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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. 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

  1. 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

  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. 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.

  4. 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.

  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. 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.

  16. 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.

  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. 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

  5. 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.

  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. 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.

  8. 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.

  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. 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

  14. 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.

  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. 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.

  18. 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…

  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. 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.

  11. 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

  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. 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.

  2. 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.

  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. 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

  9. 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.

  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. 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.

  12. 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.

  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. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  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. 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.

  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. 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.

  12. 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.

  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. 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.

  19. 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

  20. 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.

  1. 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.

  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. 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

  4. 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

  5. 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.

  6. 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.

  7. 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\

  8. 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.

  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. 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

  5. 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

  6. 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.

  7. 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.

  8. 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.

  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. 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.

  11. 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).

  12. 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.

  13. 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).

  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. 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.

  16. 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.

  17. 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.

  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. 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.

  20. 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

  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. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  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. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  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 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

  7. 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

  8. 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.

  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.