. Phys. 377, 30-45 (2010), 10.1016/j.chemphys.2010.08.011; B. Lasorne, M. A. Robb, H.-D. Meyer, and F. Gatti, Chem. Phys. 382, 132 (2011) (Erratum)], 10.1016/j.chemphys.2011.01.004, we investigated the electronic structure of ethylene (ethene, C2H4) in terms of 17 dominant configurations selected at the multiconfiguration self-consistent field level of theory. These were shown to be sufficient to recover most of the static electron correlation among the first valence and Rydberg states at all geometries. We also devised a strategy to build a 17-quasidiabatic-state matrix representation of the electronic Hamiltonian for curvilinear coordinates using dynamical symmetry. Here, we present fitted surfaces in the form of a generalised vibronic-coupling Hamiltonian model for two nuclear coordinates, CC bond stretching and torsion. Dynamic electron correlation is included into the electronic structure to improve the energetics of the Rydberg states at the multireference configuration interaction level of theory. The chemical interpretation of the adiabatic states of interest does not change qualitatively, which validates our choice of underlying quasidiabatic states in the model. The absorption spectrum is calculated with quantum dynamics and partially assigned. This first two-dimensional model shows a surprisingly good agreement with the experimental spectrum.

  13. A Non-Orthogonal Block-Localized Effective Hamiltonian Approach for Chemical and Enzymatic Reactions

    PubMed Central

    Cembran, Alessandro; Payaka, Apirak; Lin, Yen-lin; Xie, Wangshen; Mo, Yirong; Song, Lingchun; Gao, Jiali

    2010-01-01

    The effective Hamiltonian-molecular orbital and valence bond (EH-MOVB) method based on non-orthogonal block-localized fragment orbitals has been implemented into the program CHARMM for molecular dynamics simulations of chemical and enzymatic reactions, making use of semiempirical quantum mechanical models. Building upon ab initio MOVB theory, we make use of two parameters in the EH-MOVB method to fit the barrier height and the relative energy between the reactant and product state for a given chemical reaction to be in agreement with experiment or high-level ab initio or density functional results. Consequently, the EH-MOVB method provides a highly accurate and computationally efficient QM/MM model for dynamics simulation of chemical reactions in solution. The EH-MOVB method is illustrated by examination of the potential energy surface of the hydride transfer reaction from trimethylamine to a flavin cofactor model in the gas phase. In the present study, we employed the semiempirical AM1 model, which yields a reaction barrier that is more than 5 kcal/mol too high. We use a parameter calibration procedure for the EH-MOVB method similar to that employed to adjust the results of semiempirical and empirical models. Thus, the relative energy of these two diabatic states can be shifted to reproduce the experimental energy of reaction, and the barrier height is optimized to reproduce the desired (accurate) value by adding a constant to the off-diagonal matrix element. The present EH-MOVB method offers a viable approach to characterizing solvent and protein-reorganization effects in the realm of combined QM/MM simulations. PMID:20694172

  14. The Hamiltonian structure of the (2+1)-dimensional Ablowitz--Kaup--Newell--Segur hierarchy

    SciTech Connect

    Athorne, C. ); Dorfman, I.Y. )

    1993-08-01

    By considering Hamiltonian theory over a suitable (noncommutative) ring the nonlinear evolution equations of the Ablowitz--Kaup--Newell--Segur (2+1) hierarchy are incorporated into a Hamiltonian framework and a modified Lenard scheme.

  15. Ab Initio Calculation of the Hoyle State

    SciTech Connect

    Epelbaum, Evgeny; Krebs, Hermann; Lee, Dean; Meissner, Ulf-G.

    2011-05-13

    The Hoyle state plays a crucial role in the helium burning of stars heavier than our Sun and in the production of carbon and other elements necessary for life. This excited state of the carbon-12 nucleus was postulated by Hoyle as a necessary ingredient for the fusion of three alpha particles to produce carbon at stellar temperatures. Although the Hoyle state was seen experimentally more than a half century ago nuclear theorists have not yet uncovered the nature of this state from first principles. In this Letter we report the first ab initio calculation of the low-lying states of carbon-12 using supercomputer lattice simulations and a theoretical framework known as effective field theory. In addition to the ground state and excited spin-2 state, we find a resonance at -85(3) MeV with all of the properties of the Hoyle state and in agreement with the experimentally observed energy.

  16. Ab initio two-component Ehrenfest dynamics

    NASA Astrophysics Data System (ADS)

    Ding, Feizhi; Goings, Joshua J.; Liu, Hongbin; Lingerfelt, David B.; Li, Xiaosong

    2015-09-01

    We present an ab initio two-component Ehrenfest-based mixed quantum/classical molecular dynamics method to describe the effect of nuclear motion on the electron spin dynamics (and vice versa) in molecular systems. The two-component time-dependent non-collinear density functional theory is used for the propagation of spin-polarized electrons while the nuclei are treated classically. We use a three-time-step algorithm for the numerical integration of the coupled equations of motion, namely, the velocity Verlet for nuclear motion, the nuclear-position-dependent midpoint Fock update, and the modified midpoint and unitary transformation method for electronic propagation. As a test case, the method is applied to the dissociation of H2 and O2. In contrast to conventional Ehrenfest dynamics, this two-component approach provides a first principles description of the dynamics of non-collinear (e.g., spin-frustrated) magnetic materials, as well as the proper description of spin-state crossover, spin-rotation, and spin-flip dynamics by relaxing the constraint on spin configuration. This method also holds potential for applications to spin transport in molecular or even nanoscale magnetic devices.

  17. Ab initio two-component Ehrenfest dynamics

    SciTech Connect

    Ding, Feizhi; Goings, Joshua J.; Liu, Hongbin; Lingerfelt, David B.; Li, Xiaosong

    2015-09-21

    We present an ab initio two-component Ehrenfest-based mixed quantum/classical molecular dynamics method to describe the effect of nuclear motion on the electron spin dynamics (and vice versa) in molecular systems. The two-component time-dependent non-collinear density functional theory is used for the propagation of spin-polarized electrons while the nuclei are treated classically. We use a three-time-step algorithm for the numerical integration of the coupled equations of motion, namely, the velocity Verlet for nuclear motion, the nuclear-position-dependent midpoint Fock update, and the modified midpoint and unitary transformation method for electronic propagation. As a test case, the method is applied to the dissociation of H{sub 2} and O{sub 2}. In contrast to conventional Ehrenfest dynamics, this two-component approach provides a first principles description of the dynamics of non-collinear (e.g., spin-frustrated) magnetic materials, as well as the proper description of spin-state crossover, spin-rotation, and spin-flip dynamics by relaxing the constraint on spin configuration. This method also holds potential for applications to spin transport in molecular or even nanoscale magnetic devices.

  18. An investigation of ab initio shell-model interactions derived by no-core shell model

    NASA Astrophysics Data System (ADS)

    Wang, XiaoBao; Dong, GuoXiang; Li, QingFeng; Shen, CaiWan; Yu, ShaoYing

    2016-09-01

    The microscopic shell-model effective interactions are mainly based on the many-body perturbation theory (MBPT), the first work of which can be traced to Brown and Kuo's first attempt in 1966, derived from the Hamada-Johnston nucleon-nucleon potential. However, the convergence of the MBPT is still unclear. On the other hand, ab initio theories, such as Green's function Monte Carlo (GFMC), no-core shell model (NCSM), and coupled-cluster theory with single and double excitations (CCSD), have made many progress in recent years. However, due to the increasing demanding of computing resources, these ab initio applications are usually limited to nuclei with mass up to A = 16. Recently, people have realized the ab initio construction of valence-space effective interactions, which is obtained through a second-time renormalization, or to be more exactly, projecting the full-manybody Hamiltonian into core, one-body, and two-body cluster parts. In this paper, we present the investigation of such ab initio shell-model interactions, by the recent derived sd-shell effective interactions based on effective J-matrix Inverse Scattering Potential (JISP) and chiral effective-field theory (EFT) through NCSM. In this work, we have seen the similarity between the ab initio shellmodel interactions and the interactions obtained by MBPT or by empirical fitting. Without the inclusion of three-body (3-bd) force, the ab initio shell-model interactions still share similar defects with the microscopic interactions by MBPT, i.e., T = 1 channel is more attractive while T = 0 channel is more repulsive than empirical interactions. The progress to include more many-body correlations and 3-bd force is still badly needed, to see whether such efforts of ab initio shell-model interactions can reach similar precision as the interactions fitted to experimental data.

  19. Spin Hamiltonian, order out of a Coulomb phase, and pseudocriticality in the frustrated pyrochlore Heisenberg antiferromagnet FeF3

    NASA Astrophysics Data System (ADS)

    Sadeghi, Azam; Alaei, Mojtaba; Shahbazi, Farhad; Gingras, Michel J. P.

    2015-04-01

    FeF3, with its half-filled Fe3 +3 d orbital, hence zero orbital angular momentum and S =5 /2 , is often put forward as a prototypical highly frustrated classical Heisenberg pyrochlore antiferromagnet. By employing ab initio density functional theory, we obtain an effective spin Hamiltonian for this material. This Hamiltonian contains nearest-neighbor antiferromagnetic Heisenberg, biquadratic, and Dzyaloshinskii-Moriya interactions as dominant terms and we use Monte Carlo simulations to investigate the nonzero temperature properties of this minimal model. We find that upon decreasing temperature, the system passes through a Coulomb phase, composed of short-range correlated coplanar states, before transforming into an "all-in/all-out" (AIAO) state via a very weakly first-order transition at a critical temperature Tc≈22 K, in good agreement with the experimental value for a reasonable set of Coulomb interaction U and Hund's coupling JH describing the material. Despite the transition being first order, the AIAO order parameter evolves below Tc with a power-law behavior characterized by a pseudo "critical exponent" β ≈0.18 in accord with experiment. We comment on the origin of this unusual β value.

  20. On bi-Hamiltonian structure of two-component Novikov equation

    NASA Astrophysics Data System (ADS)

    Li, Nianhua; Liu, Q. P.

    2013-01-01

    In this Letter, we present a bi-Hamiltonian structure for the two-component Novikov equation. We also show that proper reduction of this bi-Hamiltonian structure leads to the Hamiltonian operators found by Hone and Wang for the Novikov equation.

  1. Solving a Hamiltonian Path Problem with a bacterial computer

    PubMed Central

    Baumgardner, Jordan; Acker, Karen; Adefuye, Oyinade; Crowley, Samuel Thomas; DeLoache, Will; Dickson, James O; Heard, Lane; Martens, Andrew T; Morton, Nickolaus; Ritter, Michelle; Shoecraft, Amber; Treece, Jessica; Unzicker, Matthew; Valencia, Amanda; Waters, Mike; Campbell, A Malcolm; Heyer, Laurie J; Poet, Jeffrey L; Eckdahl, Todd T

    2009-01-01

    Background The Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time. Results We programmed bacteria with a genetic circuit that enables them to evaluate all possible paths in a directed graph in order to find a Hamiltonian path. We encoded a three node directed graph as DNA segments that were autonomously shuffled randomly inside bacteria by a Hin/hixC recombination system we previously adapted from Salmonella typhimurium for use in Escherichia coli. We represented nodes in the graph as linked halves of two different genes encoding red or green fluorescent proteins. Bacterial populations displayed phenotypes that reflected random ordering of edges in the graph. Individual bacterial clones that found a Hamiltonian path reported their success by fluorescing both red and green, resulting in yellow colonies. We used DNA sequencing to verify that the yellow phenotype resulted from genotypes that represented Hamiltonian path solutions, demonstrating that our bacterial computer functioned as expected. Conclusion We successfully designed, constructed, and tested a bacterial computer capable of finding a Hamiltonian path in a three node directed graph. This proof

  2. Ab Initio Multiple Spawning Method for Intersystem Crossing Dynamics: Spin-Forbidden Transitions between (3)B1 and (1)A1 States of GeH2.

    PubMed

    Fedorov, Dmitry A; Pruitt, Spencer R; Keipert, Kristopher; Gordon, Mark S; Varganov, Sergey A

    2016-05-12

    Dynamics at intersystem crossings are fundamental to many processes in chemistry, physics, and biology. The ab initio multiple spawning (AIMS) method was originally developed to describe internal conversion dynamics at conical intersections where derivative coupling is responsible for nonadiabatic transitions between electronic states with the same spin multiplicity. Here, the applicability of the AIMS method is extended to intersystem crossing dynamics in which transitions between electronic states with different spin multiplicities are mediated by relativistic spin-orbit coupling. In the direct AIMS dynamics, the nuclear wave function is expanded in the basis of frozen multidimensional Gaussians propagating on the coupled electronic potential energy surfaces calculated on the fly. The AIMS method for intersystem crossing is used to describe the nonadiabatic transitions between the (3)B1 and (1)A1 states of GeH2. The potential energies and gradients were obtained at the CASSCF(6,6)/6-31G(d) level of theory. The spin-orbit coupling matrix elements were calculated with the configuration interaction method using the two-electron Breit-Pauli Hamiltonian. The excited (3)B1 state lifetime and intersystem crossing rate constants were estimated by fitting the AIMS state population with the first-order kinetics equation for a reversible unimolecular reaction. The obtained rate constants are compared with the values predicted by the statistical nonadiabatic transition state theory with transition probabilities calculated using the Landau-Zener and weak coupling formulas. PMID:27064356

  3. AB 1725: A Comprehensive Analysis.

    ERIC Educational Resources Information Center

    California Community Colleges, Sacramento. Board of Governors.

    A summary and analysis is provided of California Assembly Bill (AB) 1725, a reform bill that provides new direction and support for the state's community colleges. The analysis addresses each of the eight sections of the bill: (1) mission, highlighting reforms related to mission statements, transfer core curriculum, remedial limits, articulation…

  4. Ab initio investigation of light-induced relativistic spin-flip effects in magneto-optics

    NASA Astrophysics Data System (ADS)

    Mondal, Ritwik; Berritta, Marco; Carva, Karel; Oppeneer, Peter M.

    2015-05-01

    Excitation of a metallic ferromagnet such as Ni with an intensive femtosecond laser pulse causes an ultrafast demagnetization within approximately 300 fs. It was proposed that the ultrafast demagnetization measured in femtosecond magneto-optical experiments could be due to relativistic light-induced processes. We perform an ab initio investigation of the influence of relativistic effects on the magneto-optical response of Ni. To this end, first, we develop a response theory formulation of the additional appearing ultrarelativistic terms in the Foldy-Wouthuysen transformed Dirac Hamiltonian due to the electromagnetic field, and second, we compute the influence of relativistic light-induced spin-flip transitions on the magneto-optics. Our ab initio calculations of relativistic spin-flip optical excitations predict that these can give only a very small contribution (≤0.1 %) to the laser-induced magnetization change in Ni.

  5. Bohr Hamiltonian with a deformation-dependent mass term for the Davidson potential

    SciTech Connect

    Bonatsos, Dennis; Georgoudis, P. E.; Lenis, D.; Minkov, N.; Quesne, C.

    2011-04-15

    Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for separable potentials consisting of a Davidson potential in the {beta} variable, in the cases of {gamma}-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. The solution, called the deformation-dependent mass (DDM) Davidson model, is achieved by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, reduces the rate of increase of the moment of inertia with deformation, removing a main drawback of the model.

  6. Generalized massive gravity in arbitrary dimensions and its Hamiltonian formulation

    SciTech Connect

    Huang, Qing-Guo; Zhang, Ke-Chao; Zhou, Shuang-Yong E-mail: zkc@itp.ac.cn

    2013-08-01

    We extend the four-dimensional de Rham-Gabadadze-Tolley (dRGT) massive gravity model to a general scalar massive-tensor theory in arbitrary dimensions, coupling a dRGT massive graviton to multiple scalars and allowing for generic kinetic and mass matrix mixing between the massive graviton and the scalars, and derive its Hamiltonian formulation and associated constraint system. When passing to the Hamiltonian formulation, two different sectors arise: a general sector and a special sector. Although obtained via different ways, there are two second class constraints in either of the two sectors, eliminating the BD ghost. However, for the special sector, there are still ghost instabilities except for the case of two dimensions. In particular, for the special sector with one scalar, there is a ''second BD ghost''.

  7. Double null hamiltonian dynamics and the gravitational degrees of freedom

    NASA Astrophysics Data System (ADS)

    Vickers, J. A.

    2011-12-01

    In this paper we review the Hamiltonian description of General Relativity using a double null foliation. We start by looking at the 2+2 version of geometrodynamics and show the role of the conformal 2-structure of the 2-metric in encoding (through the shear) the 2 gravitational degrees of freedom. In the second part of the paper we consider instead a canonical analysis of a double null 2+2 Hamiltonian description of General Relativity in terms of self-dual 2-forms and the associated SO(3) connection variables. The algebra of first class constraints is obtained and forms a Lie algebra that consists of two constraints that generate diffeomorphisms in the two surface, a constraint that generates diffeomorphisms along the null generators and a constraint that generates self-dual spin and boost transformations.

  8. Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory

    SciTech Connect

    Andreussi, T.; Morrison, P. J.; Pegoraro, F.

    2013-09-15

    Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.

  9. Effective Hamiltonian for bound states in Yukawa theory

    SciTech Connect

    Weber, Axel

    2013-07-15

    A generalization of the Gell-Mann–Low theorem is applied to lowest nontrivial order to determine an effective Hamiltonian for two-fermion states in relativistic Yukawa theory. The consistency of the corresponding effective Schrödinger equation is thoroughly investigated in various aspects, among others the nonrelativistic and one-body limits, and the small-distance or large-momentum regime of the bound state solutions is discussed in detail. -- Highlights: •A generalization of the Gell-Mann–Low theorem is applied to Yukawa theory. •The effective Hamiltonian for two-fermion states is derived to lowest order. •The nonrelativistic and one-body limits are consistent. •The large-momentum behavior of the bound-state solutions is analyzed. •A critical value for the coupling constant is determined.

  10. Commuting Pauli Hamiltonians as Maps between Free Modules

    NASA Astrophysics Data System (ADS)

    Haah, Jeongwan

    2013-12-01

    We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, a family of Hamiltonians that belong to the same phase of matter is described by a map between modules over the translation-group algebra, so homological methods are applicable. In any dimension every point-like charge appears as a vertex of a fractal operator, and can be isolated with energy barrier at most logarithmic in the separation distance. For a topologically ordered system in three dimensions, there must exist a point-like nontrivial charge. A connection between the ground state degeneracy and the number of points on an algebraic set is discussed. Tools to handle local Clifford unitary transformations are given.

  11. Hamiltonian formulation towards minimization of viscous fluid fingering

    NASA Astrophysics Data System (ADS)

    Batista, Carlos; Dias, Eduardo O.; Miranda, José A.

    2016-07-01

    A variational approach has been recently employed to determine the ideal time-dependent injection rate Q (t ) that minimizes fingering formation when a fluid is injected in a Hele-Shaw cell filled with another fluid of much greater viscosity. However, such a calculation is approximate in nature, since it has been performed by assuming a high capillary number regime. In this work, we go one step further, and utilize a Hamiltonian formulation to obtain an analytical exact solution for Q (t ) , now valid for arbitrary values of the capillary number. Moreover, this Hamiltonian scheme is applied to calculate the corresponding injection rate that minimizes fingering formation in a uniform three-dimensional porous media. An analysis of the improvement offered by these exact injection rate expressions in comparison with previous approximate results is also provided.

  12. Exactly solvable Hamiltonian for the chiral spin liquid

    NASA Astrophysics Data System (ADS)

    Schroeter, Darrell; Kapit, Eliot

    2006-03-01

    An exact spin Hamiltonian for the chiral spin liquid will be presented. The model starts with the quantum Hall wave function on a lattice of N sites in a toroidal geometry, a state that describes a spin liquid that violates the symmetries of parity and time reversal. A parent Hamiltonian for which the state is the exact ground state is constructed out of vector operators that annihilate the ground state. This model avoids the subtle error that has been identified [D. F. Schroeter, Ann. Phys. 310, 155 (2004)] in Laughlin's original solution to the problem [R. B. Laughlin, Ann. Phys. 191, 163 (1989)]. The construction of the model and its numerical verification will be presented.

  13. Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

    NASA Astrophysics Data System (ADS)

    Al-Hashimi, M. H.; Salman, M.; Shalaby, A.; Wiese, U.-J.

    2013-10-01

    We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.

  14. Dirichlet and Neumann eigenvalues for half-plane magnetic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Bruneau, Vincent; Miranda, Pablo; Raikov, Georgi

    2014-02-01

    Let H0,D (respectively, H0,N) be the Schrödinger operator in constant magnetic field on the half-plane with Dirichlet (respectively, Neumann) boundary conditions, and let Hℓ := H0,ℓ - V, ℓ = D, N, where the scalar potential V is non-negative, bounded, does not vanish identically, and decays at infinity. We compare the distribution of the eigenvalues of HD and HN below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behavior of the discrete spectrum of Hℓ near inf σess(Hℓ) = inf σ(H0,ℓ), ℓ = D, N. Applying these Hamiltonians, we show that σdisc(HD) is infinite even if V has a compact support, while σdisc(HN) could be finite or infinite depending on the decay rate of V.

  15. Hamiltonian formulation towards minimization of viscous fluid fingering.

    PubMed

    Batista, Carlos; Dias, Eduardo O; Miranda, José A

    2016-07-01

    A variational approach has been recently employed to determine the ideal time-dependent injection rate Q(t) that minimizes fingering formation when a fluid is injected in a Hele-Shaw cell filled with another fluid of much greater viscosity. However, such a calculation is approximate in nature, since it has been performed by assuming a high capillary number regime. In this work, we go one step further, and utilize a Hamiltonian formulation to obtain an analytical exact solution for Q(t), now valid for arbitrary values of the capillary number. Moreover, this Hamiltonian scheme is applied to calculate the corresponding injection rate that minimizes fingering formation in a uniform three-dimensional porous media. An analysis of the improvement offered by these exact injection rate expressions in comparison with previous approximate results is also provided. PMID:27575219

  16. Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.

    PubMed

    Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza

    2016-08-12

    We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986

  17. Solving SAT and Hamiltonian Cycle Problem Using Asynchronous P Systems

    NASA Astrophysics Data System (ADS)

    Tagawa, Hirofumi; Fujiwara, Akihiro

    In the present paper, we consider fully asynchronous parallelism in membrane computing, and propose two asynchronous P systems for the satisfiability (SAT) and Hamiltonian cycle problem. We first propose an asynchronous P system that solves SAT with n variables and m clauses, and show that the proposed P system computes SAT in O(mn2n) sequential steps or O(mn) parallel steps using O(mn) kinds of objects. We next propose an asynchronous P system that solves the Hamiltonian cycle problem with n nodes, and show that the proposed P system computes the problem in O(n!) sequential steps or O(n2) parallel steps using O(n2) kinds of objects.

  18. Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza

    2016-08-01

    We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.

  19. A Hamiltonian Model of Generator With AVR and PSS Parameters*

    NASA Astrophysics Data System (ADS)

    Qian, Jing.; Zeng, Yun.; Zhang, Lixiang.; Xu, Tianmao.

    Take the typical thyristor excitation system including the automatic voltage regulator (AVR) and the power system stabilizer (PSS) as an example, the supply rate of AVR and PSS branch are selected as the energy function of controller, and that is added to the Hamiltonian function of the generator to compose the total energy function. By proper transformation, the standard form of the Hamiltonian model of the generator including AVR and PSS is derived. The structure matrix and damping matrix of the model include feature parameters of AVR and PSS, which gives a foundation to study the interaction mechanism of parameters between AVR, PSS and the generator. Finally, the structural relationships and interactions of the system model are studied, the results show that the relationship of structure and damping characteristic reflected by model consistent with practical system.

  20. Hamiltonian structure of a drift-kinetic model and Hamiltonian closures for its two-moment fluid reductions

    NASA Astrophysics Data System (ADS)

    Tassi, Emanuele

    2014-07-01

    We address the problem of the existence of the Hamiltonian structure for an electrostatic drift-kinetic model and for the related fluid models describing the evolution of the first two moments of the distribution function with respect to the parallel velocity. The drift-kinetic model, which accounts for background density and temperature gradients as well as polarization effects, is shown to possess a noncanonical Hamiltonian structure. The corresponding Poisson bracket is expressed in terms of the fluid moments and it is found that the set of functionals of the zero order moment forms a sub-algebra, thus automatically leading to a class of one-moment Hamiltonian fluid models. In particular, in the limit of weak spatial variations of the background quantities, the Charney-Hasegawa-Mima equation, with its Hamiltonian structure, is recovered. For the set of functionals of the first two moments, which, unlike the case of the Vlasov equation, turns out not to form a sub-algebra, we look for closures that lead to a closed Poisson bracket restricted to this set of functionals. The constraint of the Jacobi identity turns out to select the adiabatic equation of state for an ideal gas with one-degree-of-freedom molecules, as the only admissible closure in this sense. When the so called δf ordering is applied to the model, on the other hand, a Poisson bracket is obtained if the second order moment is a linear combination of the first two moments of the total distribution function. By means of this procedure, three-dimensional Hamiltonian fluid models that couple a generalized Charney-Hasegawa-Mima equation with an evolution equation for the parallel velocity are derived. Among these, a model adopted by Meiss and Horton [Phys. Fluids 26, 990 (1983)] to describe drift waves coupled to ion-acoustic waves, is obtained and its Hamiltonian structure is provided explicitly. Contribution to the Topical Issue "Theory and Applications of the Vlasov Equation", edited by Francesco

  1. Quantum integrals of motion for variable quadratic Hamiltonians

    SciTech Connect

    Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.

    2010-09-15

    We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

  2. When a local Hamiltonian must be frustration-free

    NASA Astrophysics Data System (ADS)

    Sattath, Or; Morampudi, Siddhardh C.; Laumann, Chris R.; Moessner, Roderich

    2016-06-01

    A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion—a sufficient condition—under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer’s theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian’s interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.

  3. Some preliminary thoughts on the invention of constrained Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    Salisbury, Donald

    2011-10-01

    I will present some tentative remarks on the origins of constrained Hamiltonian dynamics, based in part on interviews recently conducted by myself and Dean Rickles with several key contributers. These interviews with James Anderson, Stanley Deser, Charles Misner, and Josh Goldberg were partially supported by the Center for the History of Physics of the American Institute of Physics, and will eventually be made available on the Center web page.

  4. Energy Transfer in a Fast-Slow Hamiltonian System

    NASA Astrophysics Data System (ADS)

    Dolgopyat, Dmitry; Liverani, Carlangelo

    2011-11-01

    We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a nonlinear diffusion equation. This is a first step toward the derivation of macroscopic equations from a Hamiltonian microscopic dynamics in the case of weakly coupled systems.

  5. Hamiltonian structure for rotational capillary waves in stratified flows

    NASA Astrophysics Data System (ADS)

    Martin, Calin Iulian

    2016-07-01

    We show that the governing equations of two-dimensional water waves driven by surface tension propagating over two-layered stratified flows admit a Hamiltonian formulation. Moreover, the underlying flows that we consider here, have piecewise constant distribution of vorticity, the jump in vorticity being located along the interface separating the fluid of bigger density at the bottom from the lighter fluid adjacent to the free surface.

  6. Exact Solution of the Isovector Proton Neutron Pairing Hamiltonian

    SciTech Connect

    Dukelsky, J; Gueorguiev, V G; Van Isacker, P; Dimitrova, S S; Errea, B; H., S L

    2005-12-02

    The complete exact solution of the T = 1 neutron-proton pairing Hamiltonian is presented in the context of the SO(5) Richardson-Gaudin model with non-degenerate single-particle levels and including isospin-symmetry breaking terms. The power of the method is illustrated with a numerical calculation for {sup 64}Ge for a pf + g{sub 9/2} model space which is out of reach of modern shell-model codes.

  7. Superfield Hamiltonian quantization in terms of quantum antibrackets

    NASA Astrophysics Data System (ADS)

    Batalin, Igor A.; Lavrov, Peter M.

    2016-04-01

    We develop a new version of the superfield Hamiltonian quantization. The main new feature is that the BRST-BFV charge and the gauge fixing Fermion are introduced on equal footing within the sigma model approach, which provides for the actual use of the quantum/derived antibrackets. We study in detail the generating equations for the quantum antibrackets and their primed counterparts. We discuss the finite quantum anticanonical transformations generated by the quantum antibracket.

  8. On Hamiltonian and Action Principle Formulations of Plasma Dynamics

    SciTech Connect

    Morrison, P. J.

    2009-11-10

    A general discussion of Hamiltonian and action principle formulations for fluid and plasma models is given. A procedure, based on Hamilton's principle of mechanics but adapted for continua, for the construction of action principles for fluid and kinetic models is given. The transformation from action principles in terms of the Lagrangian variable description to the Eulerian variable description in terms of noncanonical Poisson brackets is described. Two examples are developed: ideal MHD and Braginskii's fluid model with gyroviscosity.

  9. PT -symmetric Hamiltonians and their application in quantum information

    NASA Astrophysics Data System (ADS)

    Croke, Sarah

    2015-05-01

    We discuss the prospect of PT -symmetric Hamiltonians finding applications in quantum information science, and conclude that such evolution is unlikely to provide any benefit over existing techniques. Although it has been known for some time that PT -symmetric quantum theory, when viewed as a unitary theory, is exactly equivalent to standard quantum mechanics, proposals continue to be put forward for schemes in which PT -symmetric quantum theory can outperform standard quantum theory. The most recent of these is the suggestion to use PT -symmetric Hamiltonians to perform an exponentially fast database search, a task known to be impossible with a quantum computer. Further, such a scheme has been shown to apparently produce effects in conflict with fundamental information-theoretic principles, such as the impossibility of superluminal information transfer, and the invariance of entanglement under local operations. In this paper we propose three inequivalent experimental implementations of PT -symmetric Hamiltonians, with careful attention to the resources required to realize each such evolution. Such an operational approach allows us to resolve these apparent conflicts, and evaluate fully schemes proposed in the literature for faster time evolution and state discrimination.

  10. Gyroaverage effects on nontwist Hamiltonians: separatrix reconnection and chaos suppression

    SciTech Connect

    Del-Castillo-Negrete, Diego B; Martinell, J.

    2012-01-01

    A study of nite Larmor radius (FLR) eects on E B test particle chaotic transport in non- monotonic zonal ows with drift waves in magnetized plasmas is presented. Due to the non- monotonicity of the zonal ow, the Hamiltonian does not satisfy the twist condition. The electro- static potential is modeled as a linear superposition of a zonal ow and regular neutral modes of the Hasegawa-Mima equation. FLR eects are incorporated by gyro-averaging the EB Hamiltonian. It is shown that there is a critical value the Larmor radius for which the zonal ow transitions from a prole with one maximum to a prole with two maxima and a minimum. This bifurcation leads to the creation of additional shearless curves and resonances. The gyroaveraged nontwist Hamiltonian exhibits complex patterns of separatrix reconnection. A change in the Larmor ra- dius can lead to heteroclinic-homoclinic bifurcations and dipole formation. For Larmor radii for which the zonal ow has bifurcated, double heteroclinic-heteroclinic, homoclinic-homoclinic and heteroclinic-homoclinic topologies are observed. It is also shown that chaotic transport is typically reduced as the Larmor radius increases. Poincare sections shows that, for large enough Larmor radius, chaos can be practically suppressed. In particular, small changes on the Larmor radius can restore the shearless curve.

  11. Gyroaverage effects on nontwist Hamiltonians: Separatrix reconnection and chaos suppression

    SciTech Connect

    Del-Castillo-Negrete, Diego B; Martinell, J.

    2012-01-01

    A study of finite Larmor radius (FLR) effects on E x B test particle chaotic transport in non-monotonic zonal flows with drift waves in magnetized plasmas is presented. Due to the non-monotonicity of the zonal flow, the Hamiltonian does not satisfy the twist condition. The electrostatic potential is modeled as a linear superposition of a zonal flow and the regular neutral modes of the Hasegawa-Mima equation. FLR effects are incorporated by gyro-averaging the E x B Hamiltonian. It is shown that there is a critical value of the Larmor radius for which the zonal flow transitions from a profile with one maximum to a profile with two maxima and a minimum. This bifurcation leads to the creation of additional shearless curves and resonances. The gyroaveraged nontwist Hamiltonian exhibits complex patterns of separatrix reconnection. A change in the Larmor radius can lead to heteroclinic-homoclinic bifurcations and dipole formation. For Larmor radii for which the zonal flow has bifurcated, double heteroclinic-heteroclinic, homoclinic-homoclinic and heteroclinic-homoclinic separatrix topologies are observed. It is also shown that chaotic transport is typically reduced as the Larmor radius increases. Poincare sections show that, for large enough Larmor radius, chaos can be practically suppressed. In particular, changes of the Larmor radius can restore the shearless curve.

  12. Driver Hamiltonians for constrained optimization in quantum annealing

    NASA Astrophysics Data System (ADS)

    Hen, Itay; Sarandy, Marcelo S.

    2016-06-01

    One of the current major challenges surrounding the use of quantum annealers for solving practical optimization problems is their inability to encode even moderately sized problems, the main reason for this being the rigid layout of their quantum bits as well as their sparse connectivity. In particular, the implementation of constraints has become a major bottleneck in the embedding of practical problems, because the latter is typically achieved by adding harmful penalty terms to the problem Hamiltonian, a technique that often requires an all-to-all connectivity between the qubits. Recently, a novel technique designed to obviate the need for penalty terms was suggested; it is based on the construction of driver Hamiltonians that commute with the constraints of the problem, rendering the latter constants of motion. In this work we propose general guidelines for the construction of such driver Hamiltonians given an arbitrary set of constraints. We illustrate the broad applicability of our method by analyzing several diverse examples, namely, graph isomorphism, not-all-equal three-satisfiability, and the so-called Lechner-Hauke-Zoller constraints. We also discuss the significance of our approach in the context of current and future experimental quantum annealers.

  13. On the Right Hamiltonian for Singular Perturbations:. General Theory

    NASA Astrophysics Data System (ADS)

    Neidhardt, Hagen; Zagrebnov, Valentin

    Let the pair of self-adjoint operators {A≥0,W≤0} be such that: (a) there is a dense domain { D} subseteqdom (A)∩ dom(W) such that ˙ {H}=(A+W)|{ D} is semibounded from below (stability domain), (b) the symmetric operator ˙ {H} is not essentially self-adjoint (singularity of the perturbation), (c) the Friedrichs extension hat {A} of ˙ {A}=A|{ D} is maximal with respect to W, i.e., dom(√ {-W})∩ ker (˙ {A}*-{η }I)=\\{0\\}. η < 0. Let \\{Wn\\}∞ n=1 be a regularizing sequence of bounded operators which tends in the strong resolvent sense to W. The abstract problem of the right Hamiltonian is: (i) to give conditions such that the limit H of self-adjoint regularized Hamiltonians ˜ {H}n=˜ {A}+W_n exists and is unique for any self-adjoint extension ˜ {A} of ˙ {A}, (ii) to describe the limit H. We show that under the conditions (a)-(c) there is a regularizing sequence \\{Wn\\}∞ n=1 such that ˜ {H}n=˜ {A}+W_n tends in the strong resolvent sense to unique (right Hamiltonian) hat {H}=hat {A}.+W, otherwise the limit is not unique.

  14. Trojan dynamics well approximated by a new Hamiltonian normal form

    NASA Astrophysics Data System (ADS)

    Páez, Rocío Isabel; Locatelli, Ugo

    2015-10-01

    We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the planar circular restricted three-body problem, by introducing a number of key new ideas in the formulation. In some sense, we adapt the approach of Garfinkel to the context of the normal form theory and its modern techniques. First, we make use of Delaunay variables for a physically accurate representation of the system. Therefore, we introduce a novel manipulation of the variables so as to respect the natural behaviour of the model. We develop a normalization procedure over the fast angle which exploits the fact that singularities in this model are essentially related to the slow angle. Thus, we produce a new normal form, i.e. an integrable approximation to the Hamiltonian. We emphasize some practical examples of the applicability of our normalizing scheme, e.g. the estimation of the stable libration region. Finally, we compare the level curves produced by our normal form with surfaces of section provided by the integration of the non-normalized Hamiltonian, with very good agreement. Further precision tests are also provided. In addition, we give a step-by-step description of the algorithm, allowing for extensions to more complicated models.

  15. Production and Transfer of Energy and Information in Hamiltonian Systems

    PubMed Central

    Antonopoulos, Chris G.; Bianco-Martinez, Ezequiel; Baptista, Murilo S.

    2014-01-01

    We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an “experimental” implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented. PMID:24586891

  16. Solution of the problem of uniqueness and Hermiticity of Hamiltonians for Dirac particles in gravitational fields

    SciTech Connect

    Gorbatenko, M. V.; Neznamov, V. P.

    2010-11-15

    The authors prove that the dynamics of spin 1/2 particles in stationary gravitational fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three expressions for Hamiltonians, which are derived from the Dirac equation and describe the dynamics of spin 1/2 particles in the gravitational field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. The differences between the Hamiltonians confirm the conclusion known from many studies that the Hamiltonians derived from the Dirac equation are nonunique. Application of standard pseudo-Hermitian quantum mechanics rules to each of these Hamiltonians produces the same Hermitian Hamiltonian. The eigenvalue spectrum of the resulting Hamiltonian is the same as that of the Hamiltonians derived from the Dirac equation with any chosen system of tetrad vectors. For description of the dynamics of spin 1/2 particles in stationary gravitational fields can be used not only the formalism of pseudo-Hermitian Hamiltonians but also an alternative approach, which employs the Parker scalar product. The authors show that the alternative approach is equivalent to the formalism of pseudo-Hermitian Hamiltonians.

  17. Estimation of a general time-dependent Hamiltonian for a single qubit.

    PubMed

    de Clercq, L E; Oswald, R; Flühmann, C; Keitch, B; Kienzler, D; Lo, H-Y; Marinelli, M; Nadlinger, D; Negnevitsky, V; Home, J P

    2016-01-01

    The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control. PMID:27075230

  18. Estimation of a general time-dependent Hamiltonian for a single qubit

    NASA Astrophysics Data System (ADS)

    de Clercq, L. E.; Oswald, R.; Flühmann, C.; Keitch, B.; Kienzler, D.; Lo, H.-Y.; Marinelli, M.; Nadlinger, D.; Negnevitsky, V.; Home, J. P.

    2016-04-01

    The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.

  19. Estimation of a general time-dependent Hamiltonian for a single qubit

    PubMed Central

    de Clercq, L. E.; Oswald, R.; Flühmann, C.; Keitch, B.; Kienzler, D.; Lo, H. -Y.; Marinelli, M.; Nadlinger, D.; Negnevitsky, V.; Home, J. P.

    2016-01-01

    The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control. PMID:27075230

  20. Realistic multiband k .p approach from ab initio and spin-orbit coupling effects of InAs and InP in wurtzite phase

    NASA Astrophysics Data System (ADS)

    Faria Junior, Paulo E.; Campos, Tiago; Bastos, Carlos M. O.; Gmitra, Martin; Fabian, Jaroslav; Sipahi, Guilherme M.

    2016-06-01

    Semiconductor nanowires based on non-nitride III-V compounds can be synthesized under certain growth conditions to favor the appearance of the wurtzite crystal phase. Despite reports in the literature of ab initio band structures for these wurtzite compounds, we still lack effective multiband models and parameter sets that can be simply used to investigate physical properties of such systems, for instance, under quantum confinement effects. In order to address this deficiency, in this study we calculate the ab initio band structure of bulk InAs and InP in the wurtzite phase and develop an 8 ×8 k .p Hamiltonian to describe the energy bands around the Γ point. We show that our k .p model is robust and can be fitted to describe the important features of the ab initio band structure. The correct description of the spin-splitting effects that arise due to the lack of inversion symmetry in wurtzite crystals is obtained with the k -dependent spin-orbit term in the Hamiltonian, often neglected in the literature. All the energy bands display a Rashba-like spin texture for the in-plane spin expectation value. We also provide the density of states and the carrier density as functions of the Fermi energy. Alternatively, we show an analytical description of the conduction band, valid close to the Γ point. The same fitting procedure is applied to the 6 ×6 valence band Hamiltonian. However, we find that the most reliable approach is the 8 ×8 k .p Hamiltonian for both compounds. The k .p Hamiltonians and parameter sets that we develop in this paper provide a reliable theoretical framework that can be easily applied to investigate electronic, transport, optical, and spin properties of InAs- and InP-based nanostructures.

  1. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

    NASA Astrophysics Data System (ADS)

    Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.

    2016-07-01

    Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

  2. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

    PubMed

    Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R

    2016-07-01

    Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms. PMID:27394094

  3. NUCLEAR REACTORS

    DOEpatents

    Long, E.; Ashby, J.W.

    1958-09-16

    ABS>A graphite moderator structure is presented for a nuclear reactor compriscd of an assembly of similarly orientated prismatic graphite blocks arranged on spaced longitudinal axes lying in common planes wherein the planes of the walls of the blocks are positioned so as to be twisted reintive to the planes of said axes so thatthe unlmpeded dtrect paths in direction wholly across the walls of the blocks are limited to the width of the blocks plus spacing between the blocks.

  4. Dressed qubits in nuclear spin baths

    SciTech Connect

    Wu Lianao

    2010-04-15

    We present a method to encode a dressed qubit into the product state of an electron spin localized in a quantum dot and its surrounding nuclear spins via a dressing transformation. In this scheme, the hyperfine coupling and a portion of a nuclear dipole-dipole interaction become logic gates, while they are the sources of decoherence in electron-spin qubit proposals. We discuss errors and corrections for the dressed qubits. Interestingly, the effective Hamiltonian of nuclear spins is equivalent to a pairing Hamiltonian, which provides the microscopic mechanism to protect dressed qubits against decoherence.

  5. Stability and Clustering for Lattice Many-Body Quantum Hamiltonians with Multiparticle Potentials

    NASA Astrophysics Data System (ADS)

    Faria da Veiga, Paulo A.; O'Carroll, Michael

    2015-11-01

    We analyze a quantum system of N identical spinless particles of mass m, in the lattice Z^d, given by a Hamiltonian H_N=T_N+V_N, with kinetic energy T_N≥ 0 and potential V_N=V_{N,2}+V_{N,3} composed of attractive pair and repulsive 3-body contact-potentials. This Hamiltonian is motivated by the desire to understand the stability of quantum field theories, with massive single particles and bound states in the energy-momentum spectrum, in terms of an approximate Hamiltonian for their N-particle sector. We determine the role of the potentials V_{N,2} and V_{N,3} on the physical stability of the system, such as to avoid a collapse of the N particles. Mathematically speaking, stability is associated with an N-linear lower bound for the infimum of the H_N spectrum, \\underline{σ }(H_N)≥ -cN, for c>0 independent of N. For V_{N,3}=0, H_N is unstable, and the system collapses. If V_{N,3}not =0, H_N is stable and, for strong enough repulsion, we obtain \\underline{σ }(H_N)≥ -c' N, where c'N is the energy of ( N/2) isolated bound pairs. This result is physically expected. A much less trivial result is that, as N varies, we show [ \\underline{σ }(V_N)/N ] has qualitatively the same behavior as the well-known curve for minus the nuclear binding energy per nucleon. Moreover, it turns out that there exists a saturation value N_s of N at and above which the system presents a clustering: the N particles distributed in two fragments and, besides lattice translations of particle positions, there is an energy degeneracy of all two fragments with particle numbers N_r and N_s-N_r, with N_r=1,ldots ,N_s-1.

  6. Participation spectroscopy and entanglement Hamiltonian of quantum spin models

    NASA Astrophysics Data System (ADS)

    Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien

    2014-08-01

    Shannon-Rényi entropies and associated participation spectra quantify how much a many-body wave-function is localized in a given configuration basis. Using these tools, we present an analysis of the ground-state wave functions of various quantum spin systems in one and two dimensions. General ideas and a review of the current status of this field are first given, with a particular emphasis on universal subleading terms characterizing different quantum phases of matter, and associated transitions. We highlight the connection with the related entanglement entropies and spectra when this is possible. In a second part, new results are presented for the participation spectra of interacting spin models, mostly based on quantum Monte Carlo simulations, but also using perturbation theory in some cases. For full antiferromagnetic one-dimensional systems, participation spectra are analyzed in terms of ferromagnetic domain walls which experience a pairwise attractive interaction. This confinement potential is either linear for long-range Néel order, or logarithmic for quasi-long-range order. The case of subsystems is also analyzed in great detail for a 2d dimerized Heisenberg model undergoing a quantum phase transition between a gapped paramagnet and a Néel phase. Participation spectra of line shaped (1d) sub-systems are quantitatively compared with finite temperature participation spectra of ansatz effective boundary (1d) entanglement Hamiltonians. While short-range models describe almost perfectly the gapped side, the Néel regime is best compared using long-range effective Hamiltonians. Spectral comparisons performed using Kullback-Leibler divergences, a tool potentially useful for entanglement spectra, provide a quantitative way to identify both the best boundary entanglement Hamiltonian and effective temperature.

  7. Nonconventional fluctuation dissipation process in non-Hamiltonian dynamical systems

    NASA Astrophysics Data System (ADS)

    Bianucci, Marco

    2016-08-01

    Here, we introduce a statistical approach derived from dynamics, for the study of the geophysical fluid dynamics phenomena characterized by a weak interaction among the variables of interest and the rest of the system. The approach is reminiscent of the one developed some years ago [M. Bianucci, R. Mannella, P. Grigolini and B. J. West, Phys. Rev. E 51, 3002 (1995)] to derive statistical mechanics of macroscopic variables on interest starting from Hamiltonian microscopic dynamics. However, in the present work, we are interested to generalize this approach beyond the context of the foundation of thermodynamics, in fact, we take into account the cases where the system of interest could be non-Hamiltonian (dissipative) and also the interaction with the irrelevant part can be of a more general type than Hamiltonian. As such example, we will refer to a typical case from geophysical fluid dynamics: the complex ocean-atmosphere interaction that gives rise to the El Niño Southern Oscillation (ENSO). Here, changing all the scales, the role of the “microscopic” system is played by the atmosphere, while the ocean (or some ocean variables) plays the role of the intrinsically dissipative macroscopic system of interest. Thus, the chaotic and divergent features of the fast atmosphere dynamics remains in the decaying properties of the correlation functions and of the response function of the atmosphere variables, while the exponential separation of the perturbed (or close) single trajectories does not play a direct role. In the present paper, we face this problem in the frame of a not formal Langevin approach, limiting our discussion to physically based rather than mathematics arguments. Elsewhere, we obtain these results via a much more formal procedure, using the Zwanzing projection method and some elements from the Lie Algebra field.

  8. Degenerate approach to the mean field Bose-Hubbard Hamiltonian

    NASA Astrophysics Data System (ADS)

    Belemuk, Alexander M.; Ryzhov, Valentin N.

    2016-04-01

    A degenerate variant of mean field perturbation theory for the on-site Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms and perform exact diagonalization in the two-dimensional subspace corresponding to the degenerate states. The final relations for the second order ground state energy and first order wave function do not contain singularities at integer values of the chemical potentials. The resulting equation for the phase boundary between superfluid and Mott states coincides with the prediction from the conventional mean field perturbation approach.

  9. Hamiltonian treatment of the gravitational collapse of thin shells

    NASA Astrophysics Data System (ADS)

    Crisóstomo, Juan; Olea, Rodrigo

    2004-05-01

    A Hamiltonian treatment of the gravitational collapse of thin shells is presented. The direct integration of the canonical constraints reproduces the standard shell dynamics for a number of known cases. The formalism is applied in detail to three-dimensional spacetime and the properties of the (2+1)-dimensional charged black hole collapse are further elucidated. The procedure is also extended to deal with rotating solutions in three dimensions. The general form of the equations providing the shell dynamics implies the stability of black holes, as they cannot be converted into naked singularities by any shell collapse process.

  10. An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Chandre, C.; Jauslin, H. R.; Benfatto, G.

    1999-01-01

    We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori.

  11. Non-self-adjoint Hamiltonians with complex eigenvalues

    NASA Astrophysics Data System (ADS)

    Bagarello, F.

    2016-05-01

    Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In particular, we consider the functional structure related to systems living in finite-dimensional Hilbert spaces, and we show that certain intertwining relations can be deduced also in this case if we introduce suitable antilinear operators. We also analyze a simple model, computing the transition probabilities in the broken and in the unbroken regime.

  12. Trilinear hamiltonian with trapped ions and its applications

    NASA Astrophysics Data System (ADS)

    Ding, Shiqian; Maslennikov, Gleb; Hablutzel, Roland; Matsukevich, Dzmitry

    2016-05-01

    The model of three harmonic oscillators coupled by the trilinear Hamiltonian of the form a† bc + ab†c† can describe wide range of physical processes. We experimentally realize such interaction between three modes of motion in the system of 3 trapped Yb ions. We discuss several application of this coupling, including implementation of the quantum absorption refrigerator, simulation of the interaction between light and atoms described by a Tavis-Cummings model, simulation of the non-degenerate parametric down conversion process in the fully quantum regime and studies of a simple model of Hawking radiation.

  13. Calculation of Higher-Order Foldy-Wouthuysen Transformation Hamiltonian

    NASA Astrophysics Data System (ADS)

    Mei, Xue-Song; Zhao, Shu-Min; Qiao, Hao-Xue

    2014-06-01

    The Foldy—Wouthuysen Hamiltonian of a light atomic system that has an mα8 contribution to energy levels is calculated. The case of a Dirac—Coulomb field is discussed. The results can be used for relativistic and radiative corrections to energy levels in the low-energy part. A divergent operator δ2(r) emerges. This is probably due to the nature of the point-like charge source. The effective method of radiation calculation may be re-checked.

  14. Non-Hermitian quantum Hamiltonians with PT symmetry

    SciTech Connect

    Jones-Smith, Katherine; Mathur, Harsh

    2010-10-15

    We formulate quantum mechanics for non-Hermitian Hamiltonians that are invariant under PT, where P is the parity and T denotes time reversal, for the case that time-reversal symmetry is odd (T{sup 2}=-1), generalizing prior work for the even case (T{sup 2}=1). We discover an analog of Kramer's theorem for PT quantum mechanics, present a prototypical example of a PT quantum system with odd time reversal, and discuss potential applications of the formalism.

  15. The symmetry groups of bifurcations of integrable Hamiltonian systems

    SciTech Connect

    Orlova, E I

    2014-11-30

    Two-dimensional atoms are investigated; these are used to code bifurcations of the Liouville foliations of nondegenerate integrable Hamiltonian systems. To be precise, the symmetry groups of atoms with complexity at most 3 are under study. Atoms with symmetry group Z{sub p}⊕Z{sub q} are considered. It is proved that Z{sub p}⊕Z{sub q} is the symmetry group of a toric atom. The symmetry groups of all nonorientable atoms with complexity at most 3 are calculated. The concept of a geodesic atom is introduced. Bibliography: 9 titles.

  16. Modular Hamiltonian for Excited States in Conformal Field Theory.

    PubMed

    Lashkari, Nima

    2016-07-22

    We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories. PMID:27494465

  17. Modular Hamiltonian for Excited States in Conformal Field Theory

    NASA Astrophysics Data System (ADS)

    Lashkari, Nima

    2016-07-01

    We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Zn replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.

  18. Hamiltonian structure of scalar-tensor theories beyond Horndeski

    SciTech Connect

    Lin, Chunshan; Mukohyama, Shinji; Namba, Ryo; Saitou, Rio E-mail: shinji.mukohyama@yukawa.kyoto-u.ac.jp E-mail: rio.saitou@ipmu.jp

    2014-10-01

    We study the nature of constraints and the Hamiltonian structure in a scalar-tensor theory of gravity recently proposed by Gleyzes, Langlois, Piazza and Vernizzi (GLPV). For the simple case with A{sub 5}=0, namely when the canonical momenta conjugate to the spatial metric are linear in the extrinsic curvature, we prove that the number of physical degrees of freedom is three at fully nonlinear level, as claimed by GLPV. Therefore, while this theory extends Horndeski's scalar-tensor gravity theory, it is protected against additional degrees of freedom.

  19. Dynamics symmetries of Hamiltonian system on time scales

    SciTech Connect

    Peng, Keke Luo, Yiping

    2014-04-15

    In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.

  20. Renormalization Group Reduction of Non Integrable Hamiltonian Systems

    SciTech Connect

    Stephan I. Tzenov

    2002-05-09

    Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail.

  1. Particle on a Torus Knot: A Hamiltonian Analysis

    NASA Astrophysics Data System (ADS)

    Das, Praloy; Ghosh, Subir

    2016-08-01

    We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The equations of motion are obtained for a path in general where the knot is present in the particle orbit but it is not restricted to a particular torus. We also study the motion when it is restricted to a specific torus. The rotational symmetries are studied as well. We have also considered the behavior of small fluctuations of the particle motion about a fixed torus knot.

  2. Polynomial approximation of Poincare maps for Hamiltonian system

    NASA Technical Reports Server (NTRS)

    Froeschle, Claude; Petit, Jean-Marc

    1992-01-01

    Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

  3. Nonequilibrium work energy relation for non-Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    Mandal, Dibyendu; DeWeese, Michael R.

    2016-04-01

    Recent years have witnessed major advances in our understanding of nonequilibrium processes. The Jarzynski equality, for example, provides a link between equilibrium free energy differences and finite-time nonequilibrium dynamics. We propose a generalization of this relation to non-Hamiltonian dynamics, relevant for active matter systems, continuous feedback, and computer simulation. Surprisingly, this relation allows us to calculate the free energy difference between the desired initial and final equilibrium states using arbitrary dynamics. As a practical matter, this dissociation between the dynamics and the initial and final states promises to facilitate a range of techniques for free energy estimation in a single universal expression.

  4. Simulating Hamiltonian dynamics with a truncated Taylor series.

    PubMed

    Berry, Dominic W; Childs, Andrew M; Cleve, Richard; Kothari, Robin; Somma, Rolando D

    2015-03-01

    We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification. PMID:25793789

  5. Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices

    NASA Astrophysics Data System (ADS)

    Habib, K. M. Masum; Sajjad, Redwan N.; Ghosh, Avik W.

    2016-03-01

    Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.

  6. Full configuration-interaction calculations with the simplest iterative complement method: Merit of the inverse Hamiltonian

    SciTech Connect

    Nakatsuji, Hiroshi

    2011-12-15

    The simplest iterative complement (SIC) calculations starting from Hartree-Fock and giving full configuration interaction (CI) at convergence were performed using regular and inverse Hamiltonians. Each iteration step is variational and involves only one variable. The convergence was slow when we used the regular Hamiltonian, but became very fast when we used the inverse Hamiltonian. This difference is due to the Coulomb singularity problem inherent in the regular Hamiltonian; the inverse Hamiltonian does not have such a problem. For this reason, the merit of the inverse Hamiltonian over the regular one becomes even more dramatic when we use a better-quality basis set. This was seen by comparing the calculations due to the minimal and double-{zeta} basis sets. Similar problematic situations exist in the Krylov sequence and in the Lanczos and Arnoldi methods.

  7. Ab initio Monte Carlo investigation of small lithium clusters.

    SciTech Connect

    Srinivas, S.

    1999-06-16

    Structural and thermal properties of small lithium clusters are studied using ab initio-based Monte Carlo simulations. The ab initio scheme uses a Hartree-Fock/density functional treatment of the electronic structure combined with a jump-walking Monte Carlo sampling of nuclear configurations. Structural forms of Li{sub 8} and Li{sub 9}{sup +} clusters are obtained and their thermal properties analyzed in terms of probability distributions of the cluster potential energy, average potential energy and configurational heat capacity all considered as a function of the cluster temperature. Details of the gradual evolution with temperature of the structural forms sampled are examined. Temperatures characterizing the onset of structural changes and isomer coexistence are identified for both clusters.

  8. The gravitational Hamiltonian in the presence of non-orthogonal boundaries

    NASA Astrophysics Data System (ADS)

    Hawking, S. W.; Hunter, C. J.

    1996-10-01

    This paper generalizes earlier work on Hamiltonian boundary terms by omitting the requirement that the spacelike hypersurfaces 0264-9381/13/10/012/img1 intersect the timelike boundary 0264-9381/13/10/012/img2 orthogonally. The expressions for the action and Hamiltonian are calculated and the required subtraction of a background contribution is discussed. The new features of a Hamiltonian formulation with non-orthogonal boundaries are then illustrated in two examples.

  9. Hamiltonian fluid reductions of drift-kinetic equations and the link with water-bags

    NASA Astrophysics Data System (ADS)

    Perin, M.; Chandre, C.; Tassi, E.

    2016-07-01

    Hamiltonian models for the first three moments of the drift-kinetic distribution function, namely the density, the fluid velocity and the parallel pressure, are derived from the Hamiltonian structure of the drift-kinetic equations. The link with the water-bag closure is established, showing that, unlike the one-dimensional Vlasov equations, these solutions are the only Hamiltonian fluid reductions for the drift-kinetic equation. These models are discussed through their equations of motion and their Casimir invariants.

  10. The Hamiltonian Laceability of some Generalized Honeycomb Tori

    SciTech Connect

    Hsu Liyen; Lin Tungyi; Kao Shinshin

    2008-11-06

    Assume that m, n and s are integers with m{>=}2, n{>=}4, 0{<=}s{<=}n and s is of the same parity of m. The generalized honeycomb torus GHT (m,n,s) is recognized as another attractive alternative to existing torus interconnection networks in parallel and distributed applications. It is known that any GHT (m,n,s) is 3-regular, hamiltonian, bipartite graph. We are interested in two special types of the generalized honeycomb torus, GHT (m,n,(n/2)) and GHT (m,n,0). Let G = GHT(m,n,s), where s(set-membership sign){l_brace}(n/2),0{r_brace}. We prove that any G is hamiltonian laceable. More precisely, given a pair of vertices P = {l_brace}u,v|u(set-membership sign)B,v(set-membership sign)W{r_brace} where B and W are the bipartition of V(G), there exists a path Q between u and v such that Q contains all vertices of G.

  11. Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes

    NASA Astrophysics Data System (ADS)

    Ivancevic, Vladimir G.; Reid, Darryn J.

    2015-11-01

    In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).

  12. Lars Onsager Prize Talk: Flow Equations for Hamiltonians

    NASA Astrophysics Data System (ADS)

    Wegner, Franz

    2015-03-01

    The equation dH (l) = GH (l) can describe the renormalization group equation for the Hamiltonian/Lagrangian H (l) and the generator G of the group. But it can also describe a Hamiltonian flow for bosons/fermions, which eliminates the off-diagonal matrix elements or (quasi)-particle violating terms by means of unitary transformations dH (l) / dl = [ η (l) , H (l) ] . Typically off-diagonal matrix elements are eliminated for ΔE >l - 1 / 2 . The flow equation has been applied to numerous systems (F. Wegner, J. Phys. A: Math. Gen. 39 (2006) 8221, arXiv: cond-mat/0511660; S. Kehrein, The Flow Equation Approach to Many-Particle Systems, Springer 2006), among them to the two-dimensional Hubbard-model, spin-boson models, the Anderson impurity model, QED and QCD. A simple and surprising result (as compared to that by Frohlich) is obtained for the elimination of the electron-phonon interaction yielding an attractive interaction for all energies. (P. Lenz and F. Wegner, Nucl. Phys. B482 (1996) 693; arXiv: cond-mat/9604087).

  13. The t expansion: A nonperturbative analytic tool for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Horn, D.; Weinstein, M.

    1984-09-01

    A systematic nonperturbative scheme is developed to calculate the ground-state expectation values of arbitrary operators for any Hamiltonian system. Quantities computed in this way converge rapidly to their true expectation values. The method is based upon the use of the operator e-tH to contract any trial state onto the true ground state of the Hamiltonian H. We express all expectation values in the contracted state as a power series in t, and reconstruct t-->∞ behavior by means of Padé approximants. The problem associated with factors of spatial volume is taken care of by developing a connected graph expansion for matrix elements of arbitrary operators taken between arbitrary states. We investigate Padé methods for the t series and discuss the merits of various procedures. As examples of the power of this technique we present results obtained for the Heisenberg and Ising models in 1+1 dimensions starting from simple mean-field wave functions. The improvement upon mean-field results is remarkable for the amount of effort required. The connection between our method and conventional perturbation theory is established, and a generalization of the technique which allows us to exploit off-diagonal matrix elements is introduced. The bistate procedure is used to develop a t expansion for the ground-state energy of the Ising model which is, term by term, self-dual.

  14. Inverse problem of quadratic time-dependent Hamiltonians

    NASA Astrophysics Data System (ADS)

    Guo, Guang-Jie; Meng, Yan; Chang, Hong; Duan, Hui-Zeng; Di, Bing

    2015-08-01

    Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly. Project supported by the National Natural Science Foundation of China (Grant No. 11347171), the Natural Science Foundation of Hebei Province of China (Grant No. A2012108003), and the Key Project of Educational Commission of Hebei Province of China (Grant No. ZD2014052).

  15. Hamiltonian approach to the lattice massive Schwinger model

    SciTech Connect

    Sidorov, A.V.; Zastavenko, L.G.

    1996-08-01

    The authors consider the limit e{sup 2}/m{sup 2} {much_lt} 1 of the lattice massive Schwinger model, i.e., the lattice massive QED in two space-time dimensions, up to lowest order in the effective coupling constant e{sup 2}/m{sup 2}. Here, m is the fermion mass parameter and e is the electron charge. They compare their lattice QED model with the analogous continuous space and lattice space models, (CSM and LSM), which do not take account of the zero momentum mode, z.m.m., of the vector potential. The difference is that (due to extra z.m.m. degree of freedom) to every eigenstate of the CSM and LSM there corresponds a family of eigenstates of the authors lattice QED with the parameter {lambda}. They restrict their consideration to small values of the parameter {lambda}. Then, the energies of the particle states of their lattice QED and LSM do coincide (in their approximation). In the infinite periodicity length limit the Hamiltonian of the authors lattice QED (as well as the Hamiltonian of the LSM) possesses two different Hilbert spaces of eigenfunctions. Thus, in this limit the authors lattice QED model (as well as LSM) describes something like two connected, but different, worlds.

  16. Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

    SciTech Connect

    Al-Hashimi, M.H.; Salman, M.; Shalaby, A.; Wiese, U.-J.

    2013-10-15

    We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.

  17. Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches.

    PubMed

    Mills, Jeffrey D; Ben-Nun, Michal; Rollin, Kyle; Bromley, Michael W J; Li, Jiabo; Hinde, Robert J; Winstead, Carl L; Sheehy, Jeffrey A; Boatz, Jerry A; Langhoff, Peter W

    2016-08-25

    Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and

  18. AB INITIO AND CALPHAD THERMODYNAMICS OF MATERIALS

    SciTech Connect

    Turchi, P A

    2004-04-14

    Ab initio electronic structure methods can supplement CALPHAD in two major ways for subsequent applications to stability in complex alloys. The first one is rather immediate and concerns the direct input of ab initio energetics in CALPHAD databases. The other way, more involved, is the assessment of ab initio thermodynamics {acute a} la CALPHAD. It will be shown how these results can be used within CALPHAD to predict the equilibrium properties of multi-component alloys.

  19. AB173. TR4 nuclear receptor increases prostate cancer invasion via decreasing the miR-373-3p expression to alter TGFβR2/p-Smad3 signals

    PubMed Central

    Yang, Guosheng; Qiu, Xiaofo

    2016-01-01

    Objective Testicular nuclear receptor 4 (TR4) is a member of the nuclear receptor superfamily, which may play key roles to influence the metabolic diseases and prostate tumorigenesis. The purpose of our study is to elucidate the mechanisms how TR4 influences the prostate cancer (PCa) metastasis. Methods We constructed three different PCa cell lines including C4-2, PC3 and CWR22Rv1 with differential stable expression of TR4. RT-PCR and Western blot analysis were used to validate identified downstream genes. To explore the function of genes, we manipulated cells 2D and 3D invasion assays and mice experiment. Results we found TR4 could promote PCa cell invasion using two different cell invasion assays. Mechanism dissection revealed that TR4 might enhance PCa cell invasion via modulation of the microRNA-373-3p (miR-373-3p) expression. An interruption approach using miR-373-3p partially reversed TR4-enhanced PCa cell invasion. Furthermore, we found TR4-miR-373-3p might function through modulation of the TGFβR2/p-Smad3 signals to enhance the PCa cell invasion. The in vivo mouse model using orthotopic xenografted CWR22Rv1 cell line transfected with luciferase-reporter also confirmed in vitro cell line studies showing TR4 enhanced PCa metastasis via modulation of miR-373-3p. Conclusions Our data suggest that TR4 may represent a key player to influence the PCa metastasis and targeting TR4 miR-373-3p→ TGFβR2/p-Smad3 axis using TR4 antagonist or TR4-siRNA or miR-373-3p may become a new potential therapeutic approach to better suppress PCa metastasis.

  20. Charged shells in Lovelock gravity: Hamiltonian treatment and physical implications

    SciTech Connect

    Dias, Goncalo A. S.; Gao, Sijie; Lemos, Jose P. S.

    2007-01-15

    Using a Hamiltonian treatment, charged thin shells, static and dynamic, in spherically symmetric spacetimes, containing black holes or other specific types of solutions, in d dimensional Lovelock-Maxwell theory are studied. The free coefficients that appear in the Lovelock theory are chosen to obtain a sensible theory, with a negative cosmological constant appearing naturally. Using an Arnowitt-Deser-Misner (ADM) description, one then finds the Hamiltonian for the charged shell system. Variation of the Hamiltonian with respect to the canonical coordinates and conjugate momenta, and the relevant Lagrange multipliers, yields the dynamic and constraint equations. The vacuum solutions of these equations yield a division of the theory into two branches, namely d-2k-1>0 (which includes general relativity, Born-Infeld type theories, and other generic gravities) and d-2k-1=0 (which includes Chern-Simons type theories), where k is the parameter giving the highest power of the curvature in the Lagrangian. There appears an additional parameter {chi}=(-1){sup k+1}, which gives the character of the vacuum solutions. For {chi}=1 the solutions, being of the type found in general relativity, have a black hole character. For {chi}=-1 the solutions, being of a new type not found in general relativity, have a totally naked singularity character. Since there is a negative cosmological constant, the spacetimes are asymptotically anti-de Sitter (AdS), and AdS when empty (for zero cosmological constant the spacetimes are asymptotically flat). The integration from the interior to the exterior vacuum regions through the thin shell takes care of a smooth junction, showing the power of the method. The subsequent analysis is divided into two cases: static charged thin shell configurations, and gravitationally collapsing charged dust shells (expanding shells are the time reversal of the collapsing shells). In the collapsing case, into an initially nonsingular spacetime with generic character

  1. Nekhoroshev stability in quasi-integrable degenerate Hamiltonian systems.

    NASA Astrophysics Data System (ADS)

    Guzzo, M.

    A perturbation of a degenerate integrable Hamiltonian system has the form H(I,φ ,p,q)=h(I)+ɛ f(I,φ ,p,q) with (I,φ )in Rn x Tn, (p,q) in B subseteq R2m and the two-form is dI wedge dφ + dp wedge dq. In the case h is convex, Nekhoroshev theorem provides the usual bound to the motion of the actions I, but only for a time which is the smaller between the usual exponentially-long time and the escape time of (p,q) from B. Furthermore, the theorem does not provide any estimate for the `degenerate' variables (p,q) better than the a priori one dot p,dot q ~ ɛ, and actually in the literature there are examples of degenerate systems with degenerate variables that perform large chaotic motions in short times. Therefore, there is the problem of individuating which assumptions on the perturbation and on the initial data allows one to produce stability bounds for the degenerate variables over long times, thus preventing chaotic motions and escape. The problem is relevant to understand the long time stability of several systems, like the three body problem, the asteroid belt dynamical system and the fast rotations of the rigid body. In this work we show that if the `secular' hamiltonian of H, i.e the average of H with respect to the fast angles φ, is integrable (or quasi-integrable) and if it satisfies a suitable convexity condition, then a Nekhoroshev-like bound also holds for the degenerate variables (p,q) (actually for the actions of the secular integrable system) for all initial data except those with initial action I(0) in a small neighborhood of the resonant manifolds of order lower than ln 1 ɛ. It is worthwhile to note that even if the secular hamiltonian of H is integrable, strong chaotic motions can take place in short times near such low order resonant manifolds, as it can be shown on examples. This result was proved for the first time in connection with the problem of the long-time stability in the asteroid belt.

  2. Ultrasound Biomicroscopy Comparison of Ab Interno and Ab Externo Intraocular Lens Scleral Fixation.

    PubMed

    Horiguchi, Lie; Garcia, Patricia Novita; Malavazzi, Gustavo Ricci; Allemann, Norma; Gomes, Rachel L R

    2016-01-01

    Purpose. To compare ab interno and ab externo scleral fixation of posterior chamber intraocular lenses (PCIOL) using ultrasound biomicroscopy (UBM). Methods. Randomized patients underwent ab externo or ab interno scleral fixation of a PCIOL. Ultrasound biomicroscopy was performed 3 to 6 months postoperatively, to determine PCIOL centration, IOL distance to the iris at 12, 3, 6, and 9 hours, and haptics placement in relation to the ciliary sulcus. Results. Fifteen patients were enrolled in the study. The ab externo technique was used in 7 eyes (46.6%) and the ab interno in 8 eyes (53.3%). In the ab externo technique, 14 haptics were located: 4 (28.57%) in the ciliary sulcus; 2 (14.28%) anterior to the sulcus; and 8 (57.14%) posterior to the sulcus, 6 in the ciliary body and 2 posterior to the ciliary body. In the ab interno group, 4 haptics (25.0%) were in the ciliary sulcus, 2 (12.50%) anterior to the sulcus, and 10 (75.0%) posterior to the sulcus, 4 in the ciliary body and 6 posterior to the ciliary body. Conclusions. Ab externo and ab interno scleral fixation techniques presented similar results in haptic placement. Ab externo technique presented higher vertical tilt when compared to the ab interno. PMID:27293878

  3. Ultrasound Biomicroscopy Comparison of Ab Interno and Ab Externo Intraocular Lens Scleral Fixation

    PubMed Central

    Horiguchi, Lie; Garcia, Patricia Novita; Malavazzi, Gustavo Ricci; Allemann, Norma

    2016-01-01

    Purpose. To compare ab interno and ab externo scleral fixation of posterior chamber intraocular lenses (PCIOL) using ultrasound biomicroscopy (UBM). Methods. Randomized patients underwent ab externo or ab interno scleral fixation of a PCIOL. Ultrasound biomicroscopy was performed 3 to 6 months postoperatively, to determine PCIOL centration, IOL distance to the iris at 12, 3, 6, and 9 hours, and haptics placement in relation to the ciliary sulcus. Results. Fifteen patients were enrolled in the study. The ab externo technique was used in 7 eyes (46.6%) and the ab interno in 8 eyes (53.3%). In the ab externo technique, 14 haptics were located: 4 (28.57%) in the ciliary sulcus; 2 (14.28%) anterior to the sulcus; and 8 (57.14%) posterior to the sulcus, 6 in the ciliary body and 2 posterior to the ciliary body. In the ab interno group, 4 haptics (25.0%) were in the ciliary sulcus, 2 (12.50%) anterior to the sulcus, and 10 (75.0%) posterior to the sulcus, 4 in the ciliary body and 6 posterior to the ciliary body. Conclusions. Ab externo and ab interno scleral fixation techniques presented similar results in haptic placement. Ab externo technique presented higher vertical tilt when compared to the ab interno. PMID:27293878

  4. Structural evolution in Pt isotopes with the interacting boson model Hamiltonian derived from the Gogny energy density functional

    SciTech Connect

    Nomura, K.; Otsuka, T.; Rodriguez-Guzman, R.; Sarriguren, P.; Robledo, L. M.

    2011-01-15

    Spectroscopic calculations are carried out for the description of the shape/phase transition in Pt nuclei in terms of the interacting boson model (IBM) Hamiltonian derived from (constrained) Hartree-Fock-Bogoliubov (HFB) calculations with the finite range and density-dependent Gogny-D1S energy density functional. Assuming that the many-nucleon driven dynamics of nuclear surface deformation can be simulated by effective bosonic degrees of freedom, the Gogny-D1S potential energy surface (PES) with quadrupole degrees of freedom is mapped onto the corresponding PES of the IBM. By using this mapping procedure, the parameters of the IBM Hamiltonian, relevant to the low-lying quadrupole collective states, are derived as functions of the number of valence nucleons. Merits of both Gogny-HFB and IBM approaches are utilized so that the spectra and the wave functions in the laboratory system are calculated precisely. The experimental low-lying spectra of both ground-state and sideband levels are well reproduced. From the systematics of the calculated spectra and the reduced E2 transition probabilities B(E2), the prolate-to-oblate shape/phase transition is shown to take place quite smoothly as a function of neutron number N in the considered Pt isotopic chain, for which the {gamma} softness plays an essential role. All of these spectroscopic observables behave consistently with the relevant PES and the derived parameters of the IBM Hamiltonian as functions of N. Spectroscopic predictions are also made for those nuclei that do not have enough experimental E2 data.

  5. Nonholonomic Hamiltonian Method for Molecular Dynamics Simulations of Reacting Shocks

    NASA Astrophysics Data System (ADS)

    Fahrenthold, Eric; Bass, Joseph

    2015-06-01

    Conventional molecular dynamics simulations of reacting shocks employ a holonomic Hamiltonian formulation: the breaking and forming of covalent bonds is described by potential functions. In general these potential functions: (a) are algebraically complex, (b) must satisfy strict smoothness requirements, and (c) contain many fitted parameters. In recent research the authors have developed a new noholonomic formulation of reacting molecular dynamics. In this formulation bond orders are determined by rate equations and the bonding-debonding process need not be described by differentiable functions. This simplifies the representation of complex chemistry and reduces the number of fitted model parameters. Example applications of the method show molecular level shock to detonation simulations in nitromethane and RDX. Research supported by the Defense Threat Reduction Agency.

  6. Emission spectra of LH2 complex: full Hamiltonian model

    NASA Astrophysics Data System (ADS)

    Heřman, Pavel; Zapletal, David; Horák, Milan

    2013-05-01

    In the present contribution we study the absorption and steady-state fluorescence spectra for ring molecular system, which can model B850 ring of peripheral light-harvesting complex LH2 from purple bacterium Rhodopseudomonas acidophila (Rhodoblastus acidophilus). LH2 is a highly symmetric ring of nine pigment-protein subunits, each containing two transmembrane polypeptide helixes and three bacteriochlorophylls (BChl). The uncorrelated diagonal static disorder with Gaussian distribution (fluctuations of local excitation energies) simultaneously with the diagonal dynamic disorder (interaction with a bath) in Markovian approximation is used in our simulations. We compare calculated absorption and steady state fluorescence spectra obtained within the full Hamiltonian model of the B850 ring with our previous results calculated within the nearest neighbour approximation model and also with experimental data.

  7. Complete Hamiltonian analysis of cosmological perturbations at all orders

    NASA Astrophysics Data System (ADS)

    Nandi, Debottam; Shankaranarayanan, S.

    2016-06-01

    In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the `gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field in the Lagrangian. We compare and contrast our approach to the Lagrangian approach (Chen et al. [2006]) for extracting higher order correlations and show that our approach is efficient and robust and can be applied to any model of gravity and matter fields without invoking slow-roll approximation.

  8. Bifurcation Sequences in the Symmetric 1:1 Hamiltonian Resonance

    NASA Astrophysics Data System (ADS)

    Marchesiello, Antonella; Pucacco, Giuseppe

    We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under ℤ2 × ℤ2 symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase-space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action-angle variables. Several examples, mainly taken from astrodynamics, are used as applications.

  9. Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Lingam, Manasvi; Miloshevich, George; Morrison, Philip J.

    2016-07-01

    The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia). The generalized helicities, and other geometric expressions for these models are presented in a topological context, emphasizing their universal facets. Some of the results presented include: the generalized Kelvin circulation theorems; the existence of two Lie-dragged 2-forms; and two concomitant helicities that can be studied via the Jones polynomial, which is widely utilized in Chern-Simons theory. The ensuing commonality is traced to the existence of an underlying Hamiltonian structure for all the extended MHD models, exemplified by the presence of a unique noncanonical Poisson bracket, and its associated energy.

  10. Hamiltonian formulation of the Belinskii-Khalatnikov-Lifshitz conjecture

    SciTech Connect

    Ashtekar, Abhay; Henderson, Adam; Sloan, David

    2011-04-15

    The Belinskii, Khalatnikov, and Lifshitz conjecture [V. A. Belinskii, I. M. Khalatnikov, and E. M. Lifshitz, Adv. Phys. 19, 525 (1970)] posits that on approach to a spacelike singularity in general relativity the dynamics are well approximated by ''ignoring spatial derivatives in favor of time derivatives.'' In A. Ashtekar, A. Henderson, and D. Sloan, Classical Quantum Gravity 26, 052 001 (2009), we examined this idea from within a Hamiltonian framework and provided a new formulation of the conjecture in terms of variables well suited to loop quantum gravity. We now present the details of the analytical part of that investigation. While our motivation came from quantum considerations, thanks to some of its new features, our formulation should be useful also for future analytical and numerical investigations within general relativity.

  11. Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems

    SciTech Connect

    Doroshin, Anton V.

    2010-03-01

    This paper sets out to develop a spider-type multiple-rotor system which can be used for attitude control of spacecraft. The multirotor system contains a large number of rotor-equipped rays, so it was called a 'Spider-type System', also it can be called 'Rotary Hedgehog'. These systems allow using spinups and captures of conjugate rotors to perform compound attitude motion of spacecraft. The paper describes a new method of spacecraft attitude reorientation and new mathematical model of motion in Hamilton form. Hamiltonian dynamics of the system is investigated with the help of Andoyer-Deprit canonical variables. These variables allow obtaining exact solution for hetero- and homoclinic orbits in phase space of the system motion, which are very important for qualitative analysis.

  12. A weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1989-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  13. Gravitational Modification of the Coulomb-Breit Hamiltonian

    SciTech Connect

    Caicedo, Jose Alexander; Urrutia, Luis Fernando

    2009-04-20

    In the poster session we presented a short review of our first results in the construction of the Coulomb-Breit Hamiltonian for a pair of fermions immersed in a background gravitational field which is described by General Relativity. Here we present a resume of that construction. We make a special stress on the objectives and the hypothesis used, but there is no special attention on the explicit form of the results because actually there is an updated and optimised version of our work in the edition process for publication; however we mention some special characteristics of the effect of the background gravitational field on the quantum nature of the system composed by fermions and its electromagnetic field, particularly the possibility of the observation of centre of mass effects in matter interferometry experiments.

  14. Quantum Hamiltonian theory of an electro-optical modulator

    NASA Astrophysics Data System (ADS)

    Miroshnichenko, G. P.; Gleim, A. V.

    2015-07-01

    A Quantum Hamiltonian formalism is proposed for the description of an electro-optical modulator based on the linear Pockels effect. Optical photons interact with photons of a microwave mode in a combined high- Q cavity made of a LiNbO3 crystal. The microwave photons occupy a coherent state, while optical photons have an arbitrary density matrix. The spectrum of a photodetected modulated signal is analyzed as a function of the frequency of a tunable optical filter. Numerical estimates are obtained, and quantum effects in the spectrum, such as the red shift of the central frequency and sidebands, the possibility of modulation of the optical signal by the microwave field vacuum, and the asymmetry of the intensity of the spectral sidebands, are discussed.

  15. Analytical solutions of the Bohr Hamiltonian with the Morse potential

    SciTech Connect

    Boztosun, I.; Inci, I.; Bonatsos, D.

    2008-04-15

    Analytical solutions of the Bohr Hamiltonian are obtained in the {gamma}-unstable case, as well as in an exactly separable rotational case with {gamma}{approx_equal}0, called the exactly separable Morse (ES-M) solution. Closed expressions for the energy eigenvalues are obtained through the asymptotic iteration method (AIM), the effectiveness of which is demonstrated by solving the relevant Bohr equations for the Davidson and Kratzer potentials. All medium mass and heavy nuclei with known {beta}{sub 1} and {gamma}{sub 1} bandheads have been fitted by using the two-parameter {gamma}-unstable solution for transitional nuclei and the three-parameter ES-M for rotational ones. It is shown that bandheads and energy spacings within the bands are well reproduced for more than 50 nuclei in each case.

  16. A solvable Hamiltonian system: Integrability and action-angle variables

    SciTech Connect

    Karimipour, V.

    1997-03-01

    We prove that the dynamical system characterized by the Hamiltonian H={lambda}N{summation}{sub j}{sup N}p{sub j}+{mu}{summation} {sub j,k}{sup N}(p{sub j}p{sub k}){sup 1/2}{l_brace}cos[{nu}(q{sub j}{minus}q{sub k})]{r_brace} proposed and studied by Calogero [J. Math. Phys. {bold 36}, 9 (1994)] and Calogero and van Diejen [Phys. Lett. A {bold 205}, 143 (1995)] is equivalent to a system of {ital noninteracting} harmonic oscillators both classically and quantum mechanically. We find the explicit form of the conserved currents that are in involution. We also find the action-angle variables and solve the initial value problem in a very simple form.{copyright} {ital 1997 American Institute of Physics.}

  17. Cluster Monte Carlo methods for the FePt Hamiltonian

    NASA Astrophysics Data System (ADS)

    Lyberatos, A.; Parker, G. J.

    2016-02-01

    Cluster Monte Carlo methods for the classical spin Hamiltonian of FePt with long range exchange interactions are presented. We use a combination of the Swendsen-Wang (or Wolff) and Metropolis algorithms that satisfies the detailed balance condition and ergodicity. The algorithms are tested by calculating the temperature dependence of the magnetization, susceptibility and heat capacity of L10-FePt nanoparticles in a range including the critical region. The cluster models yield numerical results in good agreement within statistical error with the standard single-spin flipping Monte Carlo method. The variation of the spin autocorrelation time with grain size is used to deduce the dynamic exponent of the algorithms. Our cluster models do not provide a more accurate estimate of the magnetic properties at equilibrium.

  18. Investigation of Commuting Hamiltonian in Quantum Markov Network

    NASA Astrophysics Data System (ADS)

    Jouneghani, Farzad Ghafari; Babazadeh, Mohammad; Bayramzadeh, Rogayeh; Movla, Hossein

    2014-08-01

    Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions, so there are some powerful methods including mean field approximation, belief propagation algorithm and etc. Quantum graphical models have been recently developed in context of quantum information and computation, and quantum statistical physics, which is possible by generalization of classical probability theory to quantum theory. The main goal of this paper is preparing a primary generalization of Markov network, as a type of graphical models, to quantum case and applying in quantum statistical physics. We have investigated the Markov network and the role of commuting Hamiltonian terms in conditional independence with simple examples of quantum statistical physics.

  19. Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices

    NASA Astrophysics Data System (ADS)

    Romero-Bastida, M.; Pazó, Diego; López, Juan M.; Rodríguez, Miguel A.

    2010-09-01

    In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and Φ4 models. In this case, characteristic (also called covariant) LVs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal. In contrast, backward LVs (obtained via Gram-Schmidt orthonormalizations) present approximately the same scaling exponent in all cases, suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors. We are able to compute characteristic LVs in large systems thanks to a “bit reversible” algorithm, which completely obviates computer memory limitations.

  20. Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics

    SciTech Connect

    Morrison, P. J. Lingam, M.; Acevedo, R.

    2014-08-15

    A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to construct variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.

  1. Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

    NASA Astrophysics Data System (ADS)

    Ndayiragije, F.; Van Assche, W.

    2013-12-01

    Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to r > 1 different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Following a recent construction of Miki, Tsujimoto, Vinet and Zhedanov (for multiple Meixner polynomials of the first kind), we construct r > 1 non-Hermitian oscillator Hamiltonians in r dimensions which are simultaneously diagonalizable and for which the common eigenstates are expressed in terms of multiple Meixner polynomials of the second kind.

  2. Causality and relativistic localization in one-dimensional Hamiltonians

    SciTech Connect

    Wagner, R. E.; Shields, B. T.; Ware, M. R.; Su, Q.; Grobe, R.

    2011-06-15

    We compare the relativistic time evolution of an initially localized quantum particle obtained from the relativistic Schroedinger, the Klein-Gordon and the Dirac equations. By computing the amount of the spatial probability density that evolves outside the light cone we quantify the amount of causality violation for the relativistic Schroedinger Hamiltonian. We comment on the relationship between quantum field theoretical transition amplitudes, commutators of the fields and their bilinear combinations outside the light cone as indicators of a possible causality violation. We point out the relevance of the relativistic localization problem to this discussion and comment on ideas about the supposed role of quantum field theory as a vehicle of making a theory causal by introducing antiparticles.

  3. Engineering photonic Floquet Hamiltonians through Fabry-Pérot resonators

    NASA Astrophysics Data System (ADS)

    Sommer, Ariel; Simon, Jonathan

    2016-03-01

    In this paper we analyze an optical Fabry-Pérot resonator as a time-periodic driving of the (2D) optical field repeatedly traversing the resonator, uncovering that resonator twist produces a synthetic magnetic field applied to the light within the resonator, while mirror aberrations produce relativistic dynamics, anharmonic trapping and spacetime curvature. We develop a Floquet formalism to compute the effective Hamiltonian for the 2D field, generalizing the idea that the intra-cavity optical field corresponds to an ensemble of non-interacting, massive, harmonically trapped particles. This work illuminates the extraordinary potential of optical resonators for exploring the physics of quantum fluids in gauge fields and exotic space-times.

  4. A weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1990-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  5. Weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1991-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  6. Hamiltonian model of capture into mean motion resonance

    NASA Astrophysics Data System (ADS)

    Mustill, Alexander J.; Wyatt, Mark C.

    2011-11-01

    Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first and second order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. The model is applicable to many scenarios, including (i) Planet migration through gas discs trapping other planets or planetesimals in resonances; (ii) Planet migration through a debris disc; (iii) Dust migration through PR drag. The Hamiltonian model will allow quick interpretation of the resonant properties of extrasolar planets and Kuiper Belt Objects, and will allow synthetic images of debris disc structures to be quickly generated, which will be useful for predicting and interpreting disc images made with ALMA, Darwin/TPF or similar missions. Full details can be found in Mustill & Wyatt (2011).

  7. Combined first-principles and model Hamiltonian study of the perovskite series R MnO 3 (R =La ,Pr ,Nd ,Sm ,Eu , and Gd )

    NASA Astrophysics Data System (ADS)

    Kováčik, Roman; Murthy, Sowmya Sathyanarayana; Quiroga, Carmen E.; Ederer, Claude; Franchini, Cesare

    2016-02-01

    We merge advanced ab initio schemes (standard density functional theory, hybrid functionals, and the G W approximation) with model Hamiltonian approaches (tight-binding and Heisenberg Hamiltonian) to study the evolution of the electronic, magnetic, and dielectric properties of the manganite family R MnO3 (R =La,Pr,Nd,Sm,Eu, and Gd) . The link between first principles and tight binding is established by downfolding the physically relevant subset of 3 d bands with eg character by means of maximally localized Wannier functions (MLWFs) using the VASP2WANNIER90 interface. The MLWFs are then used to construct a general tight-binding Hamiltonian written as a sum of the kinetic term, the Hund's rule coupling, the JT coupling, and the electron-electron interaction. The dispersion of the tight-binding (TB) eg bands at all levels are found to match closely the MLWFs. We provide a complete set of TB parameters which can serve as guidance for the interpretation of future studies based on many-body Hamiltonian approaches. In particular, we find that the Hund's rule coupling strength, the Jahn-Teller coupling strength, and the Hubbard interaction parameter U remain nearly constant for all the members of the R MnO3 series, whereas the nearest-neighbor hopping amplitudes show a monotonic attenuation as expected from the trend of the tolerance factor. Magnetic exchange interactions, computed by mapping a large set of hybrid functional total energies onto an Heisenberg Hamiltonian, clarify the origin of the A-type magnetic ordering observed in the early rare-earth manganite series as arising from a net negative out-of-plane interaction energy. The obtained exchange parameters are used to estimate the Néel temperature by means of Monte Carlo simulations. The resulting data capture well the monotonic decrease of the ordering temperature down the series from R =La to Gd, in agreement with experiments. This trend correlates well with the modulation of structural properties, in

  8. Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems

    SciTech Connect

    Abedi-Fardad, J.; Rezaei-Aghdam, A.; Haghighatdoost, Gh.

    2014-05-15

    We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R{sup 4} and R{sup 6}. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.

  9. Generalized van der Waals Hamiltonian: periodic orbits and C1 nonintegrability.

    PubMed

    Guirao, Juan L G; Llibre, Jaume; Vera, Juan A

    2012-03-01

    The aim of this paper is to study the periodic orbits of the generalized van der Waals Hamiltonian system. The tool for studying such periodic orbits is the averaging theory. Moreover, for this Hamiltonian system we provide information on its C(1) nonintegrability, i.e., on the existence of a second first integral of class C(1). PMID:22587198

  10. Characterizing the parent Hamiltonians for a complete set of orthogonal wave functions: An inverse quantum problem

    NASA Astrophysics Data System (ADS)

    Ramezanpour, A.

    2016-06-01

    We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and our goal is to characterize the relevant wave functions and energies (the spectrum) of the system. Here, we take the opposite approach; starting from a reasonable collection of orthogonal wave functions, we try to characterize the associated parent Hamiltonians, to see how the wave functions and the energy values affect the structure of the parent Hamiltonian. Specifically, we obtain (quasi) local Hamiltonians by a complete set of (multilayer) product states and a local mapping of the energy values to the wave functions. On the other hand, a complete set of tree wave functions (having a tree structure) results to nonlocal Hamiltonians and operators which flip simultaneously all the spins in a single branch of the tree graph. We observe that even for a given set of basis states, the energy spectrum can significantly change the nature of interactions in the Hamiltonian. These effects can be exploited in a quantum engineering problem optimizing an objective functional of the Hamiltonian.

  11. Four-band Hamiltonian for fast calculations in intermediate-band solar cells

    NASA Astrophysics Data System (ADS)

    Luque, Antonio; Panchak, Aleksandr; Vlasov, Alexey; Martí, Antonio; Andreev, Viacheslav

    2016-02-01

    The 8-dimensional Luttinger-Kohn-Pikus-Bir Hamiltonian matrix may be made up of four 4-dimensional blocks. A 4-band Hamiltonian is presented, obtained from making the non-diagonal blocks zero. The parameters of the new Hamiltonian are adjusted to fit the calculated effective masses and strained QD bandgap with the measured ones. The 4-dimensional Hamiltonian thus obtained agrees well with measured quantum efficiency of a quantum dot intermediate band solar cell and the full absorption spectrum can be calculated in about two hours using Mathematica© and a notebook. This is a hundred times faster than with the commonly-used 8-band Hamiltonian and is considered suitable for helping design engineers in the development of nanostructured solar cells.

  12. Maxwell consideration of polaritonic quasi-particle Hamiltonians in multi-level systems

    SciTech Connect

    Richter, Steffen; Michalsky, Tom; Fricke, Lennart; Sturm, Chris; Franke, Helena; Grundmann, Marius; Schmidt-Grund, Rüdiger

    2015-12-07

    We address the problem of the correct description of light-matter coupling for excitons and cavity photons in the case of systems with multiple photon modes or excitons, respectively. In the literature, two different approaches for the phenomenological coupling Hamiltonian can be found: Either one single Hamiltonian with a basis whose dimension equals the sum of photonic modes and excitonic resonances is used. Or a set of independent Hamiltonians, one for each photon mode, is chosen. Both are usually used equivalently for the same kind of multi-photonic systems which cannot be correct. However, identifying the suitable Hamiltonian is difficult when modeling experimental data. By means of numerical transfer matrix calculations, we demonstrate the scope of application of each approach: The first one holds only for the coupling of a single photon state to several excitons, while in the case of multiple photon modes, separate Hamiltonians must be used for each photon mode.

  13. Spin-squared Hamiltonian of next-to-leading order gravitational interaction

    SciTech Connect

    Steinhoff, Jan; Hergt, Steven; Schaefer, Gerhard

    2008-11-15

    The static, i.e., linear momentum independent, part of the next-to-leading order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the post-Newtonian (PN) approximation is calculated from a three-dimensional covariant ansatz for the Hamilton constraint. All coefficients in this ansatz can be uniquely fixed for black holes. The resulting Hamiltonian fits into the canonical formalism of Arnowitt, Deser, and Misner (ADM) and is given in their transverse-traceless (ADMTT) gauge. This completes the recent result for the momentum dependent part of the NLO spin(1)-spin(1) ADM Hamiltonian for binary black holes (BBH). Thus, all PN NLO effects up to quadratic order in spin for BBH are now given in Hamiltonian form in the ADMTT gauge. The equations of motion resulting from this Hamiltonian are an important step toward more accurate calculations of templates for gravitational waves.

  14. A 2-dimensional optical architecture for solving Hamiltonian path problem based on micro ring resonators

    NASA Astrophysics Data System (ADS)

    Shakeri, Nadim; Jalili, Saeed; Ahmadi, Vahid; Rasoulzadeh Zali, Aref; Goliaei, Sama

    2015-01-01

    The problem of finding the Hamiltonian path in a graph, or deciding whether a graph has a Hamiltonian path or not, is an NP-complete problem. No exact solution has been found yet, to solve this problem using polynomial amount of time and space. In this paper, we propose a two dimensional (2-D) optical architecture based on optical electronic devices such as micro ring resonators, optical circulators and MEMS based mirror (MEMS-M) to solve the Hamiltonian Path Problem, for undirected graphs in linear time. It uses a heuristic algorithm and employs n+1 different wavelengths of a light ray, to check whether a Hamiltonian path exists or not on a graph with n vertices. Then if a Hamiltonian path exists, it reports the path. The device complexity of the proposed architecture is O(n2).

  15. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom. PMID:23531015

  16. Hyperfine Parameters for Aluminum Hydride: An ab Initio Molecular Orbital Study

    NASA Astrophysics Data System (ADS)

    Gee, Myrlene; Wasylishen, Roderick E.

    2001-06-01

    An extensive ab initio molecular orbital study of the 27Al nuclear spin-rotation and nuclear quadrupolar coupling constants in aluminum hydride, AlH, has been performed. The 27Al nuclear spin-rotation constant (C⊥), calculated to be approximately 300 kHz, was neglected in a previous analysis of the hyperfine structure in the microwave spectrum (M. Goto and S. Saito, Astrophys. J.452, L147-148 (1995)). Unfortunately, the ab initio calculations do not provide a definitive value for the aluminum nuclear quadrupolar coupling constant, but suggest a value of -49±4 MHz. It is apparent that the microwave study of AlH should be repeated.

  17. Ab initio phonon limited transport

    NASA Astrophysics Data System (ADS)

    Verstraete, Matthieu

    We revisit the thermoelectric (TE) transport properties of two champion materials, PbTe and SnSe, using fully first principles methods. In both cases the performance of the material is due to subtle combinations of structural effects, scattering, and phase space reduction. In PbTe anharmonic effects are completely opposite to the predicted quasiharmonic evolution of phonon frequencies and to frequently (and incorrectly) cited extrapolations of experiments. This stabilizes the material at high T, but also tends to enhance its thermal conductivity, in a non linear manner, above 600 Kelvin. This explains why PbTe is in practice limited to room temperature applications. SnSe has recently been shown to be the most efficient TE material in bulk form. This is mainly due to a strongly enhanced carrier concentration and electrical conductivity, after going through a phase transition from 600 to 800 K. We calculate the transport coefficients as well as the defect concentrations ab initio, showing excellent agreement with experiment, and elucidating the origin of the double phase transition as well as the new charge carriers. AH Romero, EKU Gross, MJ Verstraete, and O Hellman PRB 91, 214310 (2015) O. Hellman, IA Abrikosov, and SI Simak, PRB 84 180301 (2011)

  18. Ab inito investigation of hydrodesulferization

    SciTech Connect

    Tilson, J.L.; Marshall, C.L.; Brenner, J.R.

    1997-12-31

    We utilize MPP and vector computers to model the interaction of large sulfur-containing species bonded with hydrodesulfurization (HDS) catalysts. This work is made possible by the availability large aggregate memory, parallel computers. The ability of modern non-traditional computers to solve large-scale scientific problems has been demonstrated. This success is accomplished, in part, by access to portable low- and user-level software tools which exhibit good control over NUMA. ab initio SCF methods are used to characterize the energies of adsorption of poly-aromatic, sulfur-containing hydrocarbons onto a series of molecular-based models of MoS2. These hydrocarbon include thiophene (TP), benzothiophene (BT) and dibenzothiophene (DBT) which are representative of heavy crude feedstocks. Our work attempts to ascertain if a consistent model of adsorption onto a MoS2 surface exists and to determine how the electronic and steric configuration of each species affect their energies of interaction with the metal surface.

  19. GINGA Observations of AB Doradus

    NASA Astrophysics Data System (ADS)

    Vilhu, O.; Tsuru, T.; Collier Cameron, A.

    We report GINGA observations of the pre main sequence star AB Doradus (HD 36705), performed during 8 - 12 January, 1990. Some rotational modulation might be present. four X-ray flares were detected. Three of these events were similar to the EINSTEIN HRI-flare (Vilhu and Linsky, 1987), with decay times around 25 min. The last flare had long rise and decay times (100 min), resembling the EXOSAT flares observed by Collier Cameron et.al. (1988). The mean flare spectrum can be fitted by a thermal bremstrahlung with temperature 5.0 keV, or by a power-law model with photon index 2.2. The 3 upper limit of the Iron line equivalent width in the flare spectrum is 1 keV, weaker than predicted by thermal models. This Iron line anomaly was first discussed in the case of UX Ari by Tsuru et. al. (1989). However, normal equivalent widths can be derived from several EXOSAT spectra of active cool stars (Pallavicini and Tagliaferri, 1990). We discuss the possibility that the continuum from non-thermal electrons (producing also the microwave emission) could occasionally lower the apparent equivalent width. The mechanism works for reasonably low magnetic field strengths and electon power-law indexes. However, a large population of non-thermal electrons is needed (comparable to the thermal one). Stronger magnetic fields could explain the radio emission with less electrons, but then the non-thermal X-ray continuum remains small.

  20. The B AB AR detector

    NASA Astrophysics Data System (ADS)

    Aubert, B.; Bazan, A.; Boucham, A.; Boutigny, D.; De Bonis, I.; Favier, J.; Gaillard, J.-M.; Jeremie, A.; Karyotakis, Y.; Le Flour, T.; Lees, J. P.; Lieunard, S.; Petitpas, P.; Robbe, P.; Tisserand, V.; Zachariadou, K.; Palano, A.; Chen, G. P.; Chen, J. C.; Qi, N. D.; Rong, G.; Wang, P.; Zhu, Y. S.; Eigen, G.; Reinertsen, P. L.; Stugu, B.; Abbott, B.; Abrams, G. S.; Amerman, L.; Borgland, A. W.; Breon, A. B.; Brown, D. N.; Button-Shafer, J.; Clark, A. R.; Dardin, S.; Day, C.; Dow, S. F.; Fan, Q.; Gaponenko, I.; Gill, M. S.; Goozen, F. R.; Gowdy, S. J.; Gritsan, A.; Groysman, Y.; Hernikl, C.; Jacobsen, R. G.; Jared, R. C.; Kadel, R. W.; Kadyk, J.; Karcher, A.; Kerth, L. T.; Kipnis, I.; Kluth, S.; Kral, J. F.; Lafever, R.; LeClerc, C.; Levi, M. E.; Lewis, S. A.; Lionberger, C.; Liu, T.; Long, M.; Luo, L.; Lynch, G.; Luft, P.; Mandelli, E.; Marino, M.; Marks, K.; Matuk, C.; Meyer, A. B.; Minor, R.; Mokhtarani, A.; Momayezi, M.; Nyman, M.; Oddone, P. J.; Ohnemus, J.; Oshatz, D.; Patton, S.; Pedrali-Noy, M.; Perazzo, A.; Peters, C.; Pope, W.; Pripstein, M.; Quarrie, D. R.; Rasson, J. E.; Roe, N. A.; Romosan, A.; Ronan, M. T.; Shelkov, V. G.; Stone, R.; Strother, P. D.; Telnov, A. V.; von der Lippe, H.; Weber, T. F.; Wenzel, W. A.; Zizka, G.; Bright-Thomas, P. G.; Hawkes, C. M.; Kirk, A.; Knowles, D. J.; O'Neale, S. W.; Watson, A. T.; Watson, N. K.; Deppermann, T.; Koch, H.; Krug, J.; Kunze, M.; Lewandowski, B.; Peters, K.; Schmuecker, H.; Steinke, M.; Andress, J. C.; Barlow, N. R.; Bhimji, W.; Chevalier, N.; Clark, P. J.; Cottingham, W. N.; De Groot, N.; Dyce, N.; Foster, B.; Mass, A.; McFall, J. D.; Wallom, D.; Wilson, F. F.; Abe, K.; Hearty, C.; McKenna, J. A.; Thiessen, D.; Camanzi, B.; Harrison, T. J.; McKemey, A. K.; Tinslay, J.; Antohin, E. I.; Blinov, V. E.; Bukin, A. D.; Bukin, D. A.; Buzykaev, A. R.; Dubrovin, M. S.; Golubev, V. B.; Ivanchenko, V. N.; Kolachev, G. M.; Korol, A. A.; Kravchenko, E. A.; Mikhailov, S. F.; Onuchin, A. P.; Salnikov, A. A.; Serednyakov, S. I.; Skovpen, Yu. I.; Telnov, V. I.; Yushkov, A. N.; Booth, J.; Lankford, A. J.; Mandelkern, M.; Pier, S.; Stoker, D. P.; Zioulas, G.; Ahsan, A.; Arisaka, K.; Buchanan, C.; Chun, S.; Faccini, R.; MacFarlane, D. B.; Prell, S. A.; Rahatlou, Sh.; Raven, G.; Sharma, V.; Burke, S.; Callahan, D.; Campagnari, C.; Dahmes, B.; Hale, D.; Hart, P. A.; Kuznetsova, N.; Kyre, S.; Levy, S. L.; Long, O.; Lu, A.; May, J.; Richman, J. D.; Verkerke, W.; Witherell, M.; Yellin, S.; Beringer, J.; DeWitt, J.; Dorfan, D. E.; Eisner, A. M.; Frey, A.; Grillo, A. A.; Grothe, M.; Heusch, C. A.; Johnson, R. P.; Kroeger, W.; Lockman, W. S.; Pulliam, T.; Rowe, W.; Sadrozinski, H.; Schalk, T.; Schmitz, R. E.; Schumm, B. A.; Seiden, A.; Spencer, E. N.; Turri, M.; Walkowiak, W.; Wilder, M.; Williams, D. C.; Chen, E.; Dubois-Felsmann, G. P.; Dvoretskii, A.; Hanson, J. E.; Hitlin, D. G.; Kolomensky, Yu. G.; Metzler, S.; Oyang, J.; Porter, F. C.; Ryd, A.; Samuel, A.; Weaver, M.; Yang, S.; Zhu, R. Y.; Devmal, S.; Geld, T. L.; Jayatilleke, S.; Jayatilleke, S. M.; Mancinelli, G.; Meadows, B. T.; Sokoloff, M. D.; Bloom, P.; Broomer, B.; Erdos, E.; Fahey, S.; Ford, W. T.; Gaede, F.; van Hoek, W. C.; Johnson, D. R.; Michael, A. K.; Nauenberg, U.; Olivas, A.; Park, H.; Rankin, P.; Roy, J.; Sen, S.; Smith, J. G.; Wagner, D. L.; Blouw, J.; Harton, J. L.; Krishnamurthy, M.; Soffer, A.; Toki, W. H.; Warner, D. W.; Wilson, R. J.; Zhang, J.; Brandt, T.; Brose, J.; Dahlinger, G.; Dickopp, M.; Dubitzky, R. S.; Eckstein, P.; Futterschneider, H.; Kocian, M. L.; Krause, R.; Müller-Pfefferkorn, R.; Schubert, K. R.; Schwierz, R.; Spaan, B.; Wilden, L.; Behr, L.; Bernard, D.; Bonneaud, G. R.; Brochard, F.; Cohen-Tanugi, J.; Ferrag, S.; Fouque, G.; Gastaldi, F.; Matricon, P.; Mora de Freitas, P.; Renard, C.; Roussot, E.; T'Jampens, S.; Thiebaux, C.; Vasileiadis, G.; Verderi, M.; Anjomshoaa, A.; Bernet, R.; Di Lodovico, F.; Muheim, F.; Playfer, S.; Swain, J. E.; Falbo, M.; Bozzi, C.; Dittongo, S.; Folegani, M.; Piemontese, L.; Ramusino, A. C.; Treadwell, E.; Anulli, F.; Baldini-Ferroli, R.; Calcaterra, A.; de Sangro, R.; Falciai, D.; Finocchiaro, G.; Patteri, P.; Peruzzi, I. M.; Piccolo, M.; Xie, Y.; Zallo, A.; Bagnasco, S.; Buzzo, A.; Contri, R.; Crosetti, G.; Fabbricatore, P.; Farinon, S.; Lo Vetere, M.; Macri, M.; Minutoli, S.; Monge, M. R.; Musenich, R.; Pallavicini, M.; Parodi, R.; Passaggio, S.; Pastore, F. C.; Patrignani, C.; Pia, M. G.; Priano, C.; Robutti, E.; Santroni, A.; Bartoldus, R.; Dignan, T.; Hamilton, R.; Mallik, U.; Cochran, J.; Crawley, H. B.; Fischer, P. A.; Lamsa, J.; McKay, R.; Meyer, W. T.; Rosenberg, E. I.; Albert, J. N.; Beigbeder, C.; Benkebil, M.; Breton, D.; Cizeron, R.; Du, S.; Grosdidier, G.; Hast, C.; Höcker, A.; Lacker, H. M.; LePeltier, V.; Lutz, A. M.

    2002-02-01

    B AB AR, the detector for the SLAC PEP-II asymmetric e +e - B Factory operating at the ϒ(4 S) resonance, was designed to allow comprehensive studies of CP-violation in B-meson decays. Charged particle tracks are measured in a multi-layer silicon vertex tracker surrounded by a cylindrical wire drift chamber. Electromagnetic showers from electrons and photons are detected in an array of CsI crystals located just inside the solenoidal coil of a superconducting magnet. Muons and neutral hadrons are identified by arrays of resistive plate chambers inserted into gaps in the steel flux return of the magnet. Charged hadrons are identified by d E/d x measurements in the tracking detectors and by a ring-imaging Cherenkov detector surrounding the drift chamber. The trigger, data acquisition and data-monitoring systems, VME- and network-based, are controlled by custom-designed online software. Details of the layout and performance of the detector components and their associated electronics and software are presented.

  1. Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations

    NASA Astrophysics Data System (ADS)

    Geneste, Grégory; Bellaiche, L.; Kiat, Jean-Michel

    2016-06-01

    The radio-frequency dielectric response of the lead-free Ba (Zr0.5Ti0.5)O3 relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio-based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors.

  2. Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations.

    PubMed

    Geneste, Grégory; Bellaiche, L; Kiat, Jean-Michel

    2016-06-17

    The radio-frequency dielectric response of the lead-free Ba(Zr_{0.5}Ti_{0.5})O_{3} relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio-based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors. PMID:27367408

  3. A room temperature CO2 line list with ab initio computed intensities

    NASA Astrophysics Data System (ADS)

    Zak, Emil; Tennyson, Jonathan; Polyansky, Oleg L.; Lodi, Lorenzo; Zobov, Nikolay F.; Tashkun, Sergey A.; Perevalov, Valery I.

    2016-07-01

    Atmospheric carbon dioxide concentrations are being closely monitored by remote sensing experiments which rely on knowing line intensities with an uncertainty of 0.5% or better. We report a theoretical study providing rotation-vibration line intensities substantially within the required accuracy based on the use of a highly accurate ab initio dipole moment surface (DMS). The theoretical model developed is used to compute CO2 intensities with uncertainty estimates informed by cross comparing line lists calculated using pairs of potential energy surfaces (PES) and DMS's of similar high quality. This yields lines sensitivities which are utilized in reliability analysis of our results. The final outcome is compared to recent accurate measurements as well as the HITRAN2012 database. Transition frequencies are obtained from effective Hamiltonian calculations to produce a comprehensive line list covering all 12C16O2 transitions below 8000cm-1 and stronger than 10-30 cm/molecule at T = 296 K.

  4. Pressure effect on elastic anisotropy of crystals from ab initio simulations: the case of silicate garnets.

    PubMed

    Mahmoud, A; Erba, A; Doll, K; Dovesi, R

    2014-06-21

    A general methodology has been devised and implemented into the solid-state ab initio quantum-mechanical Crystal program for studying the evolution under geophysical pressure of the elastic anisotropy of crystalline materials. This scheme, which fully exploits both translational and point symmetry of the crystal, is developed within the formal frame of one-electron Hamiltonians and atom-centered basis functions. Six silicate garnet end-members, among the most important rock-forming minerals of the Earth's mantle, are considered, whose elastic anisotropy is fully characterized under high hydrostatic compressions, up to 60 GPa. The pressure dependence of azimuthal anisotropy and shear-wave birefringence of seismic wave velocities for these minerals are accurately simulated and compared with available single-crystal measurements. PMID:24952556

  5. Pressure effect on elastic anisotropy of crystals from ab initio simulations: The case of silicate garnets

    SciTech Connect

    Mahmoud, A.; Erba, A. Dovesi, R.; Doll, K.

    2014-06-21

    A general methodology has been devised and implemented into the solid-state ab initio quantum-mechanical CRYSTAL program for studying the evolution under geophysical pressure of the elastic anisotropy of crystalline materials. This scheme, which fully exploits both translational and point symmetry of the crystal, is developed within the formal frame of one-electron Hamiltonians and atom-centered basis functions. Six silicate garnet end-members, among the most important rock-forming minerals of the Earth's mantle, are considered, whose elastic anisotropy is fully characterized under high hydrostatic compressions, up to 60 GPa. The pressure dependence of azimuthal anisotropy and shear-wave birefringence of seismic wave velocities for these minerals are accurately simulated and compared with available single-crystal measurements.

  6. New Hamiltonian expansions adapted to the Trojan problem

    NASA Astrophysics Data System (ADS)

    Páez, Rocío Isabel; Locatelli, Ugo; Efthymiopoulos, Christos

    2016-07-01

    A number of studies, referring to the observed Trojan asteroids of various planets in our Solar System, or to hypothetical Trojan bodies in extrasolar planetary systems, have emphasized the importance of so-called secondary resonances in the problem of the long term stability of Trojan motions. Such resonances describe commensurabilities between the fast, synodic, and secular frequency of the Trojan body, and, possibly, additional slow frequencies produced by more than one perturbing bodies. The presence of secondary resonances sculpts the dynamical structure of the phase space. Hence, identifying their location is a relevant task for theoretical studies. In the present paper we combine the methods introduced in two recent papers (Páez and Efthymiopoulos in Celest Mech Dyn Astron 121(2):139, 2015; Páez and Locatelli in MNRAS 453(2):2177, 2015) in order to analytically predict the location of secondary resonances in the Trojan problem. In Páez and Efthymiopoulos (2015), the motion of a Trojan body was studied in the context of the planar Elliptic Restricted Three Body or the planar Restricted Multi-Planet Problem. It was shown that the Hamiltonian admits a generic decomposition H=H_b+H_{sec} . The term H_b , called the basic Hamiltonian, is a model of two degrees of freedom characterizing the short-period and synodic motions of a Trojan body. Also, it yields a constant `proper eccentricity' allowing to define a third secular frequency connected to the body's perihelion precession. H_{sec} contains all remaining secular perturbations due to the primary or to additional perturbing bodies. Here, we first investigate up to what extent the decomposition H=H_b+H_{sec} provides a meaningful model. To this end, we produce numerical examples of surfaces of section under H_b and compare with those of the full model. We also discuss how secular perturbations alter the dynamics under H_b . Secondly, we explore the normal form approach introduced in Páez and Locatelli (2015

  7. Nuclear Safety Information Center, Its Products and Services

    ERIC Educational Resources Information Center

    Buchanan, J. R.

    1970-01-01

    The Nuclear Safety Information Center (NSIC) serves as a focal point for the collection, analysis and dissemination of information related to safety problems encountered in the design, analysis, and operation of nuclear facilities. (Author/AB)

  8. An ab initio structural and spectroscopic study of acetone—An analysis of the far infrared torsional spectra of acetone-h6 and -d6

    NASA Astrophysics Data System (ADS)

    Smeyers, Y. G.; Senent, M. L.; Botella, V.; Moule, D. C.

    1993-02-01

    The far infrared torsional spectra of acetone (CH3)2CO and (CD3)2CO have been determined from ab initio calculations, and the main features of the experimental data assigned. For this purpose, the potential energy surface for the double methyl rotation was determined with fully relaxed geometry into the RHF and RHF+MP2 approximations using a 6-31G(p,d) basis set. The energy values, as well as the kinetic parameters obtained from the optimized geometry, were fitted to double Fourier expansions as functions of the rotational angles in seven terms. The torsional solutions were developed on the basis of the symmetry eigenvectors of the G36 nonrigid group, which factorize the Hamiltonian matrix into 16 boxes. The energy levels and torsional wave functions for each symmetry specie were then obtained diagonalizing each blocks separately. Intensities were obtained from the calculated electric dipole moment variations and the nuclear statistical weights, and were combined with the torsional frequencies to predict the spectra. The calculated band patterns show a multi- plet structure and reproduce the main features of the experimental data. The torsional bands of the infrared active ν17 mode were found to be clustered into quartets, (A1→A2, G→G, E1→E1, E3→E4), for the v=0→v=1 fundamental, and (A2→A1, G→G, E1→E1, E4→E3) for the v=1→v=2 first sequence transitions. The G→G transitions were found to be the more intense. The correlation between the calculated and observed spectra allows for an assignment of the major bands.

  9. Ab initio derivation of multi-orbital extended Hubbard model for molecular crystals

    NASA Astrophysics Data System (ADS)

    Tsuchiizu, Masahisa; Omori, Yukiko; Suzumura, Yoshikazu; Bonnet, Marie-Laure; Robert, Vincent

    2012-01-01

    From configuration interaction (CI) ab initio calculations, we derive an effective two-orbital extended Hubbard model based on the gerade (g) and ungerade (u) molecular orbitals (MOs) of the charge-transfer molecular conductor (TTM-TTP)I3 and the single-component molecular conductor [Au(tmdt)2]. First, by focusing on the isolated molecule, we determine the parameters for the model Hamiltonian so as to reproduce the CI Hamiltonian matrix. Next, we extend the analysis to two neighboring molecule pairs in the crystal and we perform similar calculations to evaluate the inter-molecular interactions. From the resulting tight-binding parameters, we analyze the band structure to confirm that two bands overlap and mix in together, supporting the multi-band feature. Furthermore, using a fragment decomposition, we derive the effective model based on the fragment MOs and show that the staking TTM-TTP molecules can be described by the zig-zag two-leg ladder with the inter-molecular transfer integral being larger than the intra-fragment transfer integral within the molecule. The inter-site interactions between the fragments follow a Coulomb law, supporting the fragment decomposition strategy.

  10. Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates

    NASA Astrophysics Data System (ADS)

    Shikakhwa, M. S.; Chair, N.

    2016-08-01

    The Schrödinger Hamiltonian of a spin-less particle as well as the Pauli Hamiltonian with spin-orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate are constructed. A new approach, based on the physical argument that upon squeezing the particle to the surface by a potential, then it is the physical gauge-covariant kinematical momentum operator (velocity operator) transverse to the surface that should be dropped from the Hamiltonian(s). In both cases, the resulting Hermitian gauge-invariant Hamiltonian on the surface is free from any reference to the component of the vector potential transverse to the surface, and the approach is completely gauge-independent. In particular, for the Pauli Hamiltonian these results are obtained exactly without any further assumptions or approximations. Explicit covariant plug-and-play formulae for the Schrödinger Hamiltonians on the surfaces of a cylinder, a sphere and a torus are derived.

  11. Non-commuting two-local Hamiltonians for quantum error suppression

    NASA Astrophysics Data System (ADS)

    Rieffel, Eleanor; Jiang, Zhang; QuAIL Team

    Physical constraints make it challenging to implement and control multi-body interactions. Designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge. A common approach to robust storage of quantum information is to encode in the ground subspace of a Hamiltonian. Even allowing particles with high Hilbert-space dimension, it is not possible to protect quantum information from single-site errors by encoding in the ground subspace of any Hamiltonian containing only commuting two-local terms. We demonstrate how to get around this no-go result by encoding in the ground subspace of a Hamiltonian consisting of non-commuting two-local terms arising from the gauge operators of a subsystem code. Specifically, we show how to protect stored quantum information against single-qubit errors using a Hamiltonian consisting of sums of the gauge generators from Bacon-Shor codes and generalized-Bacon-Shor code. Thus, non-commuting two-local Hamiltonians have more error-suppressing power than commuting two-local Hamiltonians. Finally, we comment briefly on the robustness of the whole scheme.

  12. Does finite-temperature decoding deliver better optima for noisy Hamiltonians?

    NASA Astrophysics Data System (ADS)

    Ochoa, Andrew J.; Nishimura, Kohji; Nishimori, Hidetoshi; Katzgraber, Helmut G.

    The minimization of an Ising spin-glass Hamiltonian is an NP-hard problem. Because many problems across disciplines can be mapped onto this class of Hamiltonian, novel efficient computing techniques are highly sought after. The recent development of quantum annealing machines promises to minimize these difficult problems more efficiently. However, the inherent noise found in these analog devices makes the minimization procedure difficult. While the machine might be working correctly, it might be minimizing a different Hamiltonian due to the inherent noise. This means that, in general, the ground-state configuration that correctly minimizes a noisy Hamiltonian might not minimize the noise-less Hamiltonian. Inspired by rigorous results that the energy of the noise-less ground-state configuration is equal to the expectation value of the energy of the noisy Hamiltonian at the (nonzero) Nishimori temperature [J. Phys. Soc. Jpn., 62, 40132930 (1993)], we numerically study the decoding probability of the original noise-less ground state with noisy Hamiltonians in two space dimensions, as well as the D-Wave Inc. Chimera topology. Our results suggest that thermal fluctuations might be beneficial during the optimization process in analog quantum annealing machines.

  13. The relativistic scheme for eliminating small components Hamiltonian: Analysis of approximations

    NASA Astrophysics Data System (ADS)

    Barysz, Maria

    2000-09-01

    The derivation of the recently proposed one-component relativistic Hamiltonian, and the resulting relativistic scheme by eliminating small components (RESC) method of Nakajima and Hirao, are analyzed in terms of the Foldy-Wouthuysen transformation of the Dirac Hamiltonian. This approach reveals the meaning of different approximations used in the derivation of the RESC Hamiltonian and its close relation to approximate relativistic Hamiltonians resulting from the free-particle Foldy-Wouthuysen transformation. Moreover, the present derivation combined with what is called the classical approximation in Nakajima and Hirao's approach shows that there is a whole family of the RESC-type Hamiltonians. Some of them, including the original RESC Hamiltonian, are analyzed numerically. It is documented that neither of the RESC-type Hamiltonians offers variational stability. As a consequence the RESC methods may suffer from the variational collapse for heavier systems. On the other hand the energy differences (e.g., ionization potentials) computed within the RESC approach turn out to be close to the values obtained in the Douglas-Kroll scheme.

  14. Ab Initio Study of Polonium

    SciTech Connect

    Zabidi, Noriza Ahmad; Kassim, Hasan Abu; Shrivastava, Keshav N.

    2008-05-20

    Polonium is the only element with a simple cubic (sc) crystal structure. Atoms in solid polonium sit at the corners of a simple cubic unit cell and no where else. Polonium has a valence electron configuration 6s{sup 2}6p{sup 4} (Z = 84). The low temperature {alpha}-phase transforms into the rhombohedral (trigonal) {beta} structure at {approx}348 K. The sc {alpha}-Po unit cell constant is a = 3.345 A. The beta form of polonium ({beta}-Po) has the lattice parameters, a{sub R} = 3.359 A and a rhombohedral angle 98 deg. 13'. We have performed an ab initio electronic structure calculation by using the density functional theory. We have performed the calculation with and without spin-orbit (SO) coupling by using both the LDA and the GGA for the exchange-correlations. The k-points in a simple cubic BZ are determined by R (0.5, 0.5, 0.5), {gamma} (0, 0, 0), X (0.5, 0, 0), M (0.5, 0.5, 0) and {gamma} (0, 0, 0). Other directions of k-points are {gamma} (0, 0, 0), X (0.5, 0, 0), R (0.5, 0.5, 0.5) and {gamma} (0, 0, 0). The SO splittings of p states at the {gamma} point in the GGA+SO scheme for {alpha}-Po are 0.04 eV and 0.02 eV while for the {beta}-Po these are 0.03 eV and 0.97 eV. We have also calculated the vibrational spectra for the unit cells in both the structures. We find that exchanging of a Po atom by Pb atom produces several more bands and destabilizes the {beta} phase.

  15. Electronic coupling calculation and pathway analysis of electron transfer reaction using ab initio fragment-based method. I. FMO-LCMO approach

    NASA Astrophysics Data System (ADS)

    Nishioka, Hirotaka; Ando, Koji

    2011-05-01

    By making use of an ab initio fragment-based electronic structure method, fragment molecular orbital-linear combination of MOs of the fragments (FMO-LCMO), developed by Tsuneyuki et al. [Chem. Phys. Lett. 476, 104 (2009)], 10.1016/j.cplett.2009.05.069, we propose a novel approach to describe long-distance electron transfer (ET) in large system. The FMO-LCMO method produces one-electron Hamiltonian of whole system using the output of the FMO calculation with computational cost much lower than conventional all-electron calculations. Diagonalizing the FMO-LCMO Hamiltonian matrix, the molecular orbitals (MOs) of the whole system can be described by the LCMOs. In our approach, electronic coupling TDA of ET is calculated from the energy splitting of the frontier MOs of whole system or perturbation method in terms of the FMO-LCMO Hamiltonian matrix. Moreover, taking into account only the valence MOs of the fragments, we can considerably reduce computational cost to evaluate TDA. Our approach was tested on four different kinds of model ET systems with non-covalent stacks of methane, non-covalent stacks of benzene, trans-alkanes, and alanine polypeptides as their bridge molecules, respectively. As a result, it reproduced reasonable TDA for all cases compared to the reference all-electron calculations. Furthermore, the tunneling pathway at fragment-based resolution was obtained from the tunneling current method with the FMO-LCMO Hamiltonian matrix.

  16. Adaptive sparse grid expansions of the vibrational Hamiltonian

    NASA Astrophysics Data System (ADS)

    Strobusch, D.; Scheurer, Ch.

    2014-02-01

    The vibrational Hamiltonian involves two high dimensional operators, the kinetic energy operator (KEO), and the potential energy surface (PES). Both must be approximated for systems involving more than a few atoms. Adaptive approximation schemes are not only superior to truncated Taylor or many-body expansions (MBE), they also allow for error estimates, and thus operators of predefined precision. To this end, modified sparse grids (SG) are developed that can be combined with adaptive MBEs. This MBE/SG hybrid approach yields a unified, fully adaptive representation of the KEO and the PES. Refinement criteria, based on the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods, are presented. The combination of the adaptive MBE/SG approach and the VSCF plus VCI methods yields a black box like procedure to compute accurate vibrational spectra. This is demonstrated on a test set of molecules, comprising water, formaldehyde, methanimine, and ethylene. The test set is first employed to prove convergence for semi-empirical PM3-PESs and subsequently to compute accurate vibrational spectra from CCSD(T)-PESs that agree well with experimental values.

  17. Landau-Heisenberg Hamiltonian model for FeRh

    NASA Astrophysics Data System (ADS)

    Derlet, P. M.

    2012-05-01

    An empirical model is developed for the FeRh system with the view of gaining further insight into the first-order antiferromagnetic-ferromagnetic (AFM-FM) and volume phase transition known to occur at 370 K. A volume-per-atom dependent minimal nearest neighbor Landau-Heisenberg Hamiltonian is employed in which longitudinal and transverse moment fluctuations are considered for both the Fe and Rh atoms. As a function of volume-per-atom, the corresponding onsite Landau function coefficients and the nearest-neighbor exchange parameters are fitted directly to a wide range of existing colinear and noncolinear density functional theory calculations. Using a developed Monte Carlo strategy the thermal properties of the AFM and FM phases are investigated, as well as the phase transition. It is found that the model is able to describe well the thermal expansion, heat capacities and the associated entropy increase that accompanies the magnetic/volume phase transition. The model suggests an equally important role for the magnetic and volume fluctuations in driving the phase transition.

  18. On the Convexity of the KdV Hamiltonian

    NASA Astrophysics Data System (ADS)

    Kappeler, Thomas; Maspero, Alberto; Molnar, Jan; Topalov, Peter

    2016-08-01

    Motivated by perturbation theory, we prove that the nonlinear part {H^{*}} of the KdV Hamiltonian {H^{kdv}}, when expressed in action variables {I = (In)_{n ≥slant 1}}, extends to a real analytic function on the positive quadrant {ℓ2+({N})} of {ℓ2({N})} and is strictly concave near {0}. As a consequence, the differential of {H^{*}} defines a local diffeomorphism near 0 of {ℓ_{{C}}2({N})}. Furthermore, we prove that the Fourier-Lebesgue spaces {{F}{L}^{s,p}} with {-1/2 ≤slant s ≤slant 0} and {2 ≤slant p < ∞}, admit global KdV-Birkhoff coordinates. In particular, it means that {ℓ2_+({N})} is the space of action variables of the underlying phase space {{F}{L}^{-1/2,4}} and that the KdV equation is globally in time {C0}-well-posed on {{F}{L}^{-1/2,4}}.

  19. Hamiltonian description of ideal fluids and MHD flows

    NASA Astrophysics Data System (ADS)

    Kuznetsov, E. A.

    2002-11-01

    Vortex line and magnetic line representations are introduced for description of flows in ideal hydrodynamics and MHD, respectively. For incompressible fluids it is shown that the equations of motion for vorticity Ω and magnetic field with the help of this transformation follow from the variational principle. By means of this representation it is possible to integrate the system of hydrodynamic type with the Hamiltonian lH=int |Ω| dr. It is also demonstrated that these representations allow to remove from the noncanonical Poisson brackets, defined on the space of divergence-free vector fields, degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD a new Weber type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent this transformation coincides with the Clebsch representation analog introduced in (V.E.Zakharov and E.A.Kuznetsov, Doklady USSR Ac. Nauk. (Soviet Doklady), 194), 1288 (1970).

  20. Energetics and Motion Planning for Hamiltonian Fishlike Locomotion

    NASA Astrophysics Data System (ADS)

    Kelly, Scott; Pujari, Parthesh

    2009-11-01

    The self-propulsion of an undulating body suspended in a fluid hinges on the judicious excitation of the fluid itself, in that forward momentum is developed by the body as equal and opposite momentum is imparted to the fluid. The manner in which this is accomplished is recorded in the structure of the body's wake; the efficiency with which it's accomplished is reflected in the fluid's evolving kinetic energy. Focusing on a model for the self-propulsion of a free hydrofoil with variable camber in an infinite planar fluid, we examine relationships between economy of deformation, wake structure, and wake energetics. The model in question simplifies the underlying physics by restricting vortex shedding to the trailing point of the foil, discretizing shed vorticity, and neglecting dissipation --- allowing the remaining dynamics to be framed in a Hamiltonian setting. We consider the self-propulsion of the foil both in a quiescent fluid and in a variety of vortex flows representing wake structures present in vehicle schools.