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Sample records for nuclear hamiltonian ab

  1. Evolved chiral NN +3N Hamiltonians for ab initio nuclear structure calculations

    NASA Astrophysics Data System (ADS)

    Roth, Robert; Calci, Angelo; Langhammer, Joachim; Binder, Sven

    2014-08-01

    We discuss the building blocks for a consistent inclusion of chiral three-nucleon (3N) interactions into ab initio nuclear structure calculations beyond the lower p shell. We highlight important technical developments, such as the similarity renormalization group (SRG) evolution in the 3N sector, a JT-coupled storage scheme for 3N matrix elements with efficient on-the-fly decoupling, and the importance-truncated no-core shell model with 3N interactions. Together, these developments make converged ab initio calculations with explicit 3N interactions possible also beyond the lower p shell. We analyze in detail the impact of various truncations of the SRG-evolved Hamiltonian, in particular the truncation of the harmonic-oscillator model space used for solving the SRG flow equations and the omission of the induced beyond-3N contributions of the evolved Hamiltonian. Both truncations lead to sizable effects in the upper p shell and beyond and we present options to remedy these truncation effects. The analysis of the different truncations is a first step towards a systematic uncertainty quantification of all stages of the calculation.

  2. 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.

  3. 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.

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

    PubMed

    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(∗)/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. PMID:26374007

  5. 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.

  6. 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.

  7. 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.

  8. From Model Hamiltonians to ab Initio Hamiltonians and Back Again: Using Single Excitation Quantum Chemistry Methods To Find Multiexciton States in Singlet Fission Materials.

    PubMed

    Mayhall, Nicholas J

    2016-09-13

    Due to the promise of significantly enhanced photovoltaic efficiencies, significant effort has been directed toward understanding and controlling the singlet fission mechanism. Although accurate quantum chemical calculations would provide a detail-rich view of the singlet fission mechanism, this is complicated by the multiexcitonic nature of one of the key intermediates, the (1)(TT) state. Being described as two simultaneous and singlet-coupled triplet excitations on a pair of nearest neighbor monomers, the (1)(TT) state is inherently a multielectronic excitation. This fact renders most single-reference ab initio quantum chemical methods incapable of providing accurate results. This paper serves two purposes: (1) to demonstrate that the multiexciton states in singlet fission materials can be described using a spin-only Hamiltonian and with each monomer treated as a biradical and (2) to propose a very simple procedure for extracting the values for this Hamiltonian from single-reference calculations. Numerical examples are included for a number of different systems, including dimers, trimers, tetramers, and a cluster comprised of seven chromophores. PMID:27472260

  9. An AB Initio Model Hamiltonian for the e' ⊗ e' and e' ⊗ e'' Singlet States of Si_3

    NASA Astrophysics Data System (ADS)

    Matthews, D. A.; Stanton, J. F.

    2012-06-01

    The recent mass-selected REMPI spectrum of the silicon trimer in the 2.25-2.6 eV region has been partially assigned in terms of a triplet-triplet transition. However, several remaining features appear to be due to transitions from the ground singlet to one of two upper singlet states, both of these belonging to the same electron configuration. To aid in the assignment of these features, a model Hamiltonian has been developed for the e' ⊗ e' and e' ⊗ e'' singlet states of Si_3 (7 states in total), including quadratic vibronic (Jahn-Teller and psuedo-Jahn-Teller) interactions and a quartic expansion of the diabatic potential. This Hamiltonian has been fit to ab initio single-point energies calculated using the full EOMDEA-CCSDT method and the Widmark-Roos ANO basis set. N. J. Reilly, D. L. Kokkin, J. F. Stanton and M. C. McCarthy, submitted.

  10. A general nuclear motion Hamiltonian and non-internal curvilinear coordinates.

    PubMed

    Strobusch, D; Scheurer, Ch

    2013-03-01

    An exact Hamiltonian for nuclear motions in general curvilinear coordinates is derived. It is demonstrated how this Hamiltonian transforms into well-established expressions, such as the Wilson Howard Hamiltonian or the Meyer Günthard Hamiltonian, if the general coordinates are restricted to be rectilinear or internal. Furthermore, a compact expression for the Hamiltonian expressed in non-internal curvilinear coordinates is provided, which makes this coordinate class available for applications in a simple way, since only the Jacobian matrix with respect to the rotating frame coordinates must be calculated. An example, employing a water model potential, exemplifies how different coordinate systems from all three coordinate classes (rectilinear, internal, and non-internal) lead to vibrational spectra, which are in excellent agreement. Thereby, the applicability of the general Hamiltonian is demonstrated and also its correctness is confirmed.

  11. 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.

  12. 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.

  13. Ab initio calculations of nuclear reactions important for astrophysics

    NASA Astrophysics Data System (ADS)

    Navratil, Petr; Dohet-Eraly, Jeremy; Calci, Angelo; Horiuchi, Wataru; Hupin, Guillaume; Quaglioni, Sofia

    2016-09-01

    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. One of the newly developed approaches is the No-Core Shell Model with Continuum (NCSMC), capable of describing both bound and scattering states in light nuclei simultaneously. We will present NCSMC results for reactions important for astrophysics that are difficult to measure at relevant low energies, such as 3He(α,γ)7Be and 3H(α,γ)7Li and 11C(p,γ)12N radiative capture, as well as the 3H(d,n)4He fusion. We will also address prospects of calculating the 2H(α,γ)6Li capture reaction within the NCSMC formalism. Prepared in part by LLNL under Contract DE-AC52-07NA27344. Supported by the U.S. DOE, OS, NP, under Work Proposal No. SCW1158, and by the NSERC Grant No. SAPIN-2016-00033. TRIUMF receives funding from the NRC Canada.

  14. 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.

  15. 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.

  16. Relativistic ab initio model potential calculations including spin-orbit effects through the Wood-Boring Hamiltonian

    NASA Astrophysics Data System (ADS)

    Seijo, Luis

    1995-05-01

    Presented in this paper, is a practical implementation of the use of the Wood-Boring Hamiltonian [Phys. Rev. B 18, 2701 (1978)] in atomic and molecular ab initio core model potential calculations (AIMP), as a means to include spin-orbit relativistic effects, in addition to the mass-velocity and Darwin operators, which were already included in the spin-free version of the relativistic AIMP method. Calculations on the neutral and singly ionized atoms of the halogen elements and sixth-row p-elements Tl-Rn are presented, as well as on the one or two lowest lying states of the diatomic molecules HX, HX+, (X=F, Cl, Br, I, At) TlH, PbH, BiH, and PoH. The calculated spin-orbit splittings and bonding properties show a stable, good quality, of the size of what can be expected from an effective potential method.

  17. Ab initio determination of bond length dependence of the correlated valence shell Hamiltonian of CH: Comparison with semiempirical theories

    NASA Astrophysics Data System (ADS)

    Sun, Hosung; Freed, Karl F.

    1984-01-01

    The exact ab initio effective valence shell Hamiltonian, which is mimicked by semiempirical theories of valence, is calculated for CH at 11 bond lengths using quasidegenerate many-body perturbation theory to incorporate extensive correlation contributions. Least squares fits of the bond length dependence of the calculated CH matrix elements provide simple formulas which are compared with the intuitive forms introduced into semiempirical theories. Some of the semiempirical formulas, e.g., one-center, one-electron integrals and two-center, two-electron integrals, are in good agreement with our correlated ab initio calculations, while others display substantial departures. For example, the bond length dependence of one-center, two-electron integrals, which are assumed to be independent of bond length in semiempirical theories, is substantial but physically understandable. Corrections are found to the assumed proportionality of resonance and overlap integrals. The bond length dependence of nonclassical three-electron integrals is presented along with the hybrid and exchange integrals that are ignored in zero differential overlap methods.

  18. 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.

  19. Particle-Particle Hole-Hole Tda - and Beyond - for the Nuclear Pairing Hamiltonian

    NASA Astrophysics Data System (ADS)

    Molique, Hervé; Dudek, Jerzy

    A comparison of different seniority zero solutions to the picket-fence model for the nuclear pairing hamiltonian problem is performed. These solutions are calculated, in the normal regime, within the self-consistent Random Phase Approximation (SCRPA) and various simplifications of this formalism, and also with the Tamm-Dancoff approach in the particle-particle-hole-hole channel (pphh-TDA). The latter formalism represents a first approximation to the earlier developped so-called P-Symmetric Many-Body method (PSY-MB). In the superfluid regime, the solutions are compared with the BCS results. By comparing the results with the exact ones, obtained by the Richardson method, it is shown that the PSY-MB method provides a powerful tool in solving the problem with good accuracy both in the normal and the superfluid regime, for single-particle space sizes adapted to typical nuclear structure calculations.

  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. Nuclear motion effects on the density matrix of crystals: an ab initio Monte Carlo harmonic approach.

    PubMed

    Pisani, Cesare; Erba, Alessandro; Ferrabone, Matteo; Dovesi, Roberto

    2012-07-28

    In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated.

  2. 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.

  3. 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.

  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. Disentangling Peptide Configurations via Two-Dimensional Electronic Spectroscopy: Ab Initio Simulations Beyond the Frenkel Exciton Hamiltonian.

    PubMed

    Nenov, Artur; Rivalta, Ivan; Cerullo, Giulio; Mukamel, Shaul; Garavelli, Marco

    2014-02-20

    Two-dimensional (2D) optical spectroscopy techniques based on ultrashort laser pulses have been recently extended to the optical domain in the ultraviolet (UV) spectral region. UV-active aromatic side chains can thus be used as local highly specific markers for tracking dynamics and structural rearrangements of proteins. Here we demonstrate that 2D electronic spectra of a model proteic system, a tetrapeptide with two aromatic side chains, contain enough structural information to distinguish between two different configurations with distant and vicinal side chains. For accurate simulations of the 2DUV spectra in solution, we combine a quantum mechanics/molecular mechanics approach based on wave function methods, accounting for interchromophores coupling and environmental effects, with nonlinear response theory. The proposed methodology reveals effects, such as charge transfer between vicinal aromatic residues that remain concealed in conventional exciton Hamiltonian approaches. Possible experimental setups are discussed, including multicolor experiments and signal manipulation techniques for limiting undesired background contributions and enhancing 2DUV signatures of specific electronic couplings.

  6. 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.

  7. Summation of Parquet diagrams as an ab initio method in nuclear structure calculations

    SciTech Connect

    Bergli, Elise; Hjorth-Jensen, Morten

    2011-05-15

    Research Highlights: > We present a Green's function based approach for doing ab initio nuclear structure calculations. > In particular the sum the subset of so-called Parquet diagrams. > Applying the theory to a simple but realistic model, results in good agreement with other ab initio methods. > This opens up for ab initio calculations for medium-heavy nuclei. - Abstract: In this work we discuss the summation of the Parquet class of diagrams within Green's function theory as a possible framework for ab initio nuclear structure calculations. The theory is presented and some numerical details are discussed, in particular the approximations employed. We apply the Parquet method to a simple model, and compare our results with those from an exact solution. The main conclusion is that even at the level of approximation presented here, the results shows good agreement with other comparable ab initio approaches.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. Hamiltonian purification

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

    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 {h1, …, hm} operating on a d-dimensional quantum system ℋd, the problem consists in identifying a set of commuting Hamiltonians {H1, …, Hm} operating on a larger dE-dimensional system ℋdE which embeds ℋd as a proper subspace, such that hj = PHjP with P being the projection which allows one to recover ℋd from ℋdE. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for 𝔲(d) are provided.

  13. Critical nuclear charge and shape resonances for the two-electron Hamiltonian

    NASA Astrophysics Data System (ADS)

    Yan, Z.-C.; Ho, Y. K.

    2015-09-01

    The hydrogen negative ion H$^-$ is the simplest two-electron system that exists in nature. This system is not only important in astrophysics but it also serves as an ideal ground to study electron-electron correlations. The peculiar balance of the correlations between the two electrons with the interaction of electron-nucleus in H$^-$ makes this system to have only two bound states, one being the ground state $1s^2\\,^{1}\\!S^e$ and the other the doubly-excited metastable state $2p^2\\,^{3}\\!P^e$ embedded below the hydrogen $n=2$ threshold. Here we report a calculation for the $2p^2\\,^{3}\\!P^e$ state of H$^-$ that yields the energy eigenvalue $E=-0.125\\,355\\,451\\,242\\,864\\,058\\,376\\,012\\,313\\,25(2)$, in atomic units. Our result substantially improves the best available result by 16 orders of magnitude. We further study the critical nuclear charge $Z_{\\rm cr}$, the minimum value of nuclear charge $Z$ that is required to bind a nucleus and two electrons. Our determination of $Z_{\\rm cr}$ for the $2p^2\\,^{3}\\!P^e$ state of two-electron systems is $Z_{\\rm cr}=0.994\\,781\\,292\\,240\\,366\\,246\\,3(1)$, corresponding to $1/Z_{\\rm cr}= 1.005\\,246\\,085\\,546\\,985\\,509\\,4(1)$, which improves the best published value of $Z_{\\rm cr}$ by about 10 orders of magnitude. We further investigate in a definitive way the unexplored regime of $Z < Z_{\\rm cr}$ using the method of complex scaling and establish precise shape resonance poles for the state of $2p^2\\,^{3}\\!P^e$ in the complex energy plane.

  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. 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.

  16. Quantum wavepacket ab initio molecular dynamics: an approach for computing dynamically averaged vibrational spectra including critical nuclear quantum effects.

    PubMed

    Sumner, Isaiah; Iyengar, Srinivasan S

    2007-10-18

    We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.

  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. 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.

  19. 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.

  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.

  1. 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

  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. 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.

  6. 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)

  7. 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.

  8. 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.

  9. Stochastic surrogate Hamiltonian

    SciTech Connect

    Katz, Gil; Kosloff, Ronnie; Gelman, David; Ratner, Mark A.

    2008-07-21

    The surrogate Hamiltonian is a general scheme to simulate the many body quantum dynamics composed of a primary system coupled to a bath. The method has been based on a representative bath Hamiltonian composed of two-level systems that is able to mimic the true system-bath dynamics up to a prespecified time. The original surrogate Hamiltonian method is limited to short time dynamics since the size of the Hilbert space required to obtain convergence grows exponentially with time. By randomly swapping bath modes with a secondary thermal reservoir, the method can simulate quantum dynamics of the primary system from short times to thermal equilibrium. By averaging a small number of realizations converged values of the system observables are obtained avoiding the exponential increase in resources. The method is demonstrated for the equilibration of a molecular oscillator with a thermal bath.

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

    PubMed

    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. PMID:27176426

  11. 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.

  12. 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.

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

    NASA Astrophysics Data System (ADS)

    Scherrer, Arne; Vuilleumier, Rodolphe; Sebastiani, Daniel

    2016-08-01

    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.

  14. The Role of Anharmonicity and Nuclear Quantum Effects in the Pyridine Molecular Crystal: An ab initio Molecular Dynamics Study

    NASA Astrophysics Data System (ADS)

    Ko, Hsin-Yu; Distasio, Robert A., Jr.; Santra, Biswajit; Car, Roberto

    Molecular crystal structure prediction has posed a substantial challenge to first-principles methods and requires sophisticated electronic structure methods to determine the stabilities of nearly degenerate polymorphs. In this work, we demonstrate that the anharmonicity from van der Waals interactions is relevant to the finite-temperature structures of pyridine and pyridine-like molecular crystals. Using such an approach, we find that the equilibrium structures are well captured with classical ab initio molecular dynamics (AIMD), despite the presence of light atoms such as hydrogen. Employing path integral AIMD simulations, we demonstrate that the success of classical AIMD results from a separation of nuclear quantum effects between the intermolecular and intramolecular degrees of freedom. In this separation, the quasiclassical and anharmonic intermolecular degrees of freedom determine the equilibrium structure, while the quantum and harmonic intramolecular degrees of freedom are averaging to the correct intramolecular structure. This work has been supported by the Department of Energy under Grants No. DE-FG02-05ER46201 and DE-SC0008626.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Quantization of Inequivalent Classical Hamiltonians.

    ERIC Educational Resources Information Center

    Edwards, Ian K.

    1979-01-01

    Shows how the quantization of a Hamiltonian which is not canonically related to the energy is ambiguous and thereby results in conflicting physical interpretations. Concludes that only the Hamiltonian corresponding to the total energy of a classical system or one canonically related to it is suitable for consistent quantization. (GA)

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. Nuclear polarization corrections to the μ4He+ Lamb shift.

    PubMed

    Ji, C; Nevo Dinur, N; Bacca, S; Barnea, N

    2013-10-01

    Stimulated by the proton radius conundrum, measurements of the Lamb shift in various light muonic atoms are planned at PSI. The aim is to extract the rms charge radius with high precision, limited by the uncertainty in the nuclear polarization corrections. We present an ab initio calculation of the nuclear polarization for μ(4)He(+) leading to an energy correction in the 2S-2P transitions of δ(pol)(A)=-2.47 meV ±6%. We use two different state-of-the-art nuclear Hamiltonians and utilize the Lorentz integral transform with hyperspherical harmonics expansion as few-body methods. We take into account the leading multipole contributions, plus Coulomb, relativistic, and finite-nucleon-size corrections. Our main source of uncertainty is the nuclear Hamiltonian, which currently limits the attainable accuracy. Our predictions considerably reduce the uncertainty with respect to previous estimates and should be instrumental to the μ(4)He(+) experiment planned for 2013.

  7. 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.

  8. Effective Hamiltonians for phosphorene and silicene

    DOE PAGES

    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

  9. 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.

  10. 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.

  11. 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.

  12. Hamiltonian formulation of general relativity.

    NASA Astrophysics Data System (ADS)

    Teitelboim, Claudio

    The following sections are included: * INTRODUCTION * HAMILTONIAN FORMULATION OF GAUGE THEORIES (PRE-BRST) * BRST HAMILTONIAN FORMULATION OF GAUGE THEORIES * DYNAMICS OF GRAVITATIONAL FIELD * DOES THE HAMILTONIAN VANISH? GENERAL COVARIANCE AS AN "ORDINARY" GAUGE INVARIANCE * GENERALLY COVARIANT SYSTEMS * TIME AS A CANONICAL VARIABLE. ZERO HAMILTONIAN * Parametrized Systems * Zero Hamiltonian * Parametrization and Explicit Time Dependence * TIME REPARAMETRIZATION INVARIANCE * Form of Gauge Transformations * Must the Hamiltonian be Zero for a Generally Covariant System? * Simple Example of a Generally Covariant System with a Nonzero Hamiltonian * "TRUE DYNAMICS" VERSUS GAUGE TRANSFORMATIONS * Interpretation of the Formalism * Reduced Phase Space * MUST TIME FLOW? * GAUGE INDEPENDENCE OF PATH INTEGRAL FOR A PARAMETRIZED SYSTEM ILLUSTRATED. EQUIVALENCE OF THE GAUGES t = τ AND t = 0 * Reduced Phase Space Transition Amplitude as a Reduced Phase Space Path Integral * Canonical Gauge Conditions * Gauge t = 0 * Gauge t α τ * BRST CHARGE OF GRAVITATIONAL FIELD * ELEMENTS OF BRST THEORY * THE GHOST, YOU'VE COME A LONG WAY BABY * Introduction * Quantum mechanics, the art of finding and combining simple elementary processes * Ghosts necessary to keep elementary processes simple * BRST symmetry: ghosts and matter become different components of single geometrical object * BRST SYMMETRY IN CLASSICAL MECHANICS * Ghosts have role in classical mechanics * Gauge invariance and constraints * Classical mechanics over Grassmann algebra necessary * Higher order structure functions * Rank defined. Open algebras * Ghosts. Ghost number. BRST generator as generating function for structure functions * A belianization of constraints. Existence of Ω * Uniqueness of Ω * Classical BRST cohomology * QUANTUM BRST THEORY * States and operators * Ghost number * BRST invariant states * Quantum BRST cohomology * Equivalence of the BRST physical subspace with the conventional gauge

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. First principles of Hamiltonian medicine.

    PubMed

    Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

    2014-05-19

    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.

  18. 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

  19. 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.

  20. Invariant metrics for Hamiltonian systems

    SciTech Connect

    Rangarajan, G. ); Dragt, A.J. ); Neri, F. )

    1991-05-01

    In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs.

  1. 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.

  2. 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.

  3. 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.

  4. 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…

  5. An effective Hamiltonian for an electronically excited solute in a polarizable molecular solvent

    NASA Astrophysics Data System (ADS)

    Maslen, P. E.; Faeder, J.; Parson, R.

    An effective Hamiltonian suitable for non-adiabatic molecular dynamics simulations is derived for the low-lying electronic states of a molecular ion interacting with an assembly of polarizable solvent molecules. The Hamiltonian includes both induction and low-frequency dispersion effects. It is based on a molecular treatment of the solvent, but is similar to effective Hamiltonians that treat the solvent as a dielectric continuum. The electronic structure of the solute is described in a space defined by the low-lying electronic states of the isolated molecule, and no assumptions are made about the form of the basis states. The effective Hamiltonian uses distributed multipoles and distributed transition multipoles, both of which may be obtained from ab initio calculations, to describe the charge distribution and polarizability of the molecular ion.

  6. Three-cluster dynamics within an ab initio framework

    DOE PAGES

    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

  7. 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.

  8. 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.

  9. 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…

  10. 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.

  11. Thermodynamics from a scaling Hamiltonian

    NASA Astrophysics Data System (ADS)

    Del Pino, L. A.; Troncoso, P.; Curilef, S.

    2007-11-01

    There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both extensive and nonextensive thermodynamic perspectives. We use a model, whose Hamiltonian takes into account spins ferromagnetically coupled in a chain via a power law that decays at large interparticle distance r as 1/rα for α⩾0 . Here, we review old nonextensive scaling. In addition, we propose a Hamiltonian scaled by 2((N/2)1-α-1)/(1-α) that explicitly includes symmetry of the lattice and dependence on the size N of the system. The approach enabled us to improve upon previous results. A numerical test is conducted through Monte Carlo simulations. In the model, periodic boundary conditions are adopted to eliminate surface effects.

  12. 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.

  13. 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.

  14. 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.

  15. On the representation of coupled adiabatic potential energy surfaces using quasi-diabatic Hamiltonians: A distributed origins expansion approach

    NASA Astrophysics Data System (ADS)

    Zhu, Xiaolei; Yarkony, David R.

    2012-05-01

    In two previous papers we have introduced a method to generate coupled quasi-diabatic Hamiltonians (Hd) that are capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, two new synergistic features are introduced. Firstly, the functional form of Hd is generalized. Rather than requiring there to be a low energy point of high symmetry to serve as the unique origin, functions centered on points distributed in nuclear coordinate space are used in the polynomials that comprise the matrix elements in Hd. The use of functions with distributed origins, allows reproduction of the ab initio data with lower order expansions, and offers the possibility of describing multichannel dissociation. The fitting algorithm is combined with a three-step procedure in which the domain of Hd is extended from a core set of nuclear configurations to a region of nuclear coordinate space appropriate for nuclear dynamics, with a prescribed accuracy. This significant extension of the domain of definition compared to our original work, which is facilitated by the distributed origin approach, is achieved largely through the use of surface hopping trajectories. The 1,21A states of NH3, which provide an archetypical example of nonadiabatic dynamics, are used to demonstrate the utility of this approach. The representation describes 21 points on the 11A-21A seam of conical intersection and their local topography flawlessly and on the entire domain, the electronic structure data is represented to an accuracy of 77.00 (46.90) cm-1, as measured by the root mean square (mean unsigned) error for energies lower than 50 000 cm-1. This error is a factor of 10 lower than that of the most accurate representation of high quality ab initio data, on a comparable domain, previously reported for this system.

  16. 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.

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

    DOE PAGES

    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

  18. 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

  19. Hamiltonian Structure: What Good Is It?

    NASA Astrophysics Data System (ADS)

    Morrison, P. J.

    2002-11-01

    Plasma physics, being a virtual bastion of classical physics, is intimately associated with the Hamiltonian structure that underlies it. Consequently, the field is riddled with Hamiltonian dynamics problems of finite and infinite degrees of freedom. Manifestations of finite degree-of-freedom Hamiltonian structure occur, for example, in the way we describe particle orbits and magnetic field lines, while manifestations of infinite degree-of-freedom Hamiltonian structure are the MHD energy principle and Gardner's stability theorem of Vlasov theory. In this review, I will describe how the Hamiltonian (or Lagrangian) formulation provides a unifying framework for describing plasmas, and I will review several types of calculations done by various researchers for which the Hamiltonian structure is an integral or essential part.

  20. Elements of (Super-)Hamiltonian Formalism

    NASA Astrophysics Data System (ADS)

    Nersessian, A.

    In these lectures we discuss some basic aspects of Hamiltonian formalism, which usually do not appear in standard textbooks on classical mechanics for physicists. We pay special attention to the procedure of Hamiltonian reduction illustrating it by the examples related to Hopf maps. Then we briefly discuss the supergeneralization(s) of the Hamiltonian formalism and present some simple models of supersymmetric mechanics on Kähler manifolds.

  1. 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.

  2. A Hamiltonian approach to Thermodynamics

    NASA Astrophysics Data System (ADS)

    Baldiotti, M. C.; Fresneda, R.; Molina, C.

    2016-10-01

    In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac's theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases.

  3. Bohr Hamiltonian with time-dependent potential

    NASA Astrophysics Data System (ADS)

    Naderi, L.; Hassanabadi, H.; Sobhani, H.

    2016-04-01

    In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.

  4. 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. ).

  5. Ab initio calculations of NMR shielding of Sc3+, Y3+ and La3+ ions in the water solution and 45Sc, 89Y, 138La and 139La nuclear magnetic dipole moments

    NASA Astrophysics Data System (ADS)

    Antušek, Andrej; Šulka, Martin

    2016-09-01

    Ab initio calculations of NMR shielding constants for water solvated trivalent scandium, yttrium and lanthanum cations are presented. The solvent effects of the first solvation shell are calculated explicitly using coupled cluster theory. The relativistic correction is calculated at non-correlated level. The influence of the second solvation shell is estimated at DFT level. The final NMR shielding constants define new NMR absolute shielding scales of scandium, yttrium and lanthanum and these shieldings were used for re-derivation of the nuclear magnetic dipole moments, eliminating long standing errors of ≈ 0.005μN .

  6. Extended Hamiltonian approach to continuous tempering

    NASA Astrophysics Data System (ADS)

    Gobbo, Gianpaolo; Leimkuhler, Benedict J.

    2015-06-01

    We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.

  7. 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.

  8. The gravity duals of modular Hamiltonians

    NASA Astrophysics Data System (ADS)

    Jafferis, Daniel L.; Suh, S. Josephine

    2016-09-01

    In this work, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region.

  9. Persistence of hyperbolic tori in Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Li, Yong; Yi, Yingfei

    We generalize the well-known result of Graff and Zehnder on the persistence of hyperbolic invariant tori in Hamiltonian systems by considering non-Floquet, frequency varying normal forms and allowing the degeneracy of the unperturbed frequencies. The preservation of part or full frequency components associated to the degree of non-degeneracy is considered. As applications, we consider the persistence problem of hyperbolic tori on a submanifold of a nearly integrable Hamiltonian system and the persistence problem of a fixed invariant hyperbolic torus in a non-integrable Hamiltonian system.

  10. Braiding fluxes in Pauli Hamiltonian

    SciTech Connect

    Kenneth, O. Avron, J.E.

    2014-10-15

    Aharonov and Casher showed that Pauli Hamiltonians in two dimensions have gapless zero modes. We study the adiabatic evolution of these modes under the slow motion of N fluxons with fluxes Φ{sub a}∈R. The positions, r{sub a}∈R{sup 2}, of the fluxons are viewed as controls. We are interested in the holonomies associated with closed paths in the space of controls. The holonomies can sometimes be abelian, but in general are not. They can sometimes be topological, but in general are not. We analyse some of the special cases and some of the general ones. Our most interesting results concern the cases where holonomy turns out to be topological which is the case when all the fluxons are subcritical, Φ{sub a}<1, and the number of zero modes is D=N−1. If N≥3 it is also non-abelian. In the special case that the fluxons carry identical fluxes the resulting anyons satisfy the Burau representations of the braid group.

  11. 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.

  12. 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.

  13. Preparing topologically ordered states by Hamiltonian interpolation

    NASA Astrophysics Data System (ADS)

    Ni, Xiaotong; Pastawski, Fernando; Yoshida, Beni; König, Robert

    2016-09-01

    We study the preparation of topologically ordered states by interpolating between an initial Hamiltonian with a unique product ground state and a Hamiltonian with a topologically degenerate ground state space. By simulating the dynamics for small systems, we numerically observe a certain stability of the prepared state as a function of the initial Hamiltonian. For small systems or long interpolation times, we argue that the resulting state can be identified by computing suitable effective Hamiltonians. For effective anyon models, this analysis singles out the relevant physical processes and extends the study of the splitting of the topological degeneracy by Bonderson (2009 Phys. Rev. Lett. 103 110403). We illustrate our findings using Kitaev’s Majorana chain, effective anyon chains, the toric code and Levin-Wen string-net models.

  14. 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.

  15. Ab initio study of radium monofluoride (RaF) as a candidate to search for parity- and time-and-parity-violation effects

    NASA Astrophysics Data System (ADS)

    Kudashov, A. D.; Petrov, A. N.; Skripnikov, L. V.; Mosyagin, N. S.; Isaev, T. A.; Berger, R.; Titov, A. V.

    2014-11-01

    Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of P - and T -and-P -violating interactions. The parameters of P - and T ,P -odd terms of the spin-rotational Hamiltonian have been calculated for the 2Σ electronic ground state of the 223RaF molecule. They include the Wa parameter, which is critical in the experimental search for nuclear anapole moment, and the parameters Wd and WSP required to obtain restrictions on the electric dipole moment of the electron and T ,P -odd scalar-pseudoscalar interactions, respectively. The parameter X corresponding to the "volume effect" in the T ,P -odd interaction of the 223Ra nuclear Schiff moment with electronic shells of RaF has also been computed. Spectroscopic and hyperfine structure constants for 223RaF and 223Ra+ have been computed as well, demonstrating the accuracy of the methods employed.

  16. 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.

  17. 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.

  18. 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

  19. Hamiltonian theory of symmetric optical network transforms

    NASA Astrophysics Data System (ADS)

    Törmä, Päivi; Stenholm, Stig

    1995-12-01

    We discuss the theory of extracting an interaction Hamiltonian from a preassigned unitary transformation of quantum states. Such a procedure is of significance in quantum computations and other optical information processing tasks. We particularize the problem to the construction of totally symmetric 2N ports as introduced by Zeilinger and his collaborators [A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, and D. M. Greenberger, in Fundamental Aspects of Quantum Theory, edited by J. Anandan and J. J. Safko (World Scientific, Singapore, 1994)]. These are realized by the discrete Fourier transform, which simplifies the construction of the Hamiltonian by known methods of linear algebra. The Hamiltonians found are discussed and alternative realizations of the Zeilinger class transformations are presented. We briefly discuss the applicability of the method to more general devices.

  20. 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.

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. Charge transfer in strongly correlated systems: An exact diagonalization approach to model Hamiltonians

    SciTech Connect

    Schöppach, Andreas; Gnandt, David; Koslowski, Thorsten

    2014-04-07

    We study charge transfer in bridged di- and triruthenium complexes from a theoretical and computational point of view. Ab initio computations are interpreted from the perspective of a simple empirical Hamiltonian, a chemically specific Mott-Hubbard model of the complexes' π electron systems. This Hamiltonian is coupled to classical harmonic oscillators mimicking a polarizable dielectric environment. The model can be solved without further approximations in a valence bond picture using the method of exact diagonalization and permits the computation of charge transfer reaction rates in the framework of Marcus' theory. In comparison to the exact solution, the Hartree-Fock mean field theory overestimates both the activation barrier and the magnitude of charge-transfer excitations significantly. For triruthenium complexes, we are able to directly access the interruthenium antiferromagnetic coupling strengths.

  9. Theoretical gas to liquid shift of (15)N isotropic nuclear magnetic shielding in nitromethane using ab initio molecular dynamics and GIAO/GIPAW calculations.

    PubMed

    Gerber, Iann C; Jolibois, Franck

    2015-05-14

    Chemical shift requires the knowledge of both the sample and a reference magnetic shielding. In few cases as nitrogen (15N), the standard experimental reference corresponds to its liquid phase. Theoretical estimate of NMR magnetic shielding parameters of compounds in their liquid phase is then mandatory but usually replaced by an easily-get gas phase value, forbidding direct comparisons with experiments. We propose here to combine ab initio molecular dynamic simulations with the calculations of magnetic shielding using GIAO approach on extracted cluster's structures from MD. Using several computational strategies, we manage to accurately calculate 15N magnetic shielding of nitromethane in its liquid phase. Theoretical comparison between liquid and gas phase allows us to extrapolate an experimental value for the 15N magnetic shielding of nitromethane in gas phase between -121.8 and -120.8 ppm.

  10. 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...

  11. 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.

  12. Bifurcations and safe regions in open Hamiltonians

    NASA Astrophysics Data System (ADS)

    Barrio, R.; Blesa, F.; Serrano, S.

    2009-05-01

    By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Hénon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.

  13. Hamiltonian gadgets with reduced resource requirements

    NASA Astrophysics Data System (ADS)

    Cao, Yudong; Babbush, Ryan; Biamonte, Jacob; Kais, Sabre

    2015-01-01

    Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental systems are typically limited to restricted forms of two-body interactions. Therefore, universal adiabatic quantum computation requires a method for approximating quantum many-body Hamiltonians up to arbitrary spectral error using at most two-body interactions. Hamiltonian gadgets, introduced around a decade ago, offer the only current means to address this requirement. Although the applications of Hamiltonian gadgets have steadily grown since their introduction, little progress has been made in overcoming the limitations of the gadgets themselves. In this experimentally motivated theoretical study, we introduce several gadgets which require significantly more realistic control parameters than similar gadgets in the literature. We employ analytical techniques which result in a reduction of the resource scaling as a function of spectral error for the commonly used subdivision, three- to two-body and k -body gadgets. Accordingly, our improvements reduce the resource requirements of all proofs and experimental proposals making use of these common gadgets. Next, we numerically optimize these gadgets to illustrate the tightness of our analytical bounds. Finally, we introduce a gadget that simulates a Y Y interaction term using Hamiltonians containing only {X ,Z ,X X ,Z Z } terms. Apart from possible implications in a theoretical context, this work could also be useful for a first experimental implementation of these key building blocks by requiring less control precision without introducing extra ancillary qubits.

  14. Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors.

    SciTech Connect

    Wang, C.-x.; Accelerator Systems Division

    2006-01-01

    A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.

  15. 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.

  16. 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

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

    DOE PAGES

    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

  18. Ab initio valence-space theory for exotic nuclei

    NASA Astrophysics Data System (ADS)

    Holt, Jason

    2015-10-01

    Recent advances in ab initio nuclear structure theory have led to groundbreaking predictions in the exotic medium-mass region, from the location of the neutron dripline to the emergence of new magic numbers far from stability. Playing a key role in this progress has been the development of sophisticated many-body techniques and chiral effective field theory, which provides a systematic basis for consistent many-nucleon forces and electroweak currents. Within the context of valence-space Hamiltonians derived from the nonperturbative in-medium similarity renormalization group (IM-SRG) approach, I will discuss the importance of 3N forces in understanding and making new discoveries in the exotic sd -shell region. Beginning in oxygen, we find that the effects of 3N forces are decisive in explaining why 24O is the last bound oxygen isotope, validating first predictions of this phenomenon from several years ago. Furthermore, 3N forces play a key role in reproducing spectroscopy, including signatures of doubly magic 22,24O, and physics beyond the dripline. Similar improvements are obtained in new spectroscopic predictions for exotic fluorine and neon isotopes, where agreement with recent experimental data is competitive with state-of-the-art phenomenology. Finally, I will discuss first applications of the IM-SRG to effective valence-space operators, such as radii and E 0 transitions, as well as extensions to general operators crucial for our future understanding of electroweak processes, such as neutrinoless double-beta decay. This work was supported by NSERC and the NRC Canada.

  19. Dynamical and Hamiltonian Formulation of General Relativity

    NASA Astrophysics Data System (ADS)

    Giulini, Domenico

    Einstein's theory of General Relativity describes spacetime as a solution of a set of non-linear partial differential equations. These equations are initially not in the form of evolution equations and it is hence not clear how to formulate and solve initial-value problems, as would be physically highly desirable. In this contribution it will be shown how to cast Einstein's equations into the form of a constrained Hamiltonian system. This will allow to formulate and solve initial-value problems, integrate Einstein's equations by numerical codes, characterize dynamical degrees of freedom, and characterize isolated systems and their conserved quantities, like energy, momentum, and angular momentum. Moreover, this reformulation of General Relativity is also the starting point for various attempts to subject the gravitational field to the program of canonical quantization. The exposition given here is, to some degree, self contained. It attempts to comprehensively account for all the relevant geometric constructions, including the relevant symplectic geometry of constrained Hamiltonian systems.

  20. Quantum mechanical Hamiltonian models of discrete processes

    SciTech Connect

    Benioff, P.

    1981-03-01

    Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement.

  1. Conformal killing tensors and covariant Hamiltonian dynamics

    SciTech Connect

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

    2014-12-15

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

  2. Hamiltonian 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.

  3. Collective pairing Hamiltonian in the GCM approximation

    NASA Astrophysics Data System (ADS)

    Góźdź, A.; Pomorski, K.; Brack, M.; Werner, E.

    1985-08-01

    Using the generator coordinate method and the gaussian overlap approximation we derived the collective Schrödinger-type equation starting from a microscopic single-particle plus pairing hamiltonian for one kind of particle. The BCS wave function was used as the generator function. The pairing energy-gap parameter Δ and the gauge transformation anglewere taken as the generator coordinates. Numerical results have been obtained for the full and the mean-field pairing hamiltonians and compared with the cranking estimates. A significant role played by the zero-point energy correction in the collective pairing potential is found. The ground-state energy dependence on the pairing strength agrees very well with the exact solution of the Richardson model for a set of equidistant doubly-degenerate single-particle levels.

  4. Hamiltonian learning and certification using quantum resources.

    PubMed

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

    2014-05-16

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

  5. General formalism for singly thermostated Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    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.

  6. 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

  7. 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

  8. 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.

  9. 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.

  10. Flat Bi-Hamiltonian Structures and Invariant Densities

    NASA Astrophysics Data System (ADS)

    Izosimov, Anton

    2016-10-01

    A bi-Hamiltonian structure is a pair of Poisson structures {{P}}, {{Q}} which are compatible, meaning that any linear combination {α {P} + β {Q}} is again a Poisson structure. A bi-Hamiltonian structure {({P}, {Q})} is called flat if {{P}} and {{Q}} can be simultaneously brought to a constant form in a neighborhood of a generic point. We prove that a generic bi-Hamiltonian structure {({P}, {Q})} on an odd-dimensional manifold is flat if and only if there exists a local density which is preserved by all vector fields Hamiltonian with respect to {{P}}, as well as by all vector fields Hamiltonian with respect to {{Q}}.

  11. 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.

  12. 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.

  13. A Hamiltonian approach to the parametric excitation

    NASA Astrophysics Data System (ADS)

    Leroy, V.; Bacri, J.-C.; Hocquet, T.; Devaud, M.

    2006-05-01

    We propose a solution of the parametrically excited oscillator problem using the Hamiltonian formalism introduced by Glauber. The main advantage is that, within the framework of this formalism, the different possible approximations appear much more naturally than in the standard textbook presentation. Experiments on adiabatic and resonant parametric excitations of a pendulum are presented as an illustration, with particular attention being paid to the role played by the phase of the excitation.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. Nonintegrability of the classical Zeeman Hamiltonian

    NASA Astrophysics Data System (ADS)

    Kummer, M.; Saenz, A. W.

    1994-05-01

    We prove that the Hamiltonian H of the three dimensional hydrogen atom in a uniform static magnetic field B does not have an integral which (i) is real analytic on the phase space ℳ of the system; (ii) is in involution with the component M 3 of the angular momentum along B; (iii) is functionally independent of H and M 3 and (iv) has a meromorphic (single-valued) extension to the complexification of ℳ in ℂ6;. This follows from the fact that the Hamiltonian K M of two degrees of freedom obtained by fixing M 3 at certain nonzero values M and reducing H w.r. to the rotational symmetry about the magnetic field, has a complexification which is nonintegrable in the Ziglin sense. We prove this nonintegrability by demonstrating that for each such M the monodromy group of the normal variational equation along a certain complexified phase curve of K M is not Ziglin, using Churchill and Rod's adaptation of Kovacic's algorithm to the Ziglin analysis. Analogous arguments prove that the Hamiltonian of the Størmer problem is nonintegrable in the same sense.

  19. 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.

  20. 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.

  1. 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.

  2. A Treatment of the Renner Effect Using the MORBID Hamiltonian

    NASA Astrophysics Data System (ADS)

    Jensen, P.; Brumm, M.; Kraemer, W. P.; Bunker, P. R.

    1995-05-01

    For a triatomic molecule, we develop the rovibronic Hamiltonian, basis functions, and matrix elements necessary to allow us to determine the energy levels and wavefunctions in the situation that two potential energy surfaces touch at the linear configuration. The calculation of the rovibronic energy levels is complicated by the effect of the electronic angular momentum (the Renner effect), and while dealing with this problem we include spin-orbit coupling. We have written a computer program to implement the procedure. We base our approach on the MORBID Hamiltonian and computer program for an isolated electronic state [P. Jensen, J. Mol. Spectrosc.128, 478-501 (1988); J. Chem. Soc. Faraday Trans. 284, 1315-1340 (1988); in "Methods in Computational Molecular Physics" (S. Wilson and G. H. F. Diercksen, Eds.), Plenum Press, New York, 1992]. The approach leads to a very efficient computational procedure that will, in the future, allow us to make fittings to data in order to determine potential energy surfaces and spin-orbit coupling functions. In this paper we test the computer program implementing the new procedure by calculating rovibronic energies for the ã1A1 and b˜1B1 electronic states of the methylene radical CH2 on the basis of ab initio data by W. H. Green, Jr., N. C. Handy, P. J. Knowles, and S. Carter [J. Chem. Phys.94, 118-132 (1991)] and comparing our results with the rovibronic energy values obtained by these authors. We also report vibronic (i.e., J = 0) energies determined on the basis of a fitted potential for the ã1A1 state by P. Jensen and P. R. Bunker [J. Chem. Phys.89, 1327-1332 (1988)]. Comparison between these vibronic energies and MORBID results determined from the fitted ã-state potential throws significant doubt on previous estimations of the ã-state barrier to linearity by Dai and co-workers [see G. V. Hartland, D. Qin, and H.-L. Dal, J. Chem. Phys.98, 2469-2472 (1993) and references therein]. Finally, we construct quantitative correlation

  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. Nonabelian N = 2 superstrings: Hamiltonian structure

    NASA Astrophysics Data System (ADS)

    Isaev, A. P.; Ivanov, E. A.

    1991-04-01

    We examine the Hamiltonian structure of nonabelian N = 2 superstring models which are the supergroup manifold extensions of N = 2 Green-Schwarz superstring. We find the Kac-Moody and Virasoro type superalgebras of the relevant constraints and present elements of the corresponding quantum theory. A comparison with the type 2A Green-Schwarz superstring moving in a general curved 10-d supergravity background is also given. We find that nonabelian superstrings (for d = 10) present a particular case of this general system corresponding to a special choice of the background.

  5. 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.

  6. 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

  7. Hamiltonian approach to internal geophysical waves

    NASA Astrophysics Data System (ADS)

    Constantin, Adrian; Ivanov, Rossen; Iulian Martin, Calin

    2015-04-01

    We study the interaction between two-dimensional surface water waves and internal waves in a flow consisting of a lower layer with an impermeable flat bed and an overlying layer with a free surface. Both layers have constant density and in each the flow is of constant vorticity, driven by gravity and the Coriolis force. This system arises as a simplified model of the coupling of surface and internal geophysical waves. By examining the governing equations of the system we provide a Hamiltonian formulation. This allows for linear and nonlinear approximations.

  8. Spectral Theory of No-Pair Hamiltonians

    NASA Astrophysics Data System (ADS)

    Matte, Oliver; Stockmeyer, Edgardo

    We prove an HVZ theorem for a general class of no-pair Hamiltonians describing an atom or positively charged ion with several electrons in the presence of a classical external magnetic field. Moreover, we show that there exist infinitely many eigenvalues below the essential spectrum and that the corresponding eigenfunctions are exponentially localized. The novelty is that the electrostatic and magnetic vector potentials as well as a non-local exchange potential are included in the projection determining the model. As a main technical tool, we derive various commutator estimates involving spectral projections of Dirac operators with external fields. Our results apply to all coupling constants e2Z < 1.

  9. 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).

  10. Squeezed states from a quantum deformed oscillator Hamiltonian

    NASA Astrophysics Data System (ADS)

    Ramírez, R.; Reboiro, M.

    2016-03-01

    The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions.

  11. The Use of Ab Initio Wavefunctions in Line-Shape Calculations for Water Vapor

    NASA Astrophysics Data System (ADS)

    Gamache, Robert R.; Lamouroux, Julien; Schwenke, David W.

    2014-06-01

    In semi-classical line-shape calculations, the internal motions of the colliding pair are treated via quantum mechanics and the collision trajectory is determined by classical dynamics. The quantum mechanical component, i.e. the determination of reduced matrix elements (RME) for the colliding pair, requires the wavefunctions of the radiating and the perturbing molecules be known. Here the reduced matrix elements for collisions in the ground vibrational state of water vapor are calculated by two methods and compared. First, wavefunctions determined by diagonalizing an effective (Watson) Hamiltonian are used to calculate the RMEs and, second, the ab initio wavefunctions of Partridge and Schwenke are used. While the ground vibrational state will yield the best approximation of the wavefunctions from the effective Hamiltonian approach, this study clearly identifies problems for states not included in the fit of the Hamiltonian and for extrapolated states. RMEs determined using ab initio wavefunctions use ˜100000 times more computational time; however, all ro-vibrational interactions are included. Hence, the ab initio approach will yield better RMEs as the number of vibrational quanta exchanged in the optical transition increases, resulting in improvements in calculated half-widths and line shifts. It is important to note that even for pure rotational transitions the use of ab initio wavefunctions will yield improved results.

  12. A Comparison of Transfer Hamiltonian vs. DFT Methods in QM/CM Multi-Scale Modeling

    NASA Astrophysics Data System (ADS)

    Mallik, Aditi; Runge, Keith; Cheng, Hai-Ping; Dufty, James

    2004-11-01

    A method for a consistent embedding of a quantum (QM) domain in its classical (CM) environment has been developed for application in QM/CM simulations for multi-scale modeling. A benchmark system is considered: a silica nanorod in which a part of the rod is treated quantum mechanically and the rest is treated classically. This system is chosen because a full ab initio quantum data can be obtained for the entire rod to assess the quality of the proposed embedding technique. However, even at the quantum level each possible choice for the ab initio method entails approximations used to optimize the accuracy and speed of the calculations. Each approximation has its own advantages and limitations, but the embedding scheme should be insensitive to these. In order to test how robust our proposed embedding scheme is, we have chosen two different methods for the underlying quantum mechanical description. The first method used is the Transfer Hamiltonian (TH) Neglect of Diatomic Differential Overlap (NDDO) (Bartlett, 2003). The TH method uses a semi empirical Hamiltonian that has been parameterized to yield coupled cluster quality forces, thereby taking electron correlations into account like post-Hartree Fock methods. The second method used is the Born-Oppenheimer local spin density (Barnett and Landman, 1993) within density functional theory (DFT) and generalized gradient approximation (GGA). We use the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional. Here, the embedding method and resulting QM/CM composite rods using the two different ab initio methods are compared for the silica nanorod. It is found that the two quantum rods have noticeable differences, although the embedding method for the equilibrium composite rods is faithful to the underlying quantum method in each case. Nonequilibrium elastic properties are discussed briefly.

  13. Ab initio Approach to Effective Single-Particle Energies in Doubly Closed Shell Nuclei

    SciTech Connect

    Duguet, T.

    2012-01-01

    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.

  14. 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.

  15. Some Hamiltonian models of friction II

    SciTech Connect

    Egli, Daniel; Gang Zhou

    2012-10-15

    In the present paper we consider the motion of a very heavy tracer particle in a medium of a very dense, non-interacting Bose gas. We prove that, in a certain mean-field limit, the tracer particle will be decelerated and come to rest somewhere in the medium. Friction is caused by emission of Cerenkov radiation of gapless modes into the gas. Mathematically, a system of semilinear integro-differential equations, introduced in Froehlich et al. ['Some hamiltonian models of friction,' J. Math. Phys. 52(8), 083508 (2011)], describing a tracer particle in a dispersive medium is investigated, and decay properties of the solution are proven. This work is an extension of Froehlich et al. ['Friction in a model of hamiltonian dynamics,' Commun. Math. Phys. 315(2), 401-444 (2012)]; it is an extension because no weak coupling limit for the interaction between tracer particle and medium is assumed. The technical methods used are dispersive estimates and a contraction principle.

  16. The Hamiltonian description of incompressible fluid ellipsoids

    SciTech Connect

    Morrison, P.J. Lebovitz, Norman R.; Biello, Joseph A.

    2009-08-15

    We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac's procedure for incorporating constraints. First, the Poisson bracket of moments of the unconstrained Euler equations is used to construct a Dirac bracket, with Casimir invariants corresponding to volume preservation and incompressibility. Second, the Dirac procedure is applied directly to the continuum, noncanonical Poisson bracket that describes the compressible Euler equations, and the moment reduction is applied to this bracket. When the Hamiltonian can be expressed exactly in terms of these moments, a closure is achieved and the resulting finite-dimensional Hamiltonian system provides exact solutions of Euler's equations. This is shown to be the case for the classical, incompressible Riemann ellipsoids, which have velocities that vary linearly with position and have constant density within an ellipsoidal boundary. The incompressible, noncanonical Poisson bracket differs from its counterpart for the compressible case in that it is not of Lie-Poisson form.

  17. 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.

  18. Thermalization Time Bounds for Pauli Stabilizer Hamiltonians

    NASA Astrophysics Data System (ADS)

    Temme, Kristan

    2016-09-01

    We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))} , where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.

  19. A New Scheme of Integrability for (bi)Hamiltonian PDE

    NASA Astrophysics Data System (ADS)

    De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

    2016-10-01

    We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

  20. 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.

  1. 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.

  2. A New Scheme of Integrability for (bi)Hamiltonian PDE

    NASA Astrophysics Data System (ADS)

    De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

    2016-06-01

    We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

  3. Fractional Hamiltonian monodromy from a Gauss-Manin monodromy

    SciTech Connect

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

    2008-04-15

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

  4. 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. Covariant hamiltonian spin dynamics in curved space-time

    NASA Astrophysics Data System (ADS)

    d'Ambrosi, G.; Satish Kumar, S.; van Holten, J. W.

    2015-04-01

    The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.

  6. Ab Initio Calculated and Experimentally Measured Raman Spectra of Spodumene (LiAlSi2O6)

    NASA Astrophysics Data System (ADS)

    Stangarone, C.; Prencipe, M.; Mantovani, L.; Bersani, D.; Tribaudino, M.; Lottici, P. P.

    2014-06-01

    Polarization Raman measurements on spodumene enabled the identification of all 30 active modes (14 Ag and 16 Bg). Ab initio CRYSTAL14 calculations (WC1LYP hamiltonian) give very good agreement for frequencies (ǀΔǀ< 4.8 cm^-1) and intensities.

  7. 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.

  8. Omega-AB

    SciTech Connect

    Siirola, John D.; Slepoy, Alexander; Sprigg, Jr., James A.; Jorgensen, Craig R.; Selzler, Gene; Pryor, Richard J.

    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" concept 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.

  9. Omega-AB

    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

  10. 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.

  11. 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.

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

    PubMed

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

  14. Hamiltonian formalism of minimal massive gravity

    NASA Astrophysics Data System (ADS)

    Mahdavian Yekta, Davood

    2015-09-01

    In this paper, we study the three-dimensional minimal massive gravity (MMG) in the Hamiltonian formalism. At first, we define the canonical gauge generators as building blocks in this formalism and then derive the canonical expressions for the asymptotic conserved charges. The construction of a consistent asymptotic structure of MMG requires introducing suitable boundary conditions. In the second step, we show that the Poisson bracket algebra of the improved canonical gauge generators produces an asymptotic gauge group, which includes two separable versions of the Virasoro algebras. For instance, we study the Banados-Teitelboim-Zanelli (BTZ) black hole as a solution of the MMG field equations, and the conserved charges give the energy and angular momentum of the BTZ black hole. Finally, we compute the black hole entropy from the Cardy formula in the dual conformal field theory and show our result is consistent with the value obtained by using the Smarr formula from the holographic principle.

  15. Fourier series expansion for nonlinear Hamiltonian oscillators.

    PubMed

    Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac

    2010-06-01

    The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate. PMID:20866495

  16. 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

  17. 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.

  18. 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.

  19. A Hamiltonian five-field gyrofluid model

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

  20. Hamiltonian indices and rational spectral densities

    NASA Technical Reports Server (NTRS)

    Byrnes, C. I.; Duncan, T. E.

    1980-01-01

    Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

  1. 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.

  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. 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

  4. Non-self-adjoint hamiltonians defined by Riesz bases

    SciTech Connect

    Bagarello, F.; Inoue, A.; Trapani, C.

    2014-03-15

    We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.

  5. The Group of Hamiltonian Automorphisms of a Star Product

    NASA Astrophysics Data System (ADS)

    La Fuente-Gravy, Laurent

    2016-09-01

    We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham( M,∗), of a formal star product ∗ on a symplectic manifold ( M, ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.

  6. A HAMILTONIAN FORMULATION FOR SPIRAL-SECTOR ACCELERATORS.

    SciTech Connect

    BERG,J.S.

    2007-11-05

    I develop a formulation for Hamiltonian dynamics in an accelerator with magnets whose edges follow a spiral. I demonstrate using this Hamiltonian that a spiral FFAG can be made perfectly 'scaling'. I examine the effect of tilting an RF cavity with respect a radial line from the center of the machine, potentially with a different angle than the spiral of the magnets.

  7. Hamiltonian flow over deformations of ordinary double points

    NASA Astrophysics Data System (ADS)

    Akahori, Takao; Garfield, Peter M.

    2007-09-01

    We cannot see from from the point of view of the Hamiltonian mechanics, even though their CR structures are so different. Nevertheless, in this paper, by using a special kind of the Hamiltonian flow, we write down the Kodaira-Spencer class of this deformation, Mt is an element of primitive forms.

  8. 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.

  9. Continuous decomposition of quantum measurements via Hamiltonian feedback

    NASA Astrophysics Data System (ADS)

    Florjanczyk, Jan; Brun, Todd A.

    2015-12-01

    We characterize the set of generalized quantum measurements that can be decomposed into a continuous measurement process using a stream of probe qubits and a tunable interaction Hamiltonian. Each probe in the stream interacts weakly with the target quantum system and then is measured projectively in a standard basis. This measurement result is used in a closed feedback loop to tune the interaction Hamiltonian for the next probe. The resulting evolution is a stochastic process with the structure of a one-dimensional random walk. To maintain this structure and require that at long times the measurement outcomes be independent of the path, the allowed interaction Hamiltonians must lie in a restricted set such that the Hamiltonian terms on the target system form a finite-dimensional Jordan algebra. This algebraic structure of the interaction Hamiltonians yields a large class of generalized measurements that can be continuously performed by our scheme and we fully describe this set.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. Ab initio molecular dynamics.

    PubMed

    Laasonen, Kari

    2013-01-01

    In this chapter, an introduction to ab initio molecular dynamics (AIMD) has been given. Many of the basic concepts, like the Hellman-Feynman forces, the difference between the Car-Parrinello molecular dynamics and AIMD, have been explained. Also a very versatile AIMD code, the CP2K, has been introduced. On the application, the emphasis was on the aqueous systems and chemical reactions. The biochemical applications have not been discussed in depth.

  15. 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.

  16. Computational studies of competing phases in model Hamiltonians

    NASA Astrophysics Data System (ADS)

    Jiang, Mi

    Model Hamiltonians play an important role in our understanding of both quantum and classical systems, such as strongly correlated unconventional superconductivity, quantum magnetism, non-fermi liquid heavy fermion materials and classical magnetic phase transitions. The central problem is how models with many degrees of freedom choose between competing ground states, e.g. magnetic, superconducting, metallic, insulating as the degree of thermal and quantum fluctuations is varied. This dissertation focuses on the numerical investigation of several important model Hamiltonians. Specifically, we used the determinant Quantum Monte Carlo (DQMC) to study three Hubbard-like models: the Fermi-Hubbard model with two regions of different interaction strength, the Fermi-Hubbard model with a spin-dependent band structure, and the related periodic Anderson model (PAM). The first model used was to explore inter-penetration of metallic and Mott insulator physics across a Metal-Mott Insulator interface by computing the magnetic properties and spectral functions. As a minimal model of a half metallic magnet, the second model was used to explore the impact of on-site Hubbard interaction U, finite temperature, and an external (Zeeman) magnetic field on a bilayer tight-binding model with spin-dependent hybridization. We use PAM to study the Knight shift anomaly in heavy fermion materials found in Nuclear magnetic resonance (NMR) experiments and confirm several predictions of the two-fluid theory accounting for the anomaly. Another application of the Hubbard model described in this dissertation is the investigation on the effects of spin-dependent disorder on s-wave superconductors based on the attractive Hubbard model. Here we used the Bogoliubov-de Gennes (BdG) self-consistent approach instead of quantum simulations. The spin-dependent random potential was shown to induce distinct transitions at which the energy gap and average order parameter vanish, generating an intermediate gapless

  17. 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

  18. 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

  19. Stability of Gabor Frames Under Small Time Hamiltonian Evolutions

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  20. New Hamiltonian constraint operator for loop quantum gravity

    NASA Astrophysics Data System (ADS)

    Yang, Jinsong; Ma, Yongge

    2015-12-01

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

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

    SciTech Connect

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

    2010-04-15

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

  2. Dirac operators on quasi-Hamiltonian G-spaces

    NASA Astrophysics Data System (ADS)

    Song, Yanli

    2016-08-01

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

  3. Entangling capacities of noisy two-qubit Hamiltonians

    SciTech Connect

    Bandyopadhyay, Somshubhro; Lidar, Daniel A.

    2004-07-01

    We study the limits imposed by intrinsic fluctuations in system-control parameters on the ability of two-qubit (exchange) Hamiltonians to generate entanglement, starting from arbitrary initial states. We find three classes for Gaussian and Laplacian fluctuations. For the Ising and XYZ models there are qualitatively distinct, sharp entanglement-generation transitions, while the class of Heisenberg, XY, and XXZ Hamiltonians is capable of generating entanglement for any finite noise level. Our findings imply that exchange Hamiltonians are surprisingly robust in their ability to generate entanglement in the presence of noise, thus potentially reducing the need for quantum error correction.

  4. Uncertainty relation for non-Hamiltonian quantum systems

    SciTech Connect

    Tarasov, Vasily E.

    2013-01-15

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

  5. Similar Hamiltonian Between Avalanche-effect & Sociophysics

    NASA Astrophysics Data System (ADS)

    Maksoed, Ssi, Wh-

    2016-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

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

    SciTech Connect

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

    2008-10-13

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

  8. Linear transformation and oscillation criteria for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Zheng, Zhaowen

    2007-08-01

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

  9. Nonextensivity: From Low-Dimensional Maps to Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Tsallis, Constantino; Rapisarda, Andrea; Latora, Vito; Baldovin, Fulvio

    We present a brief pedagogical guided tour of the most recent applications of non-extensive statistical mechanics to well defined nonlinear dynamical systems, ranging from one-dimensional dissipative maps to many-body Hamiltonian systems.

  10. The Hamiltonian property of the flow of singular trajectories

    NASA Astrophysics Data System (ADS)

    Lokutsievskiy, L. V.

    2014-03-01

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

  11. Fractional Hamiltonian monodromy from a Gauss-Manin monodromy

    NASA Astrophysics Data System (ADS)

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

    2008-04-01

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

  12. Hamiltonian formulation of the modified Hasegawa-Mima equation

    NASA Astrophysics Data System (ADS)

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

    2014-02-01

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

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

    NASA Astrophysics Data System (ADS)

    Sakovich, Sergei

    2006-07-01

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

  14. Applications of Noether conservation theorem to Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Mouchet, Amaury

    2016-09-01

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

  15. Hyperbolic tori in Hamiltonian systems with slowly varying parameter

    SciTech Connect

    Medvedev, Anton G

    2013-05-31

    This paper looks at a Hamiltonian system which depends periodically on a parameter. For each value of the parameter the system is assumed to have a hyperbolic periodic solution. Using the methods in KAM-theory it is proved that if the Hamiltonian is perturbed so that the value of the parameter varies with constant small frequency, then the nonautonomous system will have hyperbolic 2-tori in the extended phase space. Bibliography: 12 titles.

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

    NASA Astrophysics Data System (ADS)

    Vitagliano, Luca

    2010-06-01

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

  17. Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD

    SciTech Connect

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

    1980-04-01

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

  18. Time and a physical Hamiltonian for quantum gravity.

    PubMed

    Husain, Viqar; Pawłowski, Tomasz

    2012-04-01

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

  19. Modelling spin Hamiltonian parameters of molecular nanomagnets.

    PubMed

    Gupta, Tulika; Rajaraman, Gopalan

    2016-07-12

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

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

    SciTech Connect

    K. HANSON

    2001-02-01

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

  1. A particle-field Hamiltonian in relativistic quantum electrodynamics

    NASA Astrophysics Data System (ADS)

    Arai, Asao

    2000-07-01

    We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space F≔[⊕4L2(R3)]⊗Frad, where Frad is the Fock space of the quantized radiation field in the Coulomb gauge, V is an external potential in which the Dirac particle moves, g is a photon-momentum cutoff function in the interaction between the Dirac particle and the quantized radiation field, and τ∈R is a deformation parameter connecting the Hamiltonian with the "dipole approximation" (τ=0) and the original Hamiltonian (τ=1). We first discuss the self-adjointness problem of Hτ(V,g). Then we consider Hτ≔Hτ(0,g), the Hamiltonian without the external potential. It is shown that, under a general condition on g, the closure of Hτ is unitarily equivalent to a direct integral ∫R3⊕Hτ(p)¯dp with a fiber Hamiltonian Hτ(p) acting in the four direct sum ⊕4Frad of Frad, physically the polaron Hamiltonian of the Dirac particle with total momentum p∈R3.

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

    NASA Astrophysics Data System (ADS)

    Pihajoki, Pauli

    2015-03-01

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

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

    NASA Astrophysics Data System (ADS)

    Fring, Andreas; Jones, Hugh; Znojil, Miloslav

    2008-06-01

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

  4. Nuclear binding near a quantum phase transition

    NASA Astrophysics Data System (ADS)

    Lee, Dean

    2016-03-01

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

  5. Ab initio calculations of free energy barriers for chemical reactions in solution: proton transfer in [FHF]-.

    PubMed

    Muller, R P; Warshel, A

    1996-01-01

    This paper describes a hybrid ab initio quantum mechanical/molecular mechanics (QM/MM) method for calculating activation free energies of chemical reactions in solution, using molecular mechanics force fields for the solvent and an ab initio technique that incorporates the potential from the solvent in its Hamiltonian for the solute. The empirical valence bond (EVB) method is used as a reference potential for the ab initio free energy calculation, and drives the reaction along the proper coordinate, thus overcoming problems encountered by direct attempts to use molecular orbital methods in calculations of activation free energies. The utility of our method is illustrated by calculating the activation free energy for proton transfer between fluoride ions in the [FHF]-system, in both polar and nonpolar solution.

  6. Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection

    NASA Astrophysics Data System (ADS)

    Tassi, E.

    2014-11-01

    We consider a simple electromagnetic gyrokinetic model for collisionless plasmas and show that it possesses a Hamiltonian structure. Subsequently, from this model we derive a two-moment gyrofluid model by means of a procedure which guarantees that the resulting gyrofluid model is also Hamiltonian. The first step in the derivation consists of imposing a generic fluid closure in the Poisson bracket of the gyrokinetic model, after expressing such bracket in terms of the gyrofluid moments. The constraint of the Jacobi identity, which every Poisson bracket has to satisfy, selects then what closures can lead to a Hamiltonian gyrofluid system. For the case at hand, it turns out that the only closures (not involving integro/differential operators or an explicit dependence on the spatial coordinates) that lead to a valid Poisson bracket are those for which the second order parallel moment, independently for each species, is proportional to the zero order moment. In particular, if one chooses an isothermal closure based on the equilibrium temperatures and derives accordingly the Hamiltonian of the system from the Hamiltonian of the parent gyrokinetic model, one recovers a known Hamiltonian gyrofluid model for collisionless reconnection. The proposed procedure, in addition to yield a gyrofluid model which automatically conserves the total energy, provides also, through the resulting Poisson bracket, a way to derive further conservation laws of the gyrofluid model, associated with the so called Casimir invariants. We show that a relation exists between Casimir invariants of the gyrofluid model and those of the gyrokinetic parent model. The application of such Hamiltonian derivation procedure to this two-moment gyrofluid model is a first step toward its application to more realistic, higher-order fluid or gyrofluid models for tokamaks. It also extends to the electromagnetic gyrokinetic case, recent applications of the same procedure to Vlasov and drift- kinetic systems.

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

    PubMed

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

    2013-09-10

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

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

    SciTech Connect

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

    2009-12-16

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

  9. Room Temperature Line Lists for CO_2 Isotopologues with AB Initio Computed Intensities

    NASA Astrophysics Data System (ADS)

    Zak, Emil; Tennyson, Jonathan; Polyansky, Oleg; Lodi, Lorenzo; Zobov, Nikolay Fedorovich; Tashkun, Sergey; Perevalov, Valery

    2016-06-01

    We report 13 room temperature line lists for all major CO_2 isotopologues, covering 0-8000 wn. These line lists are a response to the need for line intensities of high, preferably sub-percent, accuracy by remote sensing experiments. Our scheme encompasses nuclear motion calculations supported by critical reliability analysis of the generated line intensities. Rotation-vibration wavefunctions and energy levels are computed using DVR3D and a high quality semi-empirical potential energy surface (PES) [1], followed by computation of intensities using a fully ab initio dipole moment surface (DMS). Cross comparison of line lists calculated using pairs of high-quality PES's and DMS's is used to assess imperfections in the PES, which lead to unreliable transition intensities between levels involved in resonance interactions. Four line lists are computed for each isotopologue to quantify sensitivity to minor distortions of the PES/DMS. This provides an estimate of the contribution to the overall line intensity error introduced by the underlying PES. Reliable lines are benchmarked against recent state-of-the-art measurements [2] and HITRAN-2012 supporting the claim that the majority of line intensities for strong bands are predicted with sub-percent accuracy [3]. Accurate line positions are generated using an effective Hamiltonian [4]. We recommend use of these line lists for future remote sensing studies and inclusions in databases. X. Huang, D. W. Schwenke, S. A. Tashkun, T. J. Lee, J. Chem. Phys. 136, 124311, 2012. O. L. Polyansky, K. Bielska, M. Ghysels, L. Lodi, N. F. Zobov, J. T. Hodges, J. Tennyson, PRL, 114, 243001, 2015. E. Zak, J. Tennyson, O. L. Polyansky, L. Lodi, S. A. Tashkun, V. I. Perevalov, JQSRT, in press and to be submitted. S. A. Tashkun, V. I. Perevalov, R. R. Gamache, J. Lamouroux, JQSRT, 152, 45-73, 2015.

  10. Hamiltonian thermodynamics of three-dimensional dilatonic black holes

    NASA Astrophysics Data System (ADS)

    Dias, Gonçalo A. S.; Lemos, José P. S.

    2008-08-01

    The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free ω parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity (ω→∞), a dimensionally reduced cylindrical four-dimensional general relativity theory (ω=0), and a theory representing a class of theories (ω=-3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates {M,PM}, M being the mass parameter and PM its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schrödinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.

  11. Periodic pseudo-Hermitian Hamiltonian: Nonadiabatic geometric phase

    NASA Astrophysics Data System (ADS)

    Maamache, M.

    2015-09-01

    It is well known that Hermitian operators have real eigenvalues while non-Hermitian ones may have complex eigenvalues. Recently, numerical and analytical results indicated that the spectra of many non-Hermitians Hamiltonians H are indeed real if they are invariant under the combined action of self-adjoint parity P and time reversal T . The concept of a pseudo-Hermitian operator showed that the remarkable spectral properties of the P T -symmetric Hamiltonians follow from their pseudo-Hermiticity. It is possible to explain these observations by the concept of pseudo-Hermitian operators and to formulate completeness and orthonormality relations. Most of the effort has been devoted to study time-independent non-Hermitian systems. In this paper, we study the exactly solvable time-dependent periodic pseudo-Hermitian Hamiltonians. The method introduced, to make the reality of eigenvalues and phases, is based on a Floquet decomposition of the evolution operator UH(t ) =ZH(t ) exp(i MHt ) associated with the periodic pseudo-hermitian Hamiltonian H (t )=H (t +T ) . One of the results found in this paper concerns a calculation of Berry's phase for periodic, but not necessarily adiabatic, pseudo-Hermitian Hamiltonians. A two-level pseudo-Hermitian system is discussed as an illustrative example.

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

    PubMed

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

    2016-07-12

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

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

    SciTech Connect

    Han, Huixian; Li, Anyang; Guo, Hua

    2014-12-28

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

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

    PubMed

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

    2016-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  16. Discrete Dirac Structures and Implicit Discrete Lagrangian and Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Leok, Melvin; Ohsawa, Tomoki

    2010-07-01

    We present discrete analogues of Dirac structures and the Tulczyjew's triple by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving discrete analogues of implicit Lagrangian and Hamiltonian systems. In particular, this yields implicit nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange-d'Alembert-Pontryagin and Hamilton-d'Alembert variational principles, which provide an alternative derivation of the same set of integration algorithms. In addition to providing a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of Dirac mechanics, it provides a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators.

  17. Kinematics of fluid particles on the sea surface: Hamiltonian theory

    NASA Astrophysics Data System (ADS)

    Fedele, F.; Chandre, C.; Farazmand, M.

    2016-08-01

    We derive the John-Sclavounos equations describing the motion of a fluid particle on the sea surface from first principles using Lagrangian and Hamiltonian formalisms applied to the motion of a frictionless particle constrained on an unsteady surface. The main result is that vorticity generated on a stress-free surface vanishes at a wave crest when the horizontal particle velocity equals the crest propagation speed, which is the kinematic criterion for wave breaking. If this holds for the largest crest, then the symplectic two-form associated with the Hamiltonian dynamics reduces instantaneously to that associated with the motion of a particle in free flight, as if the surface did not exist. Further, exploiting the conservation of the Hamiltonian function for steady surfaces and traveling waves we show that particle velocities remain bounded at all times, ruling out the possibility of the finite-time blowup of solutions.

  18. Cluster expansion for ground states of local Hamiltonians

    NASA Astrophysics Data System (ADS)

    Bastianello, Alvise; Sotiriadis, Spyros

    2016-08-01

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

  19. Effective Hamiltonian for the hybrid double quantum dot qubit

    NASA Astrophysics Data System (ADS)

    Ferraro, E.; De Michielis, M.; Mazzeo, G.; Fanciulli, M.; Prati, E.

    2014-05-01

    Quantum dot hybrid qubits formed from three electrons in double quantum dots represent a promising compromise between high speed and simple fabrication for solid state implementations of single-qubit and two-qubits quantum logic ports. We derive the Schrieffer-Wolff effective Hamiltonian that describes in a simple and intuitive way the qubit by combining a Hubbard-like model with a projector operator method. As a result, the Hubbard-like Hamiltonian is transformed in an equivalent expression in terms of the exchange coupling interactions between pairs of electrons. The effective Hamiltonian is exploited to derive the dynamical behavior of the system and its eigenstates on the Bloch sphere to generate qubits operation for quantum logic ports. A realistic implementation in silicon and the coupling of the qubit with a detector are discussed.

  20. Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

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

  1. Two-Dimensional Quantum Hamiltonians with Shape Invariance Symmetry

    NASA Astrophysics Data System (ADS)

    Panahi, H.

    2008-10-01

    It is shown that the Casimir operator associated with the U(1) Lie derivative defined on the S 2= SU(2)/ U(1) base manifold, can be interpreted as Hamiltonians of a pair of scalar particle and scalar anti-particle with opposite charges over the S 2 manifold in the presence of a magnetic monopole located at its origin and an external electric field. Using the SU(2) representation, the spectra of these Hamiltonians have been obtained. It is also proved that these Hamiltonians are isospectral and having the shape invariance symmetry, i.e. they are supersymmetric partner of each other. Also the Dirac’s quantization of magnetic charge comes very naturally from the finiteness of the SU(2) representation.

  2. Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians.

    PubMed

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

    2015-06-01

    We present a combination of a downfolding many-body approach with auxiliary-field quantum Monte Carlo (AFQMC) calculations for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using frozen orbitals constructed adaptively from the solid environment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We apply the method to calculate the equation of state of cubic BN under ultrahigh pressure, and determine the spin gap in NiO, a challenging prototypical material with strong electron correlation effects. PMID:26196632

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

    PubMed Central

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

    2016-01-01

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

  4. Acoustic ray chaos and billiard system in Hamiltonian formalism (L)

    NASA Astrophysics Data System (ADS)

    Kawabe, Tetsuji; Aono, Keisuke; Shin-Ya, Masakazu

    2003-02-01

    The acoustic ray model with a strong connection to the billiard problem is presented within the framework of the Hamiltonian form. Introducing the background function into the sound-speed profile to confine all rays in a closed space, we obtain the ray trajectories consistent with a billiard picture. The ray chaos is observed when the perturbation due to inhomogeneity of the medium is taken into account. Based on the Poincaré surface of section and the Lyapunov exponents, we confirm that the chaos is characterized by almost the same structure as one observed in many Hamiltonian systems with two degrees of freedom.

  5. a Reference for Our Covariant Hamiltonian Boundary Term

    NASA Astrophysics Data System (ADS)

    Nester, James M.; Chen, Chiang-Mei; Liu, Jian-Liang; Sun, Gang

    2015-01-01

    Our covariant Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the quasi-local quantities: energy-momentum, angular-momentum/center-of-mass. The boundary term depends not only on the dynamical variables but also on their reference values, the latter determine the ground state (having vanishing quasi-local quantities). For our preferred boundary term for Einstein's GR we propose using 4D isometric matching and extremizing the energy to determine the "best matched" reference metric and connection values.

  6. Hamiltonian Determination with Restricted Access in Transverse Field Ising Chain

    NASA Astrophysics Data System (ADS)

    Fasihi, Mohammad Ali; Tanaka, Shu; Nakahara, Mikio; Kondo, Yasushi

    2011-04-01

    We propose a method to evaluate parameters in the Hamiltonian of the Ising chain under site-dependent transverse fields, with a proviso that we can control and measure one of the edge spins only. We evaluate the eigenvalues of the Hamiltonian and the time-evoultion operator exactly for a three-spin chain, from which we obtain the expectation values of σx of the first spin. The parameters are found from the peak positions of the Fourier transform of the expectation value. There are four assumptions in our method, which are mild enough to be satisfied in many physical systems.

  7. Bohr Hamiltonian with Eckart potential for triaxial nuclei

    NASA Astrophysics Data System (ADS)

    Naderi, L.; Hassanabadi, H.

    2016-05-01

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

  8. Nonclassical Degrees of Freedom in the Riemann Hamiltonian

    NASA Astrophysics Data System (ADS)

    Srednicki, Mark

    2011-09-01

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

  9. Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

    NASA Astrophysics Data System (ADS)

    Román-Roy, Narciso

    2009-11-01

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

  10. A characteristic number of Hamiltonian bundles over S2

    NASA Astrophysics Data System (ADS)

    Viña, Andrés

    2006-11-01

    Each loop ψ in the group Ham(M) of Hamiltonian diffeomorphisms of a symplectic manifold M determines a fibration E on S2, whose coupling class [V. Guillemin, L. Lerman, S. Sternberg, Symplectic Fibrations and Multiplicity Diagrams, Cambridge U.P., Cambridge, 1996] is denoted by c. If VTE is the vertical tangent bundle of E, we relate the characteristic number ∫Ec1(VTE)cn to the Maslov index of the linearized flow ψ and the Chern class c1(TM). We give the value of this characteristic number for loops of Hamiltonian symplectomorphisms of Hirzebruch surfaces.

  11. Generating functions for effective hamiltonians. Symmetry, topology, combinatorics

    SciTech Connect

    Zhilinskii, B. I.

    2012-01-15

    Recent developments associated with old technique of generating functions and invariant theory which I have started to apply to molecular problems due to my collaboration with Yu.F. Smirnov about 25 years ago are discussed. Three aspects are presented: the construction of diagonal in polyad quantum number effective resonant vibrational Hamiltonians using the symmetrized Hadamard product; the decomposition of the number of state generating function into regular and oscillatory contributions and its relation with Todd polynomials and topological characterization of energy bands; qualitative aspects of resonant oscillators and fractional monodromy as one of new generalizations of Hamiltonian monodromy.

  12. The detectability lemma and its applications to quantum Hamiltonian complexity

    NASA Astrophysics Data System (ADS)

    Aharonov, Dorit; Arad, Itai; Vazirani, Umesh; Landau, Zeph

    2011-11-01

    Quantum Hamiltonian complexity, an emerging area at the intersection of condensed matter physics and quantum complexity theory, studies the properties of local Hamiltonians and their ground states. In this paper we focus on a seemingly specialized technical tool, the detectability lemma (DL), introduced in the context of the quantum PCP challenge (Aharonov et al 2009 arXiv:0811.3412), which is a major open question in quantum Hamiltonian complexity. We show that a reformulated version of the lemma is a versatile tool that can be used in place of the celebrated Lieb-Robinson (LR) bound to prove several important results in quantum Hamiltonian complexity. The resulting proofs are much simpler, more combinatorial and provide a plausible path toward tackling some fundamental open questions in Hamiltonian complexity. We provide an alternative simpler proof of the DL that removes a key restriction in the original statement (Aharonov et al 2009 arXiv:0811.3412), making it more suitable for the broader context of quantum Hamiltonian complexity. Specifically, we first use the DL to provide a one-page proof of Hastings' result that the correlations in the ground states of gapped Hamiltonians decay exponentially with distance (Hastings 2004 Phys. Rev. B 69 104431). We then apply the DL to derive a simpler and more intuitive proof of Hastings' seminal one-dimensional (1D) area law (Hastings 2007 J. Stat. Mech. (2007) P8024) (both these proofs are restricted to frustration-free systems). Proving the area law for two and higher dimensions is one of the most important open questions in the field of Hamiltonian complexity, and the combinatorial nature of the DL-based proof holds out hope for a possible generalization. Indeed, soon after the first publication of the methods presented here, they were applied to derive exponential improvements to Hastings' result (Arad et al 2011, Aharonov et al 2011) in the case of frustration-free 1D systems. Finally, we also provide a more general

  13. Ab interno trabeculectomy.

    PubMed

    Pantcheva, Mina B; Kahook, Malik Y

    2010-10-01

    Anterior chamber drainage angle surgery, namely trabeculotomy and goniotomy, has been commonly utilized in children for many years. Its' reported success has ranged between 68% and 100% in infants and young children with congenital glaucoma. However, the long-term success of these procedures has been limited in adults presumably due to the formation of anterior synechiae (AS) in the postoperative phase. Recently, ab interno trabeculectomy with the Trabectome™ has emerged as a novel surgical approach to effectively and selectively remove and ablate the trabecular meshwork and the inner wall of the Schlemm's canal in an attempt to avoid AS formation or other forms of wound healing with resultant closure of the cleft. This procedure seems to have an appealing safety profile with respect to early hypotony or infection if compared to trabeculectomy or glaucoma drainage device implantation. This might be advantageous in some of the impoverish regions of the Middle East and Africa where patients experience difficulties keeping up with their postoperative visits. It is important to note that no randomized trial comparing the Trabectome to other glaucoma procedures appears to have been published to date. Trabectome surgery is not a panacea, however, and it is associated with early postoperative intraocular pressure spikes that may require additional glaucoma surgery as well as a high incidence of hyphema. Reported results show that postoperative intraocular pressure (IOP) remains, at best, in the mid-teen range making it undesirable in patients with low-target IOP goals. A major advantage of Trabectome surgery is that it does not preclude further glaucoma surgery involving the conjunctiva, such as a trabeculectomy or drainage device implantation. As prospective randomized long-term clinical data become available, we will be better positioned to elucidate the exact role of this technique in the glaucoma surgical armamentarium. PMID:21180426

  14. Autonomous Biological System (ABS) experiments.

    PubMed

    MacCallum, T K; Anderson, G A; Poynter, J E; Stodieck, L S; Klaus, D M

    1998-12-01

    Three space flight experiments have been conducted to test and demonstrate the use of a passively controlled, materially closed, bioregenerative life support system in space. The Autonomous Biological System (ABS) provides an experimental environment for long term growth and breeding of aquatic plants and animals. The ABS is completely materially closed, isolated from human life support systems and cabin atmosphere contaminants, and requires little need for astronaut intervention. Testing of the ABS marked several firsts: the first aquatic angiosperms to be grown in space; the first higher organisms (aquatic invertebrate animals) to complete their life cycles in space; the first completely bioregenerative life support system in space; and, among the first gravitational ecology experiments. As an introduction this paper describes the ABS, its flight performance, advantages and disadvantages.

  15. Quantifying the Effects of Higher Order Jahn-Teller Coupling Terms on a Quadratic Jahn-Teller Hamiltonian in the Case of NO_3 and Li_3.

    NASA Astrophysics Data System (ADS)

    Tran, Henry; Stanton, John F.; Miller, Terry A.

    2016-06-01

    The Jahn-Teller (JT) effect represents an enormous complication in the understanding of many molecules. We have been able to assign ˜20 vibronic bands in the tilde{A}^2E'' ← tilde{X}^2A_2' transition of NO_3 and determine the linear and quadratic JT coupling terms for ν_3 and ν_4, indicating strong and weak JT coupling along these modes respectively. It was found that the experimental results quantitatively disagree with ones determined from a vibronic Hamiltonian based on high-level ab-initio theory. Typical analyses of experimental data use the quadratic JT Hamiltonian because limited measured levels tend to allow fitting only to coupling terms up to quadratic JT coupling. Hence, these analyses may neglect key contributions from cubic and quartic terms. To quantify this limitation, we have fit artificial spectra calculated with up to fourth order terms in the potential using a quadratic JT Hamiltonian and analyzed the results. The parameters chosen for this analysis are determined from ab-initio potentials for the tilde{A} state of NO_3 and tilde{X} state of Li_3 to gain further insight on these molecules. Our initial results concerning the limitations of the quadratic JT Hamiltonian will be presented. T. Codd, M.-W. Chen, M. Roudjane, J. F. Stanton, and T. A. Miller. Jet cooled cavity ringdown spectroscopy of the tilde{A}^2E'' ← tilde{X}^2A'_2 Transition of the NO_3 Radical. J. Chem. Phys., 142:184305, 2015

  16. Ab initio downfolding for electron-phonon-coupled systems: Constrained density-functional perturbation theory

    NASA Astrophysics Data System (ADS)

    Nomura, Yusuke; Arita, Ryotaro

    2015-12-01

    We formulate an ab initio downfolding scheme for electron-phonon-coupled systems. In this scheme, we calculate partially renormalized phonon frequencies and electron-phonon coupling, which include the screening effects of high-energy electrons, to construct a realistic Hamiltonian consisting of low-energy electron and phonon degrees of freedom. We show that our scheme can be implemented by slightly modifying the density functional-perturbation theory (DFPT), which is one of the standard methods for calculating phonon properties from first principles. Our scheme, which we call the constrained DFPT, can be applied to various phonon-related problems, such as superconductivity, electron and thermal transport, thermoelectricity, piezoelectricity, dielectricity, and multiferroicity. We believe that the constrained DFPT provides a firm basis for the understanding of the role of phonons in strongly correlated materials. Here, we apply the scheme to fullerene superconductors and discuss how the realistic low-energy Hamiltonian is constructed.

  17. Path-integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative systems

    NASA Astrophysics Data System (ADS)

    Barth, A. M.; Vagov, A.; Axt, V. M.

    2016-09-01

    We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.

  18. Near strongly resonant periodic orbits in a Hamiltonian system

    PubMed Central

    Gelfreich, Vassili

    2002-01-01

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

  19. Maxwell-Vlasov equations as a continuous Hamiltonian system

    SciTech Connect

    Morrison, P.J.

    1980-11-01

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

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

    NASA Astrophysics Data System (ADS)

    Kumar, Anil; Rabe, Karin M.

    2011-03-01

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

  1. Hamiltonian structure of propagation equations for ultrashort optical pulses

    SciTech Connect

    Amiranashvili, Sh.; Demircan, A.

    2010-07-15

    A Hamiltonian framework is developed for a sequence of ultrashort optical pulses propagating in a nonlinear dispersive medium. To this end a second-order nonlinear wave equation for the electric field is transformed into a first-order propagation equation for a suitably defined complex electric field. The Hamiltonian formulation is then introduced in terms of normal variables, i.e., classical complex fields referring to the quantum creation and annihilation operators. The derived z-propagated Hamiltonian accounts for forward and backward waves, arbitrary medium dispersion, and four-wave mixing processes. As a simple application we obtain integrals of motion for the pulse propagation. The integrals reflect time-averaged fluxes of energy, momentum, and photons transferred by the pulse. Furthermore, pulses in the form of stationary nonlinear waves are considered. They yield extremal values of the momentum flux for a given energy flux. Simplified propagation equations are obtained by reduction of the Hamiltonian. In particular, the complex electric field reduces to an analytic signal for the unidirectional propagation. Solutions of the full bidirectional model are numerically compared to the predictions of the simplified equation for the analytic signal and to the so-called forward Maxwell equation. The numerics is effectively tested by examining the conservation laws.

  2. The Hamiltonian property of the flow of singular trajectories

    SciTech Connect

    Lokutsievskiy, L V

    2014-03-31

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

  3. Hamiltonian flow in Coulomb gauge Yang-Mills theory

    SciTech Connect

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

    2011-01-15

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

  4. Non-Hermitian Hamiltonians with unitary and antiunitary symmetries

    SciTech Connect

    Fernández, Francisco M. Garcia, Javier

    2014-03-15

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

  5. Davidson potential and SUSYQM in the Bohr Hamiltonian

    SciTech Connect

    Georgoudis, P. E.

    2013-06-10

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

  6. Local-TQO and Stability of Frustration-Free Hamiltonians

    NASA Astrophysics Data System (ADS)

    Pytel, Justyna; Michalakis, Spyridon

    2012-02-01

    The attention of the condensed matter and mathematical physics communities has recently focused on Hamiltonians with low-energy sectors exhibiting some form of topological order. In our work [1], we present a generalization of the result of Bravyi et al. [2,3] on the stability of topological quantum order for Hamiltonians composed of commuting projections with a common zero-energy subspace. In particular, the commutativity condition can be removed: We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. Also, we will discuss the ``Local Topological Quantum Order'' and ``Local-Gap'' conditions sufficient for proving stability. [4pt] [1] S. Michalakis and J. Pytel, Stability of Frustration-Free Hamiltonians. arXiv:1109.1588 (2011).[0pt] [2] S. Bravyi and M.B. Hastings, A short proof of stability of topological order under local perturbations. arXiv:1001.4363. [0pt] [3] S. Bravyi, M.B. Hastings, and S. Michalakis, Topological quantum order: stability under local perturbations. J. Math. Phys. 51, 093512 (2010).

  7. The Calculation of Rotational Energy Levels Using Tunneling Hamiltonians

    NASA Astrophysics Data System (ADS)

    Hougen, Jon T.

    2009-06-01

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

  8. Stochastic diffusion and Kolmogorov entropy in regular and random Hamiltonians

    SciTech Connect

    Isichenko, M.B. . Inst. for Fusion Studies Kurchatov Inst. of Atomic Energy, Moscow ); Horton, W. . Inst. for Fusion Studies); Kim, D.E.; Heo, E.G.; Choi, D.I. )

    1992-05-01

    The scalings of the E x B turbulent diffusion coefficient D and the Kolmogorov entropy K with the potential amplitude {phi} {sup {approximately}} of the fluctuation are studied using the geometrical analysis of closed and extended particle orbits for several types of drift Hamiltonians. The high-amplitude scalings , D {proportional to} {phi} {sup {approximately} 2} or {phi} {sup {approximately} 0} and K {proportional to} log {phi} {sup {approximately}}, are shown to arise from different forms of a periodic (four-wave) Hamiltonian {phi}{sup {approximately}} (x,y,t), thereby explaining the controversy in earlier numerical results. For a quasi-random (six-wave) Hamiltonian numerical data for the diffusion D {proportional to} {phi} {sup {approximately} 0.92 {plus minus} 0.04} and the Kolmogorov entropy K {proportional to} {phi} {sup {approximately} 0.56 {plus minus} 0.17} are presented and compared with the percolation theory predictions D {sub p} {proportional to} {phi} {sup {approximately} 0.7}, K {sub p} {proportional to} {phi} {sup {approximately} 0.5}. To study the turbulent diffusion in a general form of Hamiltonian, a new approach of the series expansion of the Lagrangian velocity correlation function is proposed and discussed.

  9. Stochastic diffusion and Kolmogorov entropy in regular and random Hamiltonians

    SciTech Connect

    Isichenko, M.B. |; Horton, W.; Kim, D.E.; Heo, E.G.; Choi, D.I.

    1992-05-01

    The scalings of the E x B turbulent diffusion coefficient D and the Kolmogorov entropy K with the potential amplitude {phi} {sup {approximately}} of the fluctuation are studied using the geometrical analysis of closed and extended particle orbits for several types of drift Hamiltonians. The high-amplitude scalings , D {proportional_to} {phi} {sup {approximately} 2} or {phi} {sup {approximately} 0} and K {proportional_to} log {phi} {sup {approximately}}, are shown to arise from different forms of a periodic (four-wave) Hamiltonian {phi}{sup {approximately}} (x,y,t), thereby explaining the controversy in earlier numerical results. For a quasi-random (six-wave) Hamiltonian numerical data for the diffusion D {proportional_to} {phi} {sup {approximately} 0.92 {plus_minus} 0.04} and the Kolmogorov entropy K {proportional_to} {phi} {sup {approximately} 0.56 {plus_minus} 0.17} are presented and compared with the percolation theory predictions D {sub p} {proportional_to} {phi} {sup {approximately} 0.7}, K {sub p} {proportional_to} {phi} {sup {approximately} 0.5}. To study the turbulent diffusion in a general form of Hamiltonian, a new approach of the series expansion of the Lagrangian velocity correlation function is proposed and discussed.

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

    SciTech Connect

    Kobakhidze, Archil

    2010-09-15

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

  11. The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach

    ERIC Educational Resources Information Center

    Likar, A.; Razpet, N.

    2009-01-01

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

  12. Goldfish Geodesics and Hamiltonian Reduction of Matrix Dynamics

    NASA Astrophysics Data System (ADS)

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

    2008-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2012-08-01

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

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

    NASA Astrophysics Data System (ADS)

    Wurm, Alexander; Morrison, P. J.

    2012-03-01

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

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

    PubMed

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

    2016-06-01

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

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

    NASA Astrophysics Data System (ADS)

    Dias, Gonçalo A. S.; Lemos, José P. S.

    2008-10-01

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

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

    PubMed

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

    2016-06-01

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

  18. Contact Transformations and Determinable Parameters in Spectroscopic Fitting Hamiltonians

    NASA Astrophysics Data System (ADS)

    Mekhtiev, Mirza A.; Hougen, Jon T.

    2000-02-01

    In recent least-squares fits of torsion-rotation spectra of acetaldehyde and methanol it was found possible to adjust more fourth-order parameters than would be expected from traditional contact-transformation considerations. To investigate this discrepancy between theory and practice we have carried out numerical fitting experiments on the simpler three-dimensional (three-Eulerian-angle) asymmetric rotor problem, using J ≤ 20 unitless energy levels generated artificially from a full orthorhombic Hamiltonian with quadratic through octic operators in the angular momentum components. Results are analyzed using the condition number κ of the least-squares matrix, which is a measure of its invertibility in the presence of round-off and other errors. When κ is very large, parameters must be removed from the fit until κ becomes acceptably small, corresponding to procedures which lead to reduced Hamiltonians in molecular spectroscopy. We find that under certain circumstances κ can be decreased to an acceptable level for Hamiltonians which are only partially reduced when compared to Watson A and S reductions. Some insight into this behavior is obtained from classical mechanics and from the concept of delayed contact transformations. Transferring this numerical and algebraic understanding to the more complicated four-dimensional methyl-top internal rotor problem supports the empirical observation that presently existing data sets for methanol and acetaldehyde are most efficiently fit using partially reduced Hamiltonians and further suggests that expanding the methanol data set to transitions involving levels of higher J, K, and vt would favor even more strongly the use of partially reduced fourth-order Hamiltonians.

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

    SciTech Connect

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

    1993-08-01

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

  20. Ab initio studies of anisotropic magnetism in uranium and cerium monopnictides and monochalcogenides

    NASA Astrophysics Data System (ADS)

    Collins, Eric Mason

    We have applied two ab initio based methods to investigate the origin in the electronic structure of the unusual magnetic behavior of the cerium and uranium monopnictides and monochalcogenides. First, we have carried out spin-polarized electronic structure calculations, based on the full potential linear muffin tin (FPLMTO) method, with spin polarization (orbital polarization only via spin-orbit coupling) and also with orbital polarization correction. Second, we have carried out ab initio based calculations synthesizing (1) a phenomenological theory of orbitally driven magnetism based on the Anderson and Kondo, lattice model which incorporates explicitly the hybridization induced and the Coulomb exchange interactions on an equal footing, and (2) FPLMTO electronic structure calculations allowing a first principles evaluation of all the parameters entering the model Hamiltonian. For the cerium compounds, we also include the crystal field interactions on an equal footing with the hybridization and Coulomb exchange interactions with a scaling determined by experiment. The results for the uranium compound calculations show that both methods are limited to the extremes to which they are best suited. The pure band structure calculations provide the best agreement for the lighter uranium compounds, while the model hamiltonian approach provides better agreement for the heavier uranium compounds. In the case of the cerium compounds, while the pure FPLMTO calculations yield values for the magnetic moment in agreement with experiment for the lighter cerium chalcogenides, they fail to give, even qualitatively, the magnetic properties for all other systems. On the other hand, the ab initio based model Hamiltonian calculations reveal for the first time the interplay of hybridization, Coulomb exchange, and crystal field interactions across the cerium series, and give results for the low-temperature moment and ordering temperature in excellent agreement with experiment, for the

  1. NUCLEAR REACTORS

    DOEpatents

    Long, E.; Ashby, J.W.

    1958-09-16

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

  2. Hamiltonian description of a self-consistent interaction between charged particles and electromagnetic waves.

    PubMed

    Bachelard, R; Chandre, C; Vittot, M

    2008-09-01

    The Hamiltonian description of the self-consistent interaction between an electromagnetic plane wave and a copropagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson brackets. The reduction to this paradigmatic Hamiltonian model is performed using a Lie algebraic formalism which allows us to preserve the Hamiltonian character at each step of the derivation.

  3. Dressed qubits in nuclear spin baths

    SciTech Connect

    Wu Lianao

    2010-04-15

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

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

    NASA Astrophysics Data System (ADS)

    Li, Nianhua; Liu, Q. P.

    2013-01-01

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

  5. Interpolating Hamiltonians for a stochastic-web map with quasicrystalline symmetry.

    PubMed

    Lowenstein, J. H.

    1992-07-01

    A systematic Hamiltonian approximation scheme is developed for a stochastic-web map with fivefold quasicrystalline symmetry. Interpolating Hamiltonians are calculated up to tenth order in the control parameter a. The higher order Hamiltonians are used to provide bounds for closed invariant curves of the map, and to investigate the structural evolution of map's phase portrait for a

  6. Ab initio two-component Ehrenfest dynamics

    SciTech Connect

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

    2015-09-21

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

  7. Ab initio two-component Ehrenfest dynamics

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

  8. Phase diagram for a cubic-Q interacting boson model Hamiltonian: Signs of triaxiality

    SciTech Connect

    Fortunato, L.; Alonso, C. E.; Arias, J. M.; Garcia-Ramos, J. E.; Vitturi, A.

    2011-07-15

    An extension of the Interacting Boson Model that includes the cubic (QxQxQ){sup (0)} term is proposed. The potential energy surface for the cubic quadrupole interaction is explicitly calculated within the coherent state formalism using the complete ({chi}-dependent) expression for the quadrupole operator. The Q-cubic term is found to depend on the asymmetry deformation parameter {gamma} as a linear combination of cos(3{gamma}) and cos{sup 2}(3{gamma}) terms, thereby allowing for triaxiality. The phase diagram of the model in the large N limit is explored: The orders of the phase transition surfaces that define the phase diagram are described, and the possible nuclear equilibrium shapes are established. It is found that for this particular Hamiltonian, contrary to expectations, there is only a very tiny region of triaxiality, and that the transition from prolate to oblate shapes is so fast that, in most cases, the onset of triaxiality might go unnoticed.

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

    SciTech Connect

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

    2011-04-15

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

  10. Ab Initio Calculation of the Hoyle State

    SciTech Connect

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

    2011-05-13

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

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

    PubMed

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

    2016-05-12

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

  12. Fock-space diagonalization of the state-dependent pairing Hamiltonian with the Woods-Saxon mean field

    NASA Astrophysics Data System (ADS)

    Molique, H.; Dudek, J.

    1997-10-01

    A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian H⁁pair=∑αβGαβc†αc†α ¯cβ ¯cβ with an arbitrary set of matrix elements Gαβ. Symmetries of the Hamiltonians on the many-body level are discussed using the language of P symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of P symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to p~40 particles on n~80 levels and for several dozens of lowest lying states with precision ~(1-2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority s=0 solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei.

  13. STAT5A/B Gene Locus Undergoes Amplification during Human Prostate Cancer Progression

    PubMed Central

    Haddad, Bassem R.; Gu, Lei; Mirtti, Tuomas; Dagvadorj, Ayush; Vogiatzi, Paraskevi; Hoang, David T.; Bajaj, Renu; Leiby, Benjamin; Ellsworth, Elyse; Blackmon, Shauna; Ruiz, Christian; Curtis, Mark; Fortina, Paolo; Ertel, Adam; Liu, Chengbao; Rui, Hallgeir; Visakorpi, Tapio; Bubendorf, Lukas; Lallas, Costas D.; Trabulsi, Edouard J.; McCue, Peter; Gomella, Leonard; Nevalainen, Marja T.

    2014-01-01

    The molecular mechanisms underlying progression of prostate cancer (PCa) to castrate-resistant (CR) and metastatic disease are poorly understood. Our previous mechanistic work shows that inhibition of transcription factor Stat5 by multiple alternative methods induces extensive rapid apoptotic death of Stat5-positive PCa cells in vitro and inhibits PCa xenograft tumor growth in nude mice. Furthermore, STAT5A/B induces invasive behavior of PCa cells in vitro and in vivo, suggesting involvement of STAT5A/B in PCa progression. Nuclear STAT5A/B protein levels are increased in high-grade PCas, CR PCas, and distant metastases, and high nuclear STAT5A/B expression predicts early disease recurrence and PCa-specific death in clinical PCas. Based on these findings, STAT5A/B represents a therapeutic target protein for advanced PCa. The mechanisms underlying increased Stat5 protein levels in PCa are unclear. Herein, we demonstrate amplification at the STAT5A/B gene locus in a significant fraction of clinical PCa specimens. STAT5A/B gene amplification was more frequently found in PCas of high histologic grades and in CR distant metastases. Quantitative in situ analysis revealed that STAT5A/B gene amplification was associated with increased STAT5A/B protein expression in PCa. Functional studies showed that increased STAT5A/B copy numbers conferred growth advantage in PCa cells in vitro and as xenograft tumors in vivo. The work presented herein provides the first evidence of somatic STAT5A/B gene amplification in clinical PCas. PMID:23660011

  14. STAT5A/B gene locus undergoes amplification during human prostate cancer progression.

    PubMed

    Haddad, Bassem R; Gu, Lei; Mirtti, Tuomas; Dagvadorj, Ayush; Vogiatzi, Paraskevi; Hoang, David T; Bajaj, Renu; Leiby, Benjamin; Ellsworth, Elyse; Blackmon, Shauna; Ruiz, Christian; Curtis, Mark; Fortina, Paolo; Ertel, Adam; Liu, Chengbao; Rui, Hallgeir; Visakorpi, Tapio; Bubendorf, Lukas; Lallas, Costas D; Trabulsi, Edouard J; McCue, Peter; Gomella, Leonard; Nevalainen, Marja T

    2013-06-01

    The molecular mechanisms underlying progression of prostate cancer (PCa) to castrate-resistant (CR) and metastatic disease are poorly understood. Our previous mechanistic work shows that inhibition of transcription factor Stat5 by multiple alternative methods induces extensive rapid apoptotic death of Stat5-positive PCa cells in vitro and inhibits PCa xenograft tumor growth in nude mice. Furthermore, STAT5A/B induces invasive behavior of PCa cells in vitro and in vivo, suggesting involvement of STAT5A/B in PCa progression. Nuclear STAT5A/B protein levels are increased in high-grade PCas, CR PCas, and distant metastases, and high nuclear STAT5A/B expression predicts early disease recurrence and PCa-specific death in clinical PCas. Based on these findings, STAT5A/B represents a therapeutic target protein for advanced PCa. The mechanisms underlying increased Stat5 protein levels in PCa are unclear. Herein, we demonstrate amplification at the STAT5A/B gene locus in a significant fraction of clinical PCa specimens. STAT5A/B gene amplification was more frequently found in PCas of high histologic grades and in CR distant metastases. Quantitative in situ analysis revealed that STAT5A/B gene amplification was associated with increased STAT5A/B protein expression in PCa. Functional studies showed that increased STAT5A/B copy numbers conferred growth advantage in PCa cells in vitro and as xenograft tumors in vivo. The work presented herein provides the first evidence of somatic STAT5A/B gene amplification in clinical PCas.

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

  16. Optical waveguide Hamiltonians leading to step-2 difference equations

    NASA Astrophysics Data System (ADS)

    Rueda-Paz, Juvenal; Wolf, Kurt Bernardo

    2011-03-01

    We examine the evolution of an N-point signal produced and sensed at finite arrays of points transverse to a planar waveguide, within the framework of the finite quantization of geometric optics. In contradistinction to the common mechanical Hamiltonians (kinetic plus potential energy terms) the classical waveguide Hamiltonian is the square root of a difference of squares of the refractive index profile minus the optical momentum. The finitely quantized model requires the solution of the square eigenvalue and eigenfunction problem which leads to a step-two difference equation that contains two solutions and two signs of energy. We find the proper linear combinations to fit the Kravchuk functions of the finite oscillator model.

  17. Dyson boson mapping of effective bi-fermion Hamiltonians

    SciTech Connect

    Civitarese, O.; Geyer, H.B.; Reboiro, M.

    2006-03-15

    Implementation of Dyson boson mapping is discussed in connection with effective Hamiltonians. A feature of the mapping technique, when implemented in an ideal boson basis, is the possible appearance of spurious states. These spurious states typically signal the overcompleteness of the basis. Without truncation, no contamination of the physical states and spectrum takes place. However, in practice one may be required to select from the ideal boson basis the dominant components for a given interaction. It is shown that the correspondence between a perturbative expansion, ala Bloch-Horowitz, and Dyson boson mapping allows for the identification of spurious states. The proposed method is applied to the mapping of a bi-fermionic Hamiltonian.

  18. Effective Hamiltonian for bound states in Yukawa theory

    SciTech Connect

    Weber, Axel

    2013-07-15

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

  19. Analysis of a QCD Hamiltonian in the low energy regime.

    NASA Astrophysics Data System (ADS)

    Yépez-Martínez, T.; Amor Quiroz, D. A.; Hess, P. O.; Civitarese, O.

    2016-07-01

    We present a QCD motivated Hamiltonian for the light quark sector. Inspired from self-consistent analysis of the Coulomb interaction, we implement an interaction of the form (-a/r + br) between color sources, which already consider gluonic dynamics by the linear potential contribution. A prediagonalization of the kinetic energy term followed by the implementation of the Tamm-Dancoff method are used to obtain the eigenvalues of the Hamiltonian. A variational analysis is implemented to obtain the optimized basis for the low energy meson spectrum. The potential parameter is compared to the reported lattice string tension with relatively good agreement. The obtained energies are located close to the experimental values and further improvements are discussed.

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

    PubMed

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

    2016-08-12

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

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

    SciTech Connect

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

    2013-08-01

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

  3. Hamiltonian formulation towards minimization of viscous fluid fingering

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

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

    NASA Astrophysics Data System (ADS)

    Tagawa, Hirofumi; Fujiwara, Akihiro

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

  5. Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics

    SciTech Connect

    Hoover, W.G.

    1980-05-28

    Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility.

  6. Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems.

    PubMed

    Custódio, M S; Manchein, C; Beims, M W

    2012-06-01

    The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions (ICs) and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and four particles globally coupled on a discrete lattice, we show that in these models, the transition from integrable motion to weak chaos emerges via chaotic stripes as the nonlinear parameter is increased. The stripes represent intervals of initial conditions which generate chaotic trajectories and increase with the nonlinear parameter of the system. In the billiard case, the initial conditions are the injection angles. For higher-dimensional systems and small nonlinearities, the chaotic stripes are the initial condition inside which Arnold diffusion occurs.

  7. Hamiltonian formulation of the extended Green-Naghdi equations

    NASA Astrophysics Data System (ADS)

    Matsuno, Yoshimasa

    2015-05-01

    A novel method is developed for extending the Green-Naghdi (GN) shallow-water model equation to the general system which incorporates the arbitrary higher-order dispersive effects. As an illustrative example, we derive a model equation which is accurate to the fourth power of the shallowness parameter while preserving the full nonlinearity of the GN equation, and obtain its solitary wave solutions by means of a singular perturbation analysis. We show that the extended GN equations have the same Hamiltonian structure as that of the GN equation. We also demonstrate that Zakharov's Hamiltonian formulation of surface gravity waves is equivalent to that of the extended GN system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface.

  8. RG-Whitham dynamics and complex Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Gorsky, A.; Milekhin, A.

    2015-06-01

    Inspired by the Seiberg-Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG)-like Whitham behavior. We show that at the Argyres-Douglas (AD) point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne-Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory.

  9. Optimal control methods for rapidly time-varying Hamiltonians

    SciTech Connect

    Motzoi, F.; Merkel, S. T.; Wilhelm, F. K.; Gambetta, J. M.

    2011-08-15

    In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.

  10. Hamiltonian formulation towards minimization of viscous fluid fingering.

    PubMed

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

    2016-07-01

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

  11. Role of intertwined Hamiltonian in two dimensional classical optics

    NASA Astrophysics Data System (ADS)

    Dehdashti, Shahram; Li, Rujiang; Liu, Xu; Raoofi, Mohammadreza; Chen, Hongsheng

    2015-07-01

    Intertwined Hamiltonian formalism originally has its roots in quantum field theory and non-relativistic quantum mechanics. In this work, we develop the non-relativistic two dimensional intertwined Hamiltonian formalism in classical optics. We obtain the properties of the intertwined media in detail and show that the differential part of intertwining operator is a series in Euclidean algebra generators. Also, we investigate quadratic gradient-index medium as an example of this structure, and obtain the intertwining operator and intertwined medium refractive index. Moreover, we study the preservation of quantum properties in the intertwined medium. For this, we consider superposition preservation as the most important property of quantum characters. We show that when a Schrödinger cat state is generated in gradient-index medium, we can construct another Schrödinger cat state in the intertwined one.

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

    NASA Astrophysics Data System (ADS)

    Tassi, Emanuele

    2014-07-01

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

  13. When a local Hamiltonian must be frustration-free

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  14. Efficient variational diagonalization of fully many-body localized Hamiltonians

    NASA Astrophysics Data System (ADS)

    Pollmann, Frank; Khemani, Vedika; Cirac, J. Ignacio; Sondhi, S. L.

    2016-07-01

    We introduce a variational unitary matrix product operator based variational method that approximately finds all the eigenstates of fully many-body localized one-dimensional Hamiltonians. The computational cost of the variational optimization scales linearly with system size for a fixed depth of the UTN ansatz. We demonstrate the usefulness of our approach by considering the Heisenberg chain in a strongly disordered magnetic field for which we compare the approximation to exact diagonalization results.

  15. On the spectral theory of dispersive N-body Hamiltonians

    NASA Astrophysics Data System (ADS)

    Damak, Mondher

    1999-01-01

    In this work we describe a general class of dispersive N-body Hamiltonians for which we prove the Hunziker, van Winter, and Zislin (HWZ) theorem and a Mourre estimate outside a closed and countable set of energies called thresholds. As a consequence of the Mourre estimate we prove a strong form of the limiting absorption principle, which implies the absence of a singular continuous spectrum and gives criteria of local smoothness.

  16. Hamiltonian dynamics, classical R-matrices and isomonodromic deformations

    NASA Astrophysics Data System (ADS)

    Harnad, J.

    The Hamiltonian approach to the theory of dual isomonodromic deformations is developed within the framework of rational classical R-matrix structures on loop algebras. Particular solutions to the isomonodromic deformation equations appearing in the computation of correlation functions in integrable quantum field theory models are constructed through the Riemann-Hilbert problem method. The corresponding τ-functions are shown to be given by the Fredholm determinant of a special class of integral operators.

  17. Green's operator for Hamiltonians with Coulomb plus polynomial potentials

    NASA Astrophysics Data System (ADS)

    Kelbert, E.; Hyder, A.; Demir, F.; Hlousek, Z. T.; Papp, Z.

    2007-07-01

    The Hamiltonian of a Coulomb plus polynomial potential in the Coulomb-Sturmian basis has an infinite symmetric band-matrix structure. A band matrix can always be considered as a block-tridiagonal matrix. So, the corresponding Green's operator can be given as a matrix-valued continued fraction. As examples, we calculate Green's operator for the Coulomb plus linear and quadratic confinement potential problems and determine the energy levels.

  18. Exact Solution of the Isovector Proton Neutron Pairing Hamiltonian

    SciTech Connect

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

    2005-12-02

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

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

    NASA Astrophysics Data System (ADS)

    Salisbury, Donald

    2011-10-01

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

  20. Hamiltonian BRST quantization of Chern-Simons gauge theory

    SciTech Connect

    Imai, H.; So, H. . Dept. of Physics); Igarashi, Y. ); Kitakado, S. ); Kubo, J. . Coll. of Liberal Arts)

    1990-08-30

    This paper quantizes non-abelian gauge theory with only a Chern-Simons term in three dimensions by using the generalized Hamiltonian formalism of Batalin and Fradkin for irreducible first- and second-class constrained systems, and derives a covariant action for the theory which is invariant under the off-shell nilpotent BRST transformation. Some aspects of the theory, finiteness and supersymmetry are discussed.

  1. Quantum integrals of motion for variable quadratic Hamiltonians

    SciTech Connect

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

    2010-09-15

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

  2. Hamiltonian structure for rotational capillary waves in stratified flows

    NASA Astrophysics Data System (ADS)

    Martin, Calin Iulian

    2016-07-01

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

  3. Two-dimensional surrogate Hamiltonian investigation of laser-induced desorption of NO/NiO(100)

    SciTech Connect

    Dittrich, Soeren; Freund, Hans-Joachim; Koch, Christiane P.; Kosloff, Ronnie; Kluener, Thorsten

    2006-01-14

    The photodesorption of NO from NiO(100) is studied from first principles, with electronic relaxation treated by the use of the surrogate Hamiltonian approach. Two nuclear degrees of freedom of the adsorbate-substrate system are taken into account. To perform the quantum dynamical wave-packet calculations, a massively parallel implementation with a one-dimensional data decomposition had to be introduced. The calculated desorption probabilities and velocity distributions are in qualitative agreement with experimental data. The results are compared to those of stochastic wave-packet calculations where a sufficiently large number of quantum trajectories is propagated within a jumping wave-packet scenario.

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

    PubMed Central

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

    2014-01-01

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

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

    NASA Astrophysics Data System (ADS)

    del-Castillo-Negrete, D.; Martinell, J. J.

    2012-05-01

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

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

    SciTech Connect

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

    2012-01-01

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

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

    SciTech Connect

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

    2012-01-01

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

  8. Driver Hamiltonians for constrained optimization in quantum annealing

    NASA Astrophysics Data System (ADS)

    Hen, Itay; Sarandy, Marcelo S.

    2016-06-01

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

  9. Finite-time thermodynamics of port-Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Delvenne, Jean-Charles; Sandberg, Henrik

    2014-01-01

    In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time. The framework allows us to prove the First and Second Laws of thermodynamics, but also lets us apply results from optimal and stochastic control theory to physical systems. In particular, we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of Maxwell’s demon. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be physically implemented as a variable linear capacitor and transformer. We also use the theory to design a heat engine operating between two heat sources in finite-time Carnot-like cycles of maximum power, and we compare those two heat engines.

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

    NASA Astrophysics Data System (ADS)

    Croke, Sarah

    2015-05-01

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

  11. AB 1725: A Comprehensive Analysis.

    ERIC Educational Resources Information Center

    California Community Colleges, Sacramento. Board of Governors.

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

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

    PubMed Central

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

    2016-01-01

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

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

    PubMed

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

    2016-04-14

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

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

    PubMed

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

    2016-07-01

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

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

    PubMed

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

    2016-07-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

  19. A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization II

    NASA Astrophysics Data System (ADS)

    Ogata, Yoshiko

    2016-06-01

    We give a characterization of the class of gapped Hamiltonians introduced in Part I (Ogata, A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015). The Hamiltonians in this class are given as MPS (Matrix product state) Hamiltonians. In Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), we list up properties of ground state structures of Hamiltonians in this class. In this Part II, we show the converse. Namely, if a (not necessarily MPS) Hamiltonian H satisfies five of the listed properties, there is a Hamiltonian H' from the class by Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), satisfying the following: The ground state spaces of the two Hamiltonians on the infinite interval coincide. The spectral projections onto the ground state space of H on each finite intervals are approximated by that of H' exponentially well, with respect to the interval size. The latter property has an application to the classification problem with open boundary conditions.

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

    NASA Astrophysics Data System (ADS)

    Bianucci, Marco

    2016-08-01

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

  1. Participation spectroscopy and entanglement Hamiltonian of quantum spin models

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

  2. Hamiltonian treatment of the gravitational collapse of thin shells

    NASA Astrophysics Data System (ADS)

    Crisóstomo, Juan; Olea, Rodrigo

    2004-05-01

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

  3. Trilinear hamiltonian with trapped ions and its applications

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

  4. Non-Hermitian quantum Hamiltonians with PT symmetry

    SciTech Connect

    Jones-Smith, Katherine; Mathur, Harsh

    2010-10-15

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

  5. Dispersive deformations of the Hamiltonian structure of Euler's equations

    NASA Astrophysics Data System (ADS)

    Casati, M.

    2016-09-01

    Euler's equations for a two-dimensional fluid can be written in the Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated with the Lie algebra of divergence-free vector fields. For the two-dimensional hydrodynamics of ideal fluids, we propose a derivation of the Poisson brackets using a reduction from the bracket associated with the full algebra of vector fields. Taking the results of some recent studies of the deformations of Lie-Poisson brackets of vector fields into account, we investigate the dispersive deformations of the Poisson brackets of Euler's equation: we show that they are trivial up to the second order.

  6. Dynamics symmetries of Hamiltonian system on time scales

    SciTech Connect

    Peng, Keke Luo, Yiping

    2014-04-15

    In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.

  7. Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices.

    PubMed

    Romero-Bastida, M; Pazó, Diego; López, Juan M; Rodríguez, Miguel A

    2010-09-01

    In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and Φ^{4} models. In this case, characteristic (also called covariant) LVs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal. In contrast, backward LVs (obtained via Gram-Schmidt orthonormalizations) present approximately the same scaling exponent in all cases, suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors. We are able to compute characteristic LVs in large systems thanks to a "bit reversible" algorithm, which completely obviates computer memory limitations.

  8. Fluctuation theorem for Hamiltonian systems: Le Chatelier's principle.

    PubMed

    Evans, D J; Searles, D J; Mittag, E

    2001-05-01

    For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields. PMID:11414885

  9. Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

    NASA Astrophysics Data System (ADS)

    Evans, Denis J.; Searles, Debra J.; Mittag, Emil

    2001-05-01

    For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

  10. The symmetry groups of bifurcations of integrable Hamiltonian systems

    SciTech Connect

    Orlova, E I

    2014-11-30

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

  11. Modular Hamiltonian for Excited States in Conformal Field Theory

    NASA Astrophysics Data System (ADS)

    Lashkari, Nima

    2016-07-01

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

  12. Nonequilibrium work energy relation for non-Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    Mandal, Dibyendu; DeWeese, Michael R.

    2016-04-01

    Recent years have witnessed major advances in our understanding of nonequilibrium processes. The Jarzynski equality, for example, provides a link between equilibrium free energy differences and finite-time nonequilibrium dynamics. We propose a generalization of this relation to non-Hamiltonian dynamics, relevant for active matter systems, continuous feedback, and computer simulation. Surprisingly, this relation allows us to calculate the free energy difference between the desired initial and final equilibrium states using arbitrary dynamics. As a practical matter, this dissociation between the dynamics and the initial and final states promises to facilitate a range of techniques for free energy estimation in a single universal expression.

  13. Simulating Hamiltonian dynamics with a truncated Taylor series.

    PubMed

    Berry, Dominic W; Childs, Andrew M; Cleve, Richard; Kothari, Robin; Somma, Rolando D

    2015-03-01

    We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification. PMID:25793789

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

    PubMed

    Lashkari, Nima

    2016-07-22

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

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

    PubMed

    Lashkari, Nima

    2016-07-22

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

  16. Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices

    NASA Astrophysics Data System (ADS)

    Habib, K. M. Masum; Sajjad, Redwan N.; Ghosh, Avik W.

    2016-03-01

    Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.

  17. AB173. TR4 nuclear receptor increases prostate cancer invasion via decreasing the miR-373-3p expression to alter TGFβR2/p-Smad3 signals

    PubMed Central

    Yang, Guosheng; Qiu, Xiaofo

    2016-01-01

    Objective Testicular nuclear receptor 4 (TR4) is a member of the nuclear receptor superfamily, which may play key roles to influence the metabolic diseases and prostate tumorigenesis. The purpose of our study is to elucidate the mechanisms how TR4 influences the prostate cancer (PCa) metastasis. Methods We constructed three different PCa cell lines including C4-2, PC3 and CWR22Rv1 with differential stable expression of TR4. RT-PCR and Western blot analysis were used to validate identified downstream genes. To explore the function of genes, we manipulated cells 2D and 3D invasion assays and mice experiment. Results we found TR4 could promote PCa cell invasion using two different cell invasion assays. Mechanism dissection revealed that TR4 might enhance PCa cell invasion via modulation of the microRNA-373-3p (miR-373-3p) expression. An interruption approach using miR-373-3p partially reversed TR4-enhanced PCa cell invasion. Furthermore, we found TR4-miR-373-3p might function through modulation of the TGFβR2/p-Smad3 signals to enhance the PCa cell invasion. The in vivo mouse model using orthotopic xenografted CWR22Rv1 cell line transfected with luciferase-reporter also confirmed in vitro cell line studies showing TR4 enhanced PCa metastasis via modulation of miR-373-3p. Conclusions Our data suggest that TR4 may represent a key player to influence the PCa metastasis and targeting TR4 miR-373-3p→ TGFβR2/p-Smad3 axis using TR4 antagonist or TR4-siRNA or miR-373-3p may become a new potential therapeutic approach to better suppress PCa metastasis.

  18. Hamiltonian methods for the study of polarized proton beam dynamics in accelerators and storage rings

    SciTech Connect

    Balandin, Vladimir; Golubeva, Nina

    1997-02-01

    The equations of classical spin-orbit motion can be extended to a Hamiltonian system in 9-dimensional phase space by introducing a coupled spin-orbit Poisson bracket and Hamiltonian function. After this extension it becomes possible to apply the methods of the theory of Hamiltonian systems to the study of polarized particles beam dynamics in circular accelerators and storage rings. Some of those methods have been implemented in the computer code FORGET-ME-NOT.

  19. Construction of the metric and equivalent Hermitian Hamiltonian via SUSY transformation operators

    SciTech Connect

    Shamshutdinova, V. V.

    2012-10-15

    The metric operator, which is the basic ingredient for studying a quantum system described by a pseudo-Hermitian Hamiltonian, provides the necessary means for obtaining an equivalent description of the system using a Hermitian Hamiltonian. In the framework of supersymmetric quantum mechanics, we propose a method of constructing the metric operator and to obtain the Hermitian Hamiltonian equivalent to the given pseudo-Hermitian.

  20. Hamiltonian fluid reductions of drift-kinetic equations and the link with water-bags

    NASA Astrophysics Data System (ADS)

    Perin, M.; Chandre, C.; Tassi, E.

    2016-07-01

    Hamiltonian models for the first three moments of the drift-kinetic distribution function, namely the density, the fluid velocity and the parallel pressure, are derived from the Hamiltonian structure of the drift-kinetic equations. The link with the water-bag closure is established, showing that, unlike the one-dimensional Vlasov equations, these solutions are the only Hamiltonian fluid reductions for the drift-kinetic equation. These models are discussed through their equations of motion and their Casimir invariants.

  1. Lars Onsager Prize Talk: Flow Equations for Hamiltonians

    NASA Astrophysics Data System (ADS)

    Wegner, Franz

    2015-03-01

    The equation dH (l) = GH (l) can describe the renormalization group equation for the Hamiltonian/Lagrangian H (l) and the generator G of the group. But it can also describe a Hamiltonian flow for bosons/fermions, which eliminates the off-diagonal matrix elements or (quasi)-particle violating terms by means of unitary transformations dH (l) / dl = [ η (l) , H (l) ] . Typically off-diagonal matrix elements are eliminated for ΔE >l - 1 / 2 . The flow equation has been applied to numerous systems (F. Wegner, J. Phys. A: Math. Gen. 39 (2006) 8221, arXiv: cond-mat/0511660; S. Kehrein, The Flow Equation Approach to Many-Particle Systems, Springer 2006), among them to the two-dimensional Hubbard-model, spin-boson models, the Anderson impurity model, QED and QCD. A simple and surprising result (as compared to that by Frohlich) is obtained for the elimination of the electron-phonon interaction yielding an attractive interaction for all energies. (P. Lenz and F. Wegner, Nucl. Phys. B482 (1996) 693; arXiv: cond-mat/9604087).

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

    SciTech Connect

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

    2013-10-15

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

  3. Inverse problem of quadratic time-dependent Hamiltonians

    NASA Astrophysics Data System (ADS)

    Guo, Guang-Jie; Meng, Yan; Chang, Hong; Duan, Hui-Zeng; Di, Bing

    2015-08-01

    Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly. Project supported by the National Natural Science Foundation of China (Grant No. 11347171), the Natural Science Foundation of Hebei Province of China (Grant No. A2012108003), and the Key Project of Educational Commission of Hebei Province of China (Grant No. ZD2014052).

  4. The Hamiltonian Laceability of some Generalized Honeycomb Tori

    SciTech Connect

    Hsu Liyen; Lin Tungyi; Kao Shinshin

    2008-11-06

    Assume that m, n and s are integers with m{>=}2, n{>=}4, 0{<=}s{<=}n and s is of the same parity of m. The generalized honeycomb torus GHT (m,n,s) is recognized as another attractive alternative to existing torus interconnection networks in parallel and distributed applications. It is known that any GHT (m,n,s) is 3-regular, hamiltonian, bipartite graph. We are interested in two special types of the generalized honeycomb torus, GHT (m,n,(n/2)) and GHT (m,n,0). Let G = GHT(m,n,s), where s(set-membership sign){l_brace}(n/2),0{r_brace}. We prove that any G is hamiltonian laceable. More precisely, given a pair of vertices P = {l_brace}u,v|u(set-membership sign)B,v(set-membership sign)W{r_brace} where B and W are the bipartition of V(G), there exists a path Q between u and v such that Q contains all vertices of G.

  5. On Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian and Dynamically Accessible Stability

    NASA Astrophysics Data System (ADS)

    Andreussi, Tommaso; Morrison, Philip J.; Pegoraro, Francesco

    2013-10-01

    Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e. variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches. En route to our results we describe a time-dependent relabeling transformation, which to our knowledge has not heretofore been given, that will be needed in the Lagrangian variable framework in connection with the approach considered in E. A. Frieman, M. Rotenberg, Rev. Mod. Phys. 32, 898 (1960).

  6. Effects of twisted noncommutativity in multi-particle Hamiltonians

    NASA Astrophysics Data System (ADS)

    Kuznetsova, Zhanna; Toppan, Francesco

    2013-07-01

    The non-commutativity induced by a Drinfel'd twist produces Bopp-shift-like transformations for deformed operators. In a single-particle setting the Drinfel'd twist allows to recover the non-commutativity obtained from various methods which are not based on Hopf algebras. In multi-particle sector, on the other hand, the Drinfel'd twist implies novel features. In conventional approaches to non-commutativity, deformed primitive operators are postulated to act additively. A Drinfel'd twist implies non-additive effects which are controlled by the coproduct. We stress that in our framework, the central element denoted as ħ is associated to an additive operator whose physical interpretation is that of the Particle Number operator. We illustrate all these features for a class of (abelian twist-deformed) 2D Hamiltonians. Suitable choices of the parameters lead to the Hamiltonian of the non-commutative Quantum Hall Effect, the harmonic oscillator, the quantization of the configuration space. The non-additive effects in the multi-particle sector, leading to results departing from the existing literature, are pointed out.

  7. Observation of Hamiltonian chaos in wave particle interaction

    NASA Astrophysics Data System (ADS)

    Doveil, Fabrice; Macor, Alessandro; Aïssi, Anass

    2008-09-01

    The motion of charged particle in longitudinal waves is a paradigm for the transition to large scale chaos in Hamiltonian systems. Recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s) in a specially designed Traveling Wave Tube (TWT). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The resonant velocity domain associated to a single wave is observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a “devil’s staircase” behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons to escape from a given velocity region as well as its robustness are also successfully tested. Thus generic features of Hamiltonian chaos have been experimentally observed.

  8. Interest rates in quantum finance: the Wilson expansion and Hamiltonian.

    PubMed

    Baaquie, Belal E

    2009-10-01

    Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor phi(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.

  9. Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes

    NASA Astrophysics Data System (ADS)

    Ivancevic, Vladimir G.; Reid, Darryn J.

    2015-11-01

    In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).

  10. Effective Hamiltonians for Coriolis-coupled nearly degenerate modes: Illustrative examples

    NASA Astrophysics Data System (ADS)

    Krishnan, Mangala S.; Carrington, Tucker, Jr.

    1993-11-01

    Using an angular momentum dependent Bogoliubov-Tyablikov (BT) transformation technique effective rotational Hamiltonians are derived for four molecules all of which have a pair of nearly degenerate strongly coupled vibrational modes. The BT transformation is applied to a two-vibrational-mode Hamiltonian obtained by using perturbation theory to eliminate the coupling between all but the nearly degenerate modes. Energy levels computed from the BT effective rotational Hamiltonians and accurate variational calculations agree very well. BT effective Hamiltonians are derived and tested for ozone, formaldehyde, its singly deuterated analog, and chlorodifluoromethane.

  11. Towards a structure-based exciton Hamiltonian for the CP29 antenna of photosystem II.

    PubMed

    Müh, Frank; Lindorfer, Dominik; Schmidt am Busch, Marcel; Renger, Thomas

    2014-06-28

    The exciton Hamiltonian pertaining to the first excited states of chlorophyll (Chl) a and b pigments in the minor light-harvesting complex CP29 of plant photosystem II is determined based on the recent crystal structure at 2.8 Å resolution applying a combined quantum chemical/electrostatic approach as used earlier for the major light-harvesting complex LHCII. Two electrostatic methods for the calculation of the local transition energies (site energies), referred to as the Poisson-Boltzmann/quantum chemical (PBQC) and charge density coupling (CDC) method, which differ in the way the polarizable environment of the pigments is described, are compared and found to yield comparable results, when tested against fits of measured optical spectra (linear absorption, linear dichroism, circular dichroism, and fluorescence). The crystal structure shows a Chl a/b ratio of 2.25, whereas a ratio between 2.25 and 3.0 can be estimated from the simulation of experimental spectra. Thus, it is possible that up to one Chl b is lost in CP29 samples. The lowest site energy is found to be located at Chl a604 close to neoxanthin. This assignment is confirmed by the simulation of wild-type-minus-mutant difference spectra of reconstituted CP29, where a tyrosine residue next to Chl a604 is modified in the mutant. Nonetheless, the terminal emitter domain (TED), i.e. the pigments contributing mostly to the lowest exciton state, is found at the Chl a611-a612-a615 trimer due to strong excitonic coupling between these pigments, with the largest contributions from Chls a611 and a612. A major difference between CP29 and LHCII is that Chl a610 is not the energy sink in CP29, which is presumably to a large extent due to the replacement of a lysine residue with alanine close to the TED.

  12. Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches.

    PubMed

    Mills, Jeffrey D; Ben-Nun, Michal; Rollin, Kyle; Bromley, Michael W J; Li, Jiabo; Hinde, Robert J; Winstead, Carl L; Sheehy, Jeffrey A; Boatz, Jerry A; Langhoff, Peter W

    2016-08-25

    Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and

  13. Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches.

    PubMed

    Mills, Jeffrey D; Ben-Nun, Michal; Rollin, Kyle; Bromley, Michael W J; Li, Jiabo; Hinde, Robert J; Winstead, Carl L; Sheehy, Jeffrey A; Boatz, Jerry A; Langhoff, Peter W

    2016-08-25

    Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and

  14. Nuclear moment of inertia and spin distribution of nuclear levels

    SciTech Connect

    Alhassid, Y.; Fang, L.; Liu, S.; Bertsch, G.F.

    2005-12-15

    We introduce a simple model to calculate the nuclear moment of inertia at finite temperature. This moment of inertia describes the spin distribution of nuclear levels in the framework of the spin-cutoff model. Our model is based on a deformed single-particle Hamiltonian with pairing interaction and takes into account fluctuations in the pairing gap. We derive a formula for the moment of inertia at finite temperature that generalizes the Belyaev formula for zero temperature. We show that a number-parity projection explains the strong odd-even effects observed in shell model Monte Carlo studies of the nuclear moment of inertia in the iron region.

  15. Structural evolution in Pt isotopes with the interacting boson model Hamiltonian derived from the Gogny energy density functional

    SciTech Connect

    Nomura, K.; Otsuka, T.; Rodriguez-Guzman, R.; Sarriguren, P.; Robledo, L. M.

    2011-01-15

    Spectroscopic calculations are carried out for the description of the shape/phase transition in Pt nuclei in terms of the interacting boson model (IBM) Hamiltonian derived from (constrained) Hartree-Fock-Bogoliubov (HFB) calculations with the finite range and density-dependent Gogny-D1S energy density functional. Assuming that the many-nucleon driven dynamics of nuclear surface deformation can be simulated by effective bosonic degrees of freedom, the Gogny-D1S potential energy surface (PES) with quadrupole degrees of freedom is mapped onto the corresponding PES of the IBM. By using this mapping procedure, the parameters of the IBM Hamiltonian, relevant to the low-lying quadrupole collective states, are derived as functions of the number of valence nucleons. Merits of both Gogny-HFB and IBM approaches are utilized so that the spectra and the wave functions in the laboratory system are calculated precisely. The experimental low-lying spectra of both ground-state and sideband levels are well reproduced. From the systematics of the calculated spectra and the reduced E2 transition probabilities B(E2), the prolate-to-oblate shape/phase transition is shown to take place quite smoothly as a function of neutron number N in the considered Pt isotopic chain, for which the {gamma} softness plays an essential role. All of these spectroscopic observables behave consistently with the relevant PES and the derived parameters of the IBM Hamiltonian as functions of N. Spectroscopic predictions are also made for those nuclei that do not have enough experimental E2 data.

  16. Nuclear Safety Information Center, Its Products and Services

    ERIC Educational Resources Information Center

    Buchanan, J. R.

    1970-01-01

    The Nuclear Safety Information Center (NSIC) serves as a focal point for the collection, analysis and dissemination of information related to safety problems encountered in the design, analysis, and operation of nuclear facilities. (Author/AB)

  17. Charged shells in Lovelock gravity: Hamiltonian treatment and physical implications

    SciTech Connect

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

    2007-01-15

    Using a Hamiltonian treatment, charged thin shells, static and dynamic, in spherically symmetric spacetimes, containing black holes or other specific types of solutions, in d dimensional Lovelock-Maxwell theory are studied. The free coefficients that appear in the Lovelock theory are chosen to obtain a sensible theory, with a negative cosmological constant appearing naturally. Using an Arnowitt-Deser-Misner (ADM) description, one then finds the Hamiltonian for the charged shell system. Variation of the Hamiltonian with respect to the canonical coordinates and conjugate momenta, and the relevant Lagrange multipliers, yields the dynamic and constraint equations. The vacuum solutions of these equations yield a division of the theory into two branches, namely d-2k-1>0 (which includes general relativity, Born-Infeld type theories, and other generic gravities) and d-2k-1=0 (which includes Chern-Simons type theories), where k is the parameter giving the highest power of the curvature in the Lagrangian. There appears an additional parameter {chi}=(-1){sup k+1}, which gives the character of the vacuum solutions. For {chi}=1 the solutions, being of the type found in general relativity, have a black hole character. For {chi}=-1 the solutions, being of a new type not found in general relativity, have a totally naked singularity character. Since there is a negative cosmological constant, the spacetimes are asymptotically anti-de Sitter (AdS), and AdS when empty (for zero cosmological constant the spacetimes are asymptotically flat). The integration from the interior to the exterior vacuum regions through the thin shell takes care of a smooth junction, showing the power of the method. The subsequent analysis is divided into two cases: static charged thin shell configurations, and gravitationally collapsing charged dust shells (expanding shells are the time reversal of the collapsing shells). In the collapsing case, into an initially nonsingular spacetime with generic character

  18. Charged shells in Lovelock gravity: Hamiltonian treatment and physical implications

    NASA Astrophysics Data System (ADS)

    Dias, Gonçalo A. S.; Gao, Sijie; Lemos, José P. S.

    2007-01-01

    Using a Hamiltonian treatment, charged thin shells, static and dynamic, in spherically symmetric spacetimes, containing black holes or other specific types of solutions, in d dimensional Lovelock-Maxwell theory are studied. The free coefficients that appear in the Lovelock theory are chosen to obtain a sensible theory, with a negative cosmological constant appearing naturally. Using an Arnowitt-Deser-Misner (ADM) description, one then finds the Hamiltonian for the charged shell system. Variation of the Hamiltonian with respect to the canonical coordinates and conjugate momenta, and the relevant Lagrange multipliers, yields the dynamic and constraint equations. The vacuum solutions of these equations yield a division of the theory into two branches, namely d-2k-1>0 (which includes general relativity, Born-Infeld type theories, and other generic gravities) and d-2k-1=0 (which includes Chern-Simons type theories), where k is the parameter giving the highest power of the curvature in the Lagrangian. There appears an additional parameter χ=(-1)k+1, which gives the character of the vacuum solutions. For χ=1 the solutions, being of the type found in general relativity, have a black hole character. For χ=-1 the solutions, being of a new type not found in general relativity, have a totally naked singularity character. Since there is a negative cosmological constant, the spacetimes are asymptotically anti-de Sitter (AdS), and AdS when empty (for zero cosmological constant the spacetimes are asymptotically flat). The integration from the interior to the exterior vacuum regions through the thin shell takes care of a smooth junction, showing the power of the method. The subsequent analysis is divided into two cases: static charged thin shell configurations, and gravitationally collapsing charged dust shells (expanding shells are the time reversal of the collapsing shells). In the collapsing case, into an initially nonsingular spacetime with generic character or an empty

  19. AB INITIO AND CALPHAD THERMODYNAMICS OF MATERIALS

    SciTech Connect

    Turchi, P A

    2004-04-14

    Ab initio electronic structure methods can supplement CALPHAD in two major ways for subsequent applications to stability in complex alloys. The first one is rather immediate and concerns the direct input of ab initio energetics in CALPHAD databases. The other way, more involved, is the assessment of ab initio thermodynamics {acute a} la CALPHAD. It will be shown how these results can be used within CALPHAD to predict the equilibrium properties of multi-component alloys.

  20. Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics

    SciTech Connect

    Morrison, P. J. Lingam, M.; Acevedo, R.

    2014-08-15

    A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to construct variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.

  1. Weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1991-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  2. A weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1990-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  3. A weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1989-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  4. Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Morrison, P. J.; Lingam, M.; Acevedo, R.

    2014-08-01

    A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to construct variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.

  5. Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

    NASA Astrophysics Data System (ADS)

    Ndayiragije, F.; Van Assche, W.

    2013-12-01

    Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to r > 1 different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Following a recent construction of Miki, Tsujimoto, Vinet and Zhedanov (for multiple Meixner polynomials of the first kind), we construct r > 1 non-Hermitian oscillator Hamiltonians in r dimensions which are simultaneously diagonalizable and for which the common eigenstates are expressed in terms of multiple Meixner polynomials of the second kind.

  6. Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems

    SciTech Connect

    Doroshin, Anton V.

    2010-03-01

    This paper sets out to develop a spider-type multiple-rotor system which can be used for attitude control of spacecraft. The multirotor system contains a large number of rotor-equipped rays, so it was called a 'Spider-type System', also it can be called 'Rotary Hedgehog'. These systems allow using spinups and captures of conjugate rotors to perform compound attitude motion of spacecraft. The paper describes a new method of spacecraft attitude reorientation and new mathematical model of motion in Hamilton form. Hamiltonian dynamics of the system is investigated with the help of Andoyer-Deprit canonical variables. These variables allow obtaining exact solution for hetero- and homoclinic orbits in phase space of the system motion, which are very important for qualitative analysis.

  7. The falling cat as a port-controlled Hamiltonian system

    NASA Astrophysics Data System (ADS)

    Iwai, Toshihiro; Matsunaka, Hiroki

    2012-02-01

    In this article, the falling cat is modeled as two jointed axial symmetric cylinders with arbitrary twist under the constraint of the vanishing total angular momentum. As a control system with the constraint taken into account, this model is formulated as a port-controlled Hamiltonian system defined on the cotangent bundle of the shape space for the jointed cylinders. A control is then designed as a function on the cotangent bundle, according to a standard procedure. Thus, the equations of motion are determined on the cotangent bundle together with the control. The whole motion as a vibrational motion of the falling cat is obtained after integrating the constraint equation of the vanishing total angular momentum. An example of the falling cat is given in which the model turns a somersault to approach a target state in equilibrium with an expected rotation after finishing a vibrational motion.

  8. Lie algebraic similarity transformed Hamiltonians for lattice model systems

    NASA Astrophysics Data System (ADS)

    Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.

    2015-01-01

    We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.

  9. Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Lingam, Manasvi; Miloshevich, George; Morrison, Philip J.

    2016-07-01

    The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia). The generalized helicities, and other geometric expressions for these models are presented in a topological context, emphasizing their universal facets. Some of the results presented include: the generalized Kelvin circulation theorems; the existence of two Lie-dragged 2-forms; and two concomitant helicities that can be studied via the Jones polynomial, which is widely utilized in Chern-Simons theory. The ensuing commonality is traced to the existence of an underlying Hamiltonian structure for all the extended MHD models, exemplified by the presence of a unique noncanonical Poisson bracket, and its associated energy.

  10. 3-state Hamiltonians associated to solvable 33-vertex models

    NASA Astrophysics Data System (ADS)

    Crampé, N.; Frappat, L.; Ragoucy, E.; Vanicat, M.

    2016-09-01

    Using the nested coordinate Bethe ansatz, we study 3-state Hamiltonians with 33 non-vanishing entries, or 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they correspond to diffusing particles with two possible internal states which may be exchanged during the diffusion (transmutation). The first step of the nested coordinate Bethe ansatz is performed providing the eigenvalues in terms of rapidities. We give the constraints ensuring the consistency of the computations. These rapidities also satisfy Bethe equations involving 4 × 4 R-matrices, solutions of the Yang-Baxter equation which implies new constraints on the models. We solve them allowing us to list all the solvable 33-vertex models.

  11. Complete Hamiltonian analysis of cosmological perturbations at all orders

    NASA Astrophysics Data System (ADS)

    Nandi, Debottam; Shankaranarayanan, S.

    2016-06-01

    In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the `gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field in the Lagrangian. We compare and contrast our approach to the Lagrangian approach (Chen et al. [2006]) for extracting higher order correlations and show that our approach is efficient and robust and can be applied to any model of gravity and matter fields without invoking slow-roll approximation.

  12. Phase space structure and dynamics for the Hamiltonian isokinetic thermostat.

    PubMed

    Collins, Peter; Ezra, Gregory S; Wiggins, Stephen

    2010-07-01

    We investigate the phase space structure and dynamics of a Hamiltonian isokinetic thermostat, for which ergodic thermostat trajectories at fixed (zero) energy generate a canonical distribution in configuration space. Model potentials studied consist of a single bistable mode plus transverse harmonic modes. Interpreting the bistable mode as a reaction (isomerization) coordinate, we establish connections with the theory of unimolecular reaction rates, in particular the formulation of isomerization rates in terms of gap times. In the context of molecular reaction rates, the distribution of gap times (or associated lifetimes) for a microcanonical ensemble initiated on the dividing surface is of great dynamical significance; an exponential lifetime distribution is usually taken to be an indicator of "statistical" behavior. Moreover, comparison of the magnitude of the phase space volume swept out by reactive trajectories as they pass through the reactant region with the total phase space volume (classical density of states) for the reactant region provides a necessary condition for ergodic dynamics. We compute gap times, associated lifetime distributions, mean gap times, reactive fluxes, reactive volumes, and total reactant phase space volumes for model thermostat systems with three and four degrees of freedom at three different temperatures. At all three temperatures, the necessary condition for ergodicity is approximately satisfied. At high temperatures a nonexponential lifetime distribution is found, while at low temperatures the lifetime is more nearly exponential. The degree of exponentiality of the lifetime distribution is quantified by computing the information entropy deficit with respect to pure exponential decay. The efficacy of the Hamiltonian isokinetic thermostat is examined by computing coordinate distributions averaged over single long trajectories initiated on the dividing surface.

  13. Generalized van der Waals Hamiltonian: periodic orbits and C1 nonintegrability.

    PubMed

    Guirao, Juan L G; Llibre, Jaume; Vera, Juan A

    2012-03-01

    The aim of this paper is to study the periodic orbits of the generalized van der Waals Hamiltonian system. The tool for studying such periodic orbits is the averaging theory. Moreover, for this Hamiltonian system we provide information on its C(1) nonintegrability, i.e., on the existence of a second first integral of class C(1).

  14. Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems

    SciTech Connect

    Abedi-Fardad, J.; Rezaei-Aghdam, A.; Haghighatdoost, Gh.

    2014-05-15

    We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R{sup 4} and R{sup 6}. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.

  15. Characterizing the parent Hamiltonians for a complete set of orthogonal wave functions: An inverse quantum problem

    NASA Astrophysics Data System (ADS)

    Ramezanpour, A.

    2016-06-01

    We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and our goal is to characterize the relevant wave functions and energies (the spectrum) of the system. Here, we take the opposite approach; starting from a reasonable collection of orthogonal wave functions, we try to characterize the associated parent Hamiltonians, to see how the wave functions and the energy values affect the structure of the parent Hamiltonian. Specifically, we obtain (quasi) local Hamiltonians by a complete set of (multilayer) product states and a local mapping of the energy values to the wave functions. On the other hand, a complete set of tree wave functions (having a tree structure) results to nonlocal Hamiltonians and operators which flip simultaneously all the spins in a single branch of the tree graph. We observe that even for a given set of basis states, the energy spectrum can significantly change the nature of interactions in the Hamiltonian. These effects can be exploited in a quantum engineering problem optimizing an objective functional of the Hamiltonian.

  16. Combined first-principles and model Hamiltonian study of the perovskite series R MnO 3 (R =La ,Pr ,Nd ,Sm ,Eu , and Gd )

    NASA Astrophysics Data System (ADS)

    Kováčik, Roman; Murthy, Sowmya Sathyanarayana; Quiroga, Carmen E.; Ederer, Claude; Franchini, Cesare

    2016-02-01

    We merge advanced ab initio schemes (standard density functional theory, hybrid functionals, and the G W approximation) with model Hamiltonian approaches (tight-binding and Heisenberg Hamiltonian) to study the evolution of the electronic, magnetic, and dielectric properties of the manganite family R MnO3 (R =La,Pr,Nd,Sm,Eu, and Gd) . The link between first principles and tight binding is established by downfolding the physically relevant subset of 3 d bands with eg character by means of maximally localized Wannier functions (MLWFs) using the VASP2WANNIER90 interface. The MLWFs are then used to construct a general tight-binding Hamiltonian written as a sum of the kinetic term, the Hund's rule coupling, the JT coupling, and the electron-electron interaction. The dispersion of the tight-binding (TB) eg bands at all levels are found to match closely the MLWFs. We provide a complete set of TB parameters which can serve as guidance for the interpretation of future studies based on many-body Hamiltonian approaches. In particular, we find that the Hund's rule coupling strength, the Jahn-Teller coupling strength, and the Hubbard interaction parameter U remain nearly constant for all the members of the R MnO3 series, whereas the nearest-neighbor hopping amplitudes show a monotonic attenuation as expected from the trend of the tolerance factor. Magnetic exchange interactions, computed by mapping a large set of hybrid functional total energies onto an Heisenberg Hamiltonian, clarify the origin of the A-type magnetic ordering observed in the early rare-earth manganite series as arising from a net negative out-of-plane interaction energy. The obtained exchange parameters are used to estimate the Néel temperature by means of Monte Carlo simulations. The resulting data capture well the monotonic decrease of the ordering temperature down the series from R =La to Gd, in agreement with experiments. This trend correlates well with the modulation of structural properties, in

  17. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

  18. Maxwell consideration of polaritonic quasi-particle Hamiltonians in multi-level systems

    SciTech Connect

    Richter, Steffen; Michalsky, Tom; Fricke, Lennart; Sturm, Chris; Franke, Helena; Grundmann, Marius; Schmidt-Grund, Rüdiger

    2015-12-07

    We address the problem of the correct description of light-matter coupling for excitons and cavity photons in the case of systems with multiple photon modes or excitons, respectively. In the literature, two different approaches for the phenomenological coupling Hamiltonian can be found: Either one single Hamiltonian with a basis whose dimension equals the sum of photonic modes and excitonic resonances is used. Or a set of independent Hamiltonians, one for each photon mode, is chosen. Both are usually used equivalently for the same kind of multi-photonic systems which cannot be correct. However, identifying the suitable Hamiltonian is difficult when modeling experimental data. By means of numerical transfer matrix calculations, we demonstrate the scope of application of each approach: The first one holds only for the coupling of a single photon state to several excitons, while in the case of multiple photon modes, separate Hamiltonians must be used for each photon mode.

  19. Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree - 3

    NASA Astrophysics Data System (ADS)

    Llibre, Jaume; Mahdi, Adam; Valls, Claudia

    2011-12-01

    In this paper, we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k=-2,-1,…,3,4, their polynomial integrability has been characterized. Here, we have two main results. First, we characterize the polynomial integrability of those Hamiltonian systems with homogeneous potential of degree -3. Second, we extend a relation between the nontrivial eigenvalues of the Hessian of the potential calculated at a Darboux point to a family of Hamiltonian systems with potentials given by an inverse of a homogeneous polynomial. This relation was known for such Hamiltonian systems with homogeneous polynomial potentials. Finally, we present three open problems related with the polynomial integrability of Hamiltonian systems with a rational potential.

  20. Spin-squared Hamiltonian of next-to-leading order gravitational interaction

    SciTech Connect

    Steinhoff, Jan; Hergt, Steven; Schaefer, Gerhard

    2008-11-15

    The static, i.e., linear momentum independent, part of the next-to-leading order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the post-Newtonian (PN) approximation is calculated from a three-dimensional covariant ansatz for the Hamilton constraint. All coefficients in this ansatz can be uniquely fixed for black holes. The resulting Hamiltonian fits into the canonical formalism of Arnowitt, Deser, and Misner (ADM) and is given in their transverse-traceless (ADMTT) gauge. This completes the recent result for the momentum dependent part of the NLO spin(1)-spin(1) ADM Hamiltonian for binary black holes (BBH). Thus, all PN NLO effects up to quadratic order in spin for BBH are now given in Hamiltonian form in the ADMTT gauge. The equations of motion resulting from this Hamiltonian are an important step toward more accurate calculations of templates for gravitational waves.

  1. A 2-dimensional optical architecture for solving Hamiltonian path problem based on micro ring resonators

    NASA Astrophysics Data System (ADS)

    Shakeri, Nadim; Jalili, Saeed; Ahmadi, Vahid; Rasoulzadeh Zali, Aref; Goliaei, Sama

    2015-01-01

    The problem of finding the Hamiltonian path in a graph, or deciding whether a graph has a Hamiltonian path or not, is an NP-complete problem. No exact solution has been found yet, to solve this problem using polynomial amount of time and space. In this paper, we propose a two dimensional (2-D) optical architecture based on optical electronic devices such as micro ring resonators, optical circulators and MEMS based mirror (MEMS-M) to solve the Hamiltonian Path Problem, for undirected graphs in linear time. It uses a heuristic algorithm and employs n+1 different wavelengths of a light ray, to check whether a Hamiltonian path exists or not on a graph with n vertices. Then if a Hamiltonian path exists, it reports the path. The device complexity of the proposed architecture is O(n2).

  2. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom. PMID:23531015

  3. Ultrasound Biomicroscopy Comparison of Ab Interno and Ab Externo Intraocular Lens Scleral Fixation.

    PubMed

    Horiguchi, Lie; Garcia, Patricia Novita; Malavazzi, Gustavo Ricci; Allemann, Norma; Gomes, Rachel L R

    2016-01-01

    Purpose. To compare ab interno and ab externo scleral fixation of posterior chamber intraocular lenses (PCIOL) using ultrasound biomicroscopy (UBM). Methods. Randomized patients underwent ab externo or ab interno scleral fixation of a PCIOL. Ultrasound biomicroscopy was performed 3 to 6 months postoperatively, to determine PCIOL centration, IOL distance to the iris at 12, 3, 6, and 9 hours, and haptics placement in relation to the ciliary sulcus. Results. Fifteen patients were enrolled in the study. The ab externo technique was used in 7 eyes (46.6%) and the ab interno in 8 eyes (53.3%). In the ab externo technique, 14 haptics were located: 4 (28.57%) in the ciliary sulcus; 2 (14.28%) anterior to the sulcus; and 8 (57.14%) posterior to the sulcus, 6 in the ciliary body and 2 posterior to the ciliary body. In the ab interno group, 4 haptics (25.0%) were in the ciliary sulcus, 2 (12.50%) anterior to the sulcus, and 10 (75.0%) posterior to the sulcus, 4 in the ciliary body and 6 posterior to the ciliary body. Conclusions. Ab externo and ab interno scleral fixation techniques presented similar results in haptic placement. Ab externo technique presented higher vertical tilt when compared to the ab interno.

  4. Ultrasound Biomicroscopy Comparison of Ab Interno and Ab Externo Intraocular Lens Scleral Fixation

    PubMed Central

    Horiguchi, Lie; Garcia, Patricia Novita; Malavazzi, Gustavo Ricci; Allemann, Norma

    2016-01-01

    Purpose. To compare ab interno and ab externo scleral fixation of posterior chamber intraocular lenses (PCIOL) using ultrasound biomicroscopy (UBM). Methods. Randomized patients underwent ab externo or ab interno scleral fixation of a PCIOL. Ultrasound biomicroscopy was performed 3 to 6 months postoperatively, to determine PCIOL centration, IOL distance to the iris at 12, 3, 6, and 9 hours, and haptics placement in relation to the ciliary sulcus. Results. Fifteen patients were enrolled in the study. The ab externo technique was used in 7 eyes (46.6%) and the ab interno in 8 eyes (53.3%). In the ab externo technique, 14 haptics were located: 4 (28.57%) in the ciliary sulcus; 2 (14.28%) anterior to the sulcus; and 8 (57.14%) posterior to the sulcus, 6 in the ciliary body and 2 posterior to the ciliary body. In the ab interno group, 4 haptics (25.0%) were in the ciliary sulcus, 2 (12.50%) anterior to the sulcus, and 10 (75.0%) posterior to the sulcus, 4 in the ciliary body and 6 posterior to the ciliary body. Conclusions. Ab externo and ab interno scleral fixation techniques presented similar results in haptic placement. Ab externo technique presented higher vertical tilt when compared to the ab interno. PMID:27293878

  5. Exact effective Hamiltonian theory. II. Polynomial expansion of matrix functions and entangled unitary exponential operators.

    PubMed

    Siminovitch, David; Untidt, Thomas; Nielsen, Niels Chr

    2004-01-01

    Our recent exact effective Hamiltonian theory (EEHT) for exact analysis of nuclear magnetic resonance (NMR) experiments relied on a novel entanglement of unitary exponential operators via finite expansion of the logarithmic mapping function. In the present study, we introduce simple alternant quotient expressions for the coefficients of the polynomial matrix expansion of these entangled operators. These expressions facilitate an extension of our previous closed solution to the Baker-Campbell-Hausdorff problem for SU(N) systems from N< or =4 to any N, and thereby the potential application of EEHT to more complex NMR spin systems. Similarity matrix transformations of the EEHT expansion are used to develop alternant quotient expressions, which are fully general and prove useful for evaluation of any smooth matrix function. The general applicability of these expressions is demonstrated by several examples with relevance for NMR spectroscopy. The specific form of the alternant quotients is also used to demonstrate the fundamentally important equivalence of Sylvester's theorem (also known as the spectral theorem) and the EEHT expansion.

  6. Note about Hamiltonian formulation of modified F(R) Horava-Lifshitz gravities and their healthy extension

    SciTech Connect

    Kluson, J.

    2010-08-15

    This note is devoted to the study of Hamiltonian formulation of modified F(R) Horava-Lifshitz theories of gravity that were proposed recently by Chaichian and collaborators [arXiv:1001.4102]. We also study Hamiltonian formulation of the healthy extended Horava-Lifshitz gravities and show that these theories have the Hamiltonian structure that is different from Hamiltonian formulation general relativity.

  7. Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations

    NASA Astrophysics Data System (ADS)

    Geneste, Grégory; Bellaiche, L.; Kiat, Jean-Michel

    2016-06-01

    The radio-frequency dielectric response of the lead-free Ba (Zr0.5Ti0.5)O3 relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio-based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors.

  8. Simulating the Radio-Frequency Dielectric Response of Relaxor Ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo Simulations.

    PubMed

    Geneste, Grégory; Bellaiche, L; Kiat, Jean-Michel

    2016-06-17

    The radio-frequency dielectric response of the lead-free Ba(Zr_{0.5}Ti_{0.5})O_{3} relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from real-space renormalization group theories, allows us to depict the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this ab initio-based approach, and used as input data for kinetic Monte Carlo simulations. The resulting numerical scheme allows us to simulate the dielectric response for external field frequencies ranging from kHz up to a few tens of MHz for the first time and to demonstrate, e.g., that local (electric or elastic) random fields lead to the dielectric relaxation in the radio-frequency range that has been observed in relaxors.

  9. New Hamiltonian expansions adapted to the Trojan problem

    NASA Astrophysics Data System (ADS)

    Páez, Rocío Isabel; Locatelli, Ugo; Efthymiopoulos, Christos

    2016-07-01

    A number of studies, referring to the observed Trojan asteroids of various planets in our Solar System, or to hypothetical Trojan bodies in extrasolar planetary systems, have emphasized the importance of so-called secondary resonances in the problem of the long term stability of Trojan motions. Such resonances describe commensurabilities between the fast, synodic, and secular frequency of the Trojan body, and, possibly, additional slow frequencies produced by more than one perturbing bodies. The presence of secondary resonances sculpts the dynamical structure of the phase space. Hence, identifying their location is a relevant task for theoretical studies. In the present paper we combine the methods introduced in two recent papers (Páez and Efthymiopoulos in Celest Mech Dyn Astron 121(2):139, 2015; Páez and Locatelli in MNRAS 453(2):2177, 2015) in order to analytically predict the location of secondary resonances in the Trojan problem. In Páez and Efthymiopoulos (2015), the motion of a Trojan body was studied in the context of the planar Elliptic Restricted Three Body or the planar Restricted Multi-Planet Problem. It was shown that the Hamiltonian admits a generic decomposition H=H_b+H_{sec} . The term H_b , called the basic Hamiltonian, is a model of two degrees of freedom characterizing the short-period and synodic motions of a Trojan body. Also, it yields a constant `proper eccentricity' allowing to define a third secular frequency connected to the body's perihelion precession. H_{sec} contains all remaining secular perturbations due to the primary or to additional perturbing bodies. Here, we first investigate up to what extent the decomposition H=H_b+H_{sec} provides a meaningful model. To this end, we produce numerical examples of surfaces of section under H_b and compare with those of the full model. We also discuss how secular perturbations alter the dynamics under H_b . Secondly, we explore the normal form approach introduced in Páez and Locatelli (2015

  10. Shapes and stability of algebraic nuclear models

    NASA Technical Reports Server (NTRS)

    Lopez-Moreno, Enrique; Castanos, Octavio

    1995-01-01

    A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.

  11. Does finite-temperature decoding deliver better optima for noisy Hamiltonians?

    NASA Astrophysics Data System (ADS)

    Ochoa, Andrew J.; Nishimura, Kohji; Nishimori, Hidetoshi; Katzgraber, Helmut G.

    The minimization of an Ising spin-glass Hamiltonian is an NP-hard problem. Because many problems across disciplines can be mapped onto this class of Hamiltonian, novel efficient computing techniques are highly sought after. The recent development of quantum annealing machines promises to minimize these difficult problems more efficiently. However, the inherent noise found in these analog devices makes the minimization procedure difficult. While the machine might be working correctly, it might be minimizing a different Hamiltonian due to the inherent noise. This means that, in general, the ground-state configuration that correctly minimizes a noisy Hamiltonian might not minimize the noise-less Hamiltonian. Inspired by rigorous results that the energy of the noise-less ground-state configuration is equal to the expectation value of the energy of the noisy Hamiltonian at the (nonzero) Nishimori temperature [J. Phys. Soc. Jpn., 62, 40132930 (1993)], we numerically study the decoding probability of the original noise-less ground state with noisy Hamiltonians in two space dimensions, as well as the D-Wave Inc. Chimera topology. Our results suggest that thermal fluctuations might be beneficial during the optimization process in analog quantum annealing machines.

  12. Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates

    NASA Astrophysics Data System (ADS)

    Shikakhwa, M. S.; Chair, N.

    2016-08-01

    The Schrödinger Hamiltonian of a spin-less particle as well as the Pauli Hamiltonian with spin-orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate are constructed. A new approach, based on the physical argument that upon squeezing the particle to the surface by a potential, then it is the physical gauge-covariant kinematical momentum operator (velocity operator) transverse to the surface that should be dropped from the Hamiltonian(s). In both cases, the resulting Hermitian gauge-invariant Hamiltonian on the surface is free from any reference to the component of the vector potential transverse to the surface, and the approach is completely gauge-independent. In particular, for the Pauli Hamiltonian these results are obtained exactly without any further assumptions or approximations. Explicit covariant plug-and-play formulae for the Schrödinger Hamiltonians on the surfaces of a cylinder, a sphere and a torus are derived.

  13. Analysis of the rotational spectrum of methylene (CH2) in its vibronic ground state with an Euler expansion of the Hamiltonian.

    PubMed

    Brünken, Sandra; Müller, Holger S P; Lewen, Frank; Giesen, Thomas F

    2005-10-22

    We present an analysis of a global, field-free data set of the methylene radical CH2 in its X 3B1 vibronic ground state by means of a novel Euler expansion of the Hamiltonian. The data set comprises pure rotational transitions up to 2 THz obtained with microwave accuracies of 30-500 kHz as well as nu2 ground-state combination differences and pure rotational data obtained with infrared accuracies of 0.001-0.010 cm(-1). Highly accurate spectroscopic parameters have been determined. These include rotational, spin-spin, spin-rotation, and electron-spin-nuclear-spin coupling terms along with several centrifugal distortion corrections. The spectroscopic model has been tested and improved by recording newly three weak DeltaN not equalDeltaJ fine-structure components of the N(KaKc)=2(12)-3(03) and 5(05)-4(14) transitions near 434, 454, and 581 GHz. These lines were rather close to the predictions. Overall weighted root mean squares of 1.28 and 0.83 were achieved for fits in which the Euler expansion was used only for the rotational part of the Hamiltonian or for the rotational and spin-spin terms of the Hamiltonian, respectively. The resulting spectroscopic parameters allow for precise frequency predictions of astrophysically important rotational transitions of methylene.

  14. Pressure effect on elastic anisotropy of crystals from ab initio simulations: The case of silicate garnets

    SciTech Connect

    Mahmoud, A.; Erba, A. Dovesi, R.; Doll, K.

    2014-06-21

    A general methodology has been devised and implemented into the solid-state ab initio quantum-mechanical CRYSTAL program for studying the evolution under geophysical pressure of the elastic anisotropy of crystalline materials. This scheme, which fully exploits both translational and point symmetry of the crystal, is developed within the formal frame of one-electron Hamiltonians and atom-centered basis functions. Six silicate garnet end-members, among the most important rock-forming minerals of the Earth's mantle, are considered, whose elastic anisotropy is fully characterized under high hydrostatic compressions, up to 60 GPa. The pressure dependence of azimuthal anisotropy and shear-wave birefringence of seismic wave velocities for these minerals are accurately simulated and compared with available single-crystal measurements.

  15. A room temperature CO2 line list with ab initio computed intensities

    NASA Astrophysics Data System (ADS)

    Zak, Emil; Tennyson, Jonathan; Polyansky, Oleg L.; Lodi, Lorenzo; Zobov, Nikolay F.; Tashkun, Sergey A.; Perevalov, Valery I.

    2016-07-01

    Atmospheric carbon dioxide concentrations are being closely monitored by remote sensing experiments which rely on knowing line intensities with an uncertainty of 0.5% or better. We report a theoretical study providing rotation-vibration line intensities substantially within the required accuracy based on the use of a highly accurate ab initio dipole moment surface (DMS). The theoretical model developed is used to compute CO2 intensities with uncertainty estimates informed by cross comparing line lists calculated using pairs of potential energy surfaces (PES) and DMS's of similar high quality. This yields lines sensitivities which are utilized in reliability analysis of our results. The final outcome is compared to recent accurate measurements as well as the HITRAN2012 database. Transition frequencies are obtained from effective Hamiltonian calculations to produce a comprehensive line list covering all 12C16O2 transitions below 8000cm-1 and stronger than 10-30 cm/molecule at T = 296 K.

  16. Ab initio phonon limited transport

    NASA Astrophysics Data System (ADS)

    Verstraete, Matthieu

    We revisit the thermoelectric (TE) transport properties of two champion materials, PbTe and SnSe, using fully first principles methods. In both cases the performance of the material is due to subtle combinations of structural effects, scattering, and phase space reduction. In PbTe anharmonic effects are completely opposite to the predicted quasiharmonic evolution of phonon frequencies and to frequently (and incorrectly) cited extrapolations of experiments. This stabilizes the material at high T, but also tends to enhance its thermal conductivity, in a non linear manner, above 600 Kelvin. This explains why PbTe is in practice limited to room temperature applications. SnSe has recently been shown to be the most efficient TE material in bulk form. This is mainly due to a strongly enhanced carrier concentration and electrical conductivity, after going through a phase transition from 600 to 800 K. We calculate the transport coefficients as well as the defect concentrations ab initio, showing excellent agreement with experiment, and elucidating the origin of the double phase transition as well as the new charge carriers. AH Romero, EKU Gross, MJ Verstraete, and O Hellman PRB 91, 214310 (2015) O. Hellman, IA Abrikosov, and SI Simak, PRB 84 180301 (2011)

  17. Behaviors of N=1 supersymmetric Euler derivatives and Hamiltonian operators under general superconformal transformations

    NASA Astrophysics Data System (ADS)

    Tian, Kai; Liu, Q. P.

    2014-09-01

    The changing rule of super Hamiltonian operators under general superconformal transformations is established by means of investigating behavior of supersymmetric Euler derivatives under the same kind of changes of variables. In the two particular yet frequent cases such as supersymmetric Miura-type transformations and reciprocal transformations, the results are detailed and applied to construct bi-Hamiltonian structures of some supersymmetric evolution equations. As an interesting example, one of supersymmetric Harry Dym equations is shown to be a bi-Hamiltonian system through its reciprocal link to the classical Harry Dym equation.

  18. Hamiltonian methods for the study of polarized proton beam dynamics in accelerators and storage rings

    SciTech Connect

    Balandin, V. |; Golubeva, N.

    1997-02-01

    The equations of classical spin-orbit motion can be extended to a {bold Hamiltonian system} in 9-dimensional phase space by introducing a coupled spin-orbit {bold Poisson bracket} (3) and {bold Hamiltonian function} (5). After this extension it becomes possible to apply the {bold methods of the theory of Hamiltonian systems} to the study of polarized particles beam dynamics in circular accelerators and storage rings. Some of those methods have been implemented in the computer code {bold FORGET-ME-NOT} [1], [2]. {copyright} {ital 1997 American Institute of Physics.}

  19. Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices

    NASA Astrophysics Data System (ADS)

    Miyake, Hirokazu; Siviloglou, Georgios A.; Kennedy, Colin J.; Burton, William Cody; Ketterle, Wolfgang

    2013-11-01

    We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients. This Hamiltonian describes the motion of charged particles in strong magnetic fields. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. The band structure of this Hamiltonian should display Hofstadter’s butterfly. For fermions, this scheme should realize the quantum Hall effect and chiral edge states.

  20. The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

    PubMed

    Dridi, G; Julien, R; Hliwa, M; Joachim, C

    2015-08-28

    The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor. PMID:26234709

  1. Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

    NASA Astrophysics Data System (ADS)

    Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

    2011-09-01

    The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

  2. On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Giles, W.; Lamb, J. S. W.; Turaev, D.

    2016-10-01

    We consider a Hamiltonian system which has an elliptic-hyperbolic equilibrium with a homoclinic loop. We identify the set of orbits which are homoclinic to the center manifold of the equilibrium via a Lyapunov-Schmidt reduction procedure. This leads to the study of a singularity which inherits a certain structure from the Hamiltonian nature of the system. Under non-degeneracy assumptions, we classify the possible Morse indices of this singularity, permitting a local description of the set of homoclinic orbits. We also consider the case of time-reversible Hamiltonian systems.

  3. Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity

    NASA Astrophysics Data System (ADS)

    Ruz, Soumendranath; Mandal, Ranajit; Debnath, Subhra; Sanyal, Abhik Kumar

    2016-07-01

    The Hamiltonian constraint H_c = N{H} = 0, defines a diffeomorphic structure on spatial manifolds by the lapse function N in general theory of relativity. However, it is not manifest in Lanczos-Lovelock gravity, since the expression for velocity in terms of the momentum is multivalued. Thus the Hamiltonian is a branch function of momentum. Here we propose an extended theory of Lanczos-Lovelock gravity to construct a unique Hamiltonian in its minisuperspace version, which results in manifest diffeomorphic invariance and canonical quantization.

  4. The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

    PubMed

    Dridi, G; Julien, R; Hliwa, M; Joachim, C

    2015-08-28

    The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.

  5. Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

    NASA Astrophysics Data System (ADS)

    Sandoval-Santana, J. C.; Ibarra-Sierra, V. G.; Cardoso, J. L.; Kunold, A.

    2016-04-01

    We develop a Lie algebraic approach to systematically calculate the evolution operator of a system described by a generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to uniform and constant electro-magnetic fields.

  6. The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate

    NASA Astrophysics Data System (ADS)

    Dridi, G.; Julien, R.; Hliwa, M.; Joachim, C.

    2015-08-01

    The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.

  7. On the Hamiltonian structure of ion-acoustic plasma waves and water waves in channels

    NASA Astrophysics Data System (ADS)

    Menyuk, C. R.; Chen, H.-H.

    1986-04-01

    It is shown that the Hamiltonian structure of ion-acoustic waves and channel waves may be used to derive the Hamiltonian structure of the Korteweg-de Vries equation and its higher-order corrections. The Hamiltonian approach used here is more systematic and less laborious than standard methods for deriving the Korteweg-de Vries equation. It is also more revealing. In particular, it is shown that the Poisson bracket of the corrected equations equals the Korteweg-de Vries Poisson bracket at every order. It is also shown that the corrected equations become nonlocal at sufficiently high order.

  8. Spin Hamiltonian Spectroscopy in PRASEODYMIUM(3):LANTHANUM Trifluoride.

    NASA Astrophysics Data System (ADS)

    Otto, Frederick William

    An optically detected anticrossing in solid state laser spectroscopy produced by cross-relaxation is reported. Spin -spin cross-relaxation between the ^{141 }Pr and ^{19}F spin reservoirs in Pr^{+3}:LaF _3 and its influence on the ^{141}Pr NMR spectrum is observed. The detection technique employed combines optical pumping and hole burning with either an external magnetic field sweep or rf resonance saturation producing slow transient changes in resonant laser transmission. At a certain value of the external magnetic field, where the energy level splittings of Pr and F spins match, a level repulsion and discontinuity of the Pr^{+3} NMR lines is observed. This effect is interpreted as the "anticrossing" of the combined Pr-F spin-spin reservoir energy states. The Zeeman - Quadrupole Hamiltonian spectrum of the lowest hyperfine optical ground state manifold of Pr^ {+3}:LaF_3 is mapped out over a wide range of Zeeman magnetic fields. A new method is proposed for dynamically polarizing nuclei by means of optical pumping, using resonant cross-relaxation between rare spins and spin reservoirs.

  9. Hamiltonian dynamics of spatially-homogeneous Vlasov-Einstein systems

    NASA Astrophysics Data System (ADS)

    Okabe, Takahide; Morrison, P. J.; Friedrichsen, J. E., III; Shepley, L. C.

    2011-07-01

    We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in general relativity. The Bianchi models are spatially-homogeneous solutions to the Einstein field equations, classified by the three-dimensional Lie algebra that describes the symmetry group of the model. The Einstein equations for these models reduce to a set of coupled ordinary differential equations. The class A Bianchi models admit a Hamiltonian formulation in which the components of the metric tensor and their time derivatives yield the canonical coordinates. The evolution of anisotropy in the vacuum Bianchi models is determined by a potential due to the curvature of the model, according to its symmetry. For illustrative purposes, we examine the evolution of anisotropy in models with Vlasov matter. The Vlasov content is further simplified by the assumption of cold, counter-streaming matter, a kind of matter that is far from thermal equilibrium and is not describable by an ordinary fluid model nor other more simplistic matter models. Qualitative differences and similarities are found in the dynamics of certain vacuum class A Bianchi models and Bianchi type I models with cold, counter-streaming Vlasov-matter potentials analogous to the curvature potentials of corresponding vacuum models.

  10. Super loop groups, Hamiltonian actions and super Virasoro algebras

    NASA Astrophysics Data System (ADS)

    Harnad, J.; Kupershmidt, B. A.

    1990-09-01

    The quotient{{widetilde{LG}} G} of a super loop groupwidetilde{LG} by the subgroup of constant loops is given a supersymplectic structure and identified through a moment map embedding MediaObjects/220_2005_BF02096652_f1.jpg with a coadjoint orbit of the centrally extended super loop algebra. The algebra widetilde{diff}^c S^1 of super-conformal vector fields on the circle is shown to have a natural representation as Hamiltonian vector fields on{{widetilde{LG}} G} generated by an equivariant moment map. This map is obtained by composition of 315-8 with a super Poisson map defining a supersymmetric extension of the classical Sugawara formula. Upon quantization, this yields the corresponding formula of Kac and Todorov on unitary highest weight representations. For any homomorphism ρ: u(1)→ G, an associated "twisted" moment map is also derived, generating a super Poisson bracket realization of a super Virasoro subalgebra widetilde{Vir} of the semi-direct sum. The corresponding super Poisson map is interpreted as a nonabelian generalization of the super Miura map and applied to two super KdV hierarchies to derive corresponding integrable generalized super MKdV hierarchies in Figure 8.

  11. Phase Mixing in Unperturbed and Perturbed Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Kandrup, Henry E.; Novotny, Steven J.

    2004-01-01

    This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic driving, friction, and/or white and coloured noise. The evolution of initially localised ensembles of orbits was probed through lower order moments and coarse-grained distribution functions. In the absence of time-dependent perturbations, regular ensembles disperse initially as a power law in time and only exhibit a coarse-grained approach towards an invariant equilibrium over comparatively long times. Chaotic ensembles generally diverge exponentially fast on a time scale related to a typical finite time Lyapunov exponent, but can exhibit complex behaviour if they are impacted by the effects of cantori or the Arnold web. Viewed over somewhat longer times, chaotic ensembles typical converge exponentially towards an invariant or near-invariant equilibrium. This, however, need not correspond to a true equilibrium, which may only be approached over very long time scales. Time-dependent perturbations can dramatically increase the efficiency of phase mixing, both by accelerating the approach towards a near-equilibrium and by facilitating diffusion through cantori or along the Arnold web so as to accelerate the approach towards a true equilibrium. The efficacy of such perturbations typically scales logarithmically in amplitude, but is comparatively insensitive to most other details, a conclusion which reinforces the interpretation that the perturbations act via a resonant coupling.

  12. Hamiltonian analysis for linearly acceleration-dependent Lagrangians

    NASA Astrophysics Data System (ADS)

    Cruz, Miguel; Gómez-Cortés, Rosario; Molgado, Alberto; Rojas, Efraín

    2016-06-01

    We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant field theories.

  13. Adaptive sparse grid expansions of the vibrational Hamiltonian.

    PubMed

    Strobusch, D; Scheurer, Ch

    2014-02-21

    The vibrational Hamiltonian involves two high dimensional operators, the kinetic energy operator (KEO), and the potential energy surface (PES). Both must be approximated for systems involving more than a few atoms. Adaptive approximation schemes are not only superior to truncated Taylor or many-body expansions (MBE), they also allow for error estimates, and thus operators of predefined precision. To this end, modified sparse grids (SG) are developed that can be combined with adaptive MBEs. This MBE/SG hybrid approach yields a unified, fully adaptive representation of the KEO and the PES. Refinement criteria, based on the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods, are presented. The combination of the adaptive MBE/SG approach and the VSCF plus VCI methods yields a black box like procedure to compute accurate vibrational spectra. This is demonstrated on a test set of molecules, comprising water, formaldehyde, methanimine, and ethylene. The test set is first employed to prove convergence for semi-empirical PM3-PESs and subsequently to compute accurate vibrational spectra from CCSD(T)-PESs that agree well with experimental values.

  14. Two-dimensional collective Hamiltonian for chiral and wobbling modes

    NASA Astrophysics Data System (ADS)

    Chen, Q. B.; Zhang, S. Q.; Zhao, P. W.; Jolos, R. V.; Meng, J.

    2016-10-01

    A two-dimensional collective Hamiltonian (2DCH) on both azimuth and polar motions in triaxial nuclei is proposed to investigate the chiral and wobbling modes. In the 2DCH, the collective potential and the mass parameters are determined from three-dimensional tilted axis cranking (TAC) calculations. The broken chiral and signature symmetries in the TAC solutions are restored by the 2DCH. The validity of the 2DCH is illustrated with a triaxial rotor (γ =-30∘ ) coupling to one h11 /2 proton particle and one h11 /2 neutron hole. By diagonalizing the 2DCH, the angular momenta and energy spectra are obtained. These results agree with the exact solutions of the particle rotor model (PRM) at high rotational frequencies. However, at low frequencies, the energies given by the 2DCH are larger than those by the PRM due to the underestimation of the mass parameters. In addition, with increasing angular momentum, the transitions from the chiral vibration to chiral rotation and further to longitudinal wobbling motion have been presented in the 2DCH.

  15. Elliptical vortices in shear: Hamiltonian moment formulation and Melnikov analysis

    SciTech Connect

    Ngan, K.; Meacham, S.; Morrison, P.J.

    1995-07-01

    The equations of motion for interacting, elliptical vortices in a background shear flow are derived using a Hamiltonian moment formulation. The equations reduce to the 6th order system of Melander et al. [J. Fluid Mech. 167, 95 (1986)] when a pair of vortices is considered and shear is neglected. The equations for a pair of identical vortices axe analyzed with a number of methods, with particular emphasis on the basic interactions and on the implications for vortex merger. The splitting distance between the stable and unstable manifolds connecting the hyperbolic fixed points of the intercentroidal motion-the separatrix splitting-is estimated with a Melnikov analysis. This analysis differs from the standard time-periodic Melnikov analysis on two counts: (a) the ``periodic`` perturbation arises from a second degree of freedom in the system which is not wholly independent of the first degree of freedom, the intercentroidal motion; (b) this perturbation has a faster time scale than the intercentroidal motion. The resulting Melnikov integral appears to be exponentially small in the perturbation as the latter goes to zero. Numerical simulations, notably Poincare sections, provide a global view of the dynamics and indicate that there are two modes of merger. The effect of the shear on chaotic motion and on chaotic scattering is also discussed.

  16. Hamiltonian truncation approach to quenches in the Ising field theory

    NASA Astrophysics Data System (ADS)

    Rakovszky, T.; Mestyán, M.; Collura, M.; Kormos, M.; Takács, G.

    2016-10-01

    In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1 + 1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.

  17. Hamiltonian dynamics of two same-sign point vortices

    NASA Astrophysics Data System (ADS)

    Murray, Anderson V.; Groszek, Andrew J.; Kuopanportti, Pekko; Simula, Tapio

    2016-03-01

    We have studied numerically the Hamiltonian dynamics of two same-sign point vortices in an effectively two-dimensional, harmonically trapped Bose-Einstein condensate. We have found in the phase space of the system an impenetrable wall that divides the dynamics into two distinct and exhaustive types. In the two-dimensional position-coordinate space, the first type corresponds to intersecting single-vortex orbits and the second type to orbits that have no points in common. The two types are also easily distinguished in the two-dimensional space spanned by the radial and angular velocities of the vortices: In the first type, both single-vortex orbits are the same simple loop in this two-dimensional space, whereas in the second type the two orbits constitute two nonintersecting loops. The phase-space-dividing wall is distinct from the bifurcation curve of rigidly rotating states found by Navarro et al. [Phys. Rev. Lett. 110, 225301 (2013), 10.1103/PhysRevLett.110.225301].

  18. Hamiltonian description of ideal fluids and MHD flows

    NASA Astrophysics Data System (ADS)

    Kuznetsov, E. A.

    2002-11-01

    Vortex line and magnetic line representations are introduced for description of flows in ideal hydrodynamics and MHD, respectively. For incompressible fluids it is shown that the equations of motion for vorticity Ω and magnetic field with the help of this transformation follow from the variational principle. By means of this representation it is possible to integrate the system of hydrodynamic type with the Hamiltonian lH=int |Ω| dr. It is also demonstrated that these representations allow to remove from the noncanonical Poisson brackets, defined on the space of divergence-free vector fields, degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD a new Weber type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent this transformation coincides with the Clebsch representation analog introduced in (V.E.Zakharov and E.A.Kuznetsov, Doklady USSR Ac. Nauk. (Soviet Doklady), 194), 1288 (1970).

  19. From lattice Hamiltonians to tunable band structures by lithographic design

    NASA Astrophysics Data System (ADS)

    Tadjine, Athmane; Allan, Guy; Delerue, Christophe

    2016-08-01

    Recently, new materials exhibiting exotic band structures characterized by Dirac cones, nontrivial flat bands, and band crossing points have been proposed on the basis of effective two-dimensional lattice Hamiltonians. Here, we show using atomistic tight-binding calculations that these theoretical predictions could be experimentally realized in the conduction band of superlattices nanolithographed in III-V and II-VI semiconductor ultrathin films. The lithographed patterns consist of periodic lattices of etched cylindrical holes that form potential barriers for the electrons in the quantum well. In the case of honeycomb lattices, the conduction minibands of the resulting artificial graphene host several Dirac cones and nontrivial flat bands. Similar features, but organized in different ways, in energy or in k -space are found in kagome, distorted honeycomb, and Lieb superlattices. Dirac cones extending over tens of meV could be obtained in superlattices with reasonable sizes of the lithographic patterns, for instance in InAs/AlSb heterostructures. Bilayer artificial graphene could be also realized by lithography of a double quantum-well heterostructure. These new materials should be interesting for the experimental exploration of Dirac-based quantum systems, for both fundamental and applied physics.

  20. Coupling spin to velocity: collective motion of Hamiltonian polar particles

    NASA Astrophysics Data System (ADS)

    Løland Bore, Sigbjørn; Schindler, Michael; Nguyen Thu Lam, Khanh-Dang; Bertin, Eric; Dauchot, Olivier

    2016-03-01

    We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling between spin and velocity of the same particle inspired by the coupling observed in self-propelled hard discs. Because of this coupling Galilean invariance is broken and the conserved linear momentum associated to translation invariance is not proportional to the velocity of the center of mass. Also, the dynamics is not invariant under a global rotation of the spins alone. This, in principle, leaves room for collective motion and thus raises the question whether collective motion can arise in Hamiltonian systems. We study the statistical mechanics of such a system, and show that, in the fully connected (or mean-field) case, a transition to collective motion does exist in spite of momentum conservation. Interestingly, the velocity of the center of mass, which in the absence of Galilean invariance, is a relevant variable, also feeds back on the magnetization properties, as it acts as an external magnetic field that smoothens the transition. Molecular dynamics simulations of finite size systems indeed reveal a rich phase diagram, with a transition from a disordered to a homogeneous polar phase, but also more complex inhomogeneous phases with local order interrupted by topological defects.

  1. Adaptive sparse grid expansions of the vibrational Hamiltonian

    SciTech Connect

    Strobusch, D.; Scheurer, Ch.

    2014-02-21

    The vibrational Hamiltonian involves two high dimensional operators, the kinetic energy operator (KEO), and the potential energy surface (PES). Both must be approximated for systems involving more than a few atoms. Adaptive approximation schemes are not only superior to truncated Taylor or many-body expansions (MBE), they also allow for error estimates, and thus operators of predefined precision. To this end, modified sparse grids (SG) are developed that can be combined with adaptive MBEs. This MBE/SG hybrid approach yields a unified, fully adaptive representation of the KEO and the PES. Refinement criteria, based on the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods, are presented. The combination of the adaptive MBE/SG approach and the VSCF plus VCI methods yields a black box like procedure to compute accurate vibrational spectra. This is demonstrated on a test set of molecules, comprising water, formaldehyde, methanimine, and ethylene. The test set is first employed to prove convergence for semi-empirical PM3-PESs and subsequently to compute accurate vibrational spectra from CCSD(T)-PESs that agree well with experimental values.

  2. On the Convexity of the KdV Hamiltonian

    NASA Astrophysics Data System (ADS)

    Kappeler, Thomas; Maspero, Alberto; Molnar, Jan; Topalov, Peter

    2016-08-01

    Motivated by perturbation theory, we prove that the nonlinear part {H^{*}} of the KdV Hamiltonian {H^{kdv}}, when expressed in action variables {I = (In)_{n ≥slant 1}}, extends to a real analytic function on the positive quadrant {ℓ2+({N})} of {ℓ2({N})} and is strictly concave near {0}. As a consequence, the differential of {H^{*}} defines a local diffeomorphism near 0 of {ℓ_{{C}}2({N})}. Furthermore, we prove that the Fourier-Lebesgue spaces {{F}{L}^{s,p}} with {-1/2 ≤slant s ≤slant 0} and {2 ≤slant p < ∞}, admit global KdV-Birkhoff coordinates. In particular, it means that {ℓ2_+({N})} is the space of action variables of the underlying phase space {{F}{L}^{-1/2,4}} and that the KdV equation is globally in time {C0}-well-posed on {{F}{L}^{-1/2,4}}.

  3. Semiclassical Approximations for Hamiltonians with Operator-Valued Symbols

    NASA Astrophysics Data System (ADS)

    Stiepan, Hans-Michael; Teufel, Stefan

    2013-06-01

    We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter {\\varepsilon ≪ 1} controls the separation of time scales and the limit {\\varepsilonto 0} corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time {\\varepsilonto 0} is the semiclassical limit for the slow degrees of freedom. In this paper we show that the {\\varepsilon} -dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn (Phys Rev A (3) 44(8):5239-5256, 1991), coming from an {\\varepsilon} -dependent classical Hamilton function and an {\\varepsilon} -dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order {\\varepsilon^2} . In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics (Xiao et al. in Rev Mod Phys 82(3):1959-2007, 2010). Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.

  4. Electronic coupling calculation and pathway analysis of electron transfer reaction using ab initio fragment-based method. I. FMO-LCMO approach

    NASA Astrophysics Data System (ADS)

    Nishioka, Hirotaka; Ando, Koji

    2011-05-01

    By making use of an ab initio fragment-based electronic structure method, fragment molecular orbital-linear combination of MOs of the fragments (FMO-LCMO), developed by Tsuneyuki et al. [Chem. Phys. Lett. 476, 104 (2009)], 10.1016/j.cplett.2009.05.069, we propose a novel approach to describe long-distance electron transfer (ET) in large system. The FMO-LCMO method produces one-electron Hamiltonian of whole system using the output of the FMO calculation with computational cost much lower than conventional all-electron calculations. Diagonalizing the FMO-LCMO Hamiltonian matrix, the molecular orbitals (MOs) of the whole system can be described by the LCMOs. In our approach, electronic coupling TDA of ET is calculated from the energy splitting of the frontier MOs of whole system or perturbation method in terms of the FMO-LCMO Hamiltonian matrix. Moreover, taking into account only the valence MOs of the fragments, we can considerably reduce computational cost to evaluate TDA. Our approach was tested on four different kinds of model ET systems with non-covalent stacks of methane, non-covalent stacks of benzene, trans-alkanes, and alanine polypeptides as their bridge molecules, respectively. As a result, it reproduced reasonable TDA for all cases compared to the reference all-electron calculations. Furthermore, the tunneling pathway at fragment-based resolution was obtained from the tunneling current method with the FMO-LCMO Hamiltonian matrix.

  5. Investigation of Bohr Hamiltonian in the presence of time-dependent Manning-Rosen, harmonic oscillator and double ring shaped potentials

    NASA Astrophysics Data System (ADS)

    Sobhani, Hadi; Hassanabadi, Hassan

    2016-08-01

    This paper contains study of Bohr Hamiltonian considering time-dependent form of two important and famous nuclear potentials and harmonic oscillator. Dependence on time in interactions is considered in general form. In order to investigate this system, a powerful mathematical method has been employed, so-called Lewis-Riesenfeld dynamical invariant method. Appropriate dynamical invariant for considered system has been constructed. Then its eigen functions and the wave function are derived. At the end, we discussed about physical meaning of the results.

  6. Ab Initio Study of Polonium

    SciTech Connect

    Zabidi, Noriza Ahmad; Kassim, Hasan Abu; Shrivastava, Keshav N.

    2008-05-20

    Polonium is the only element with a simple cubic (sc) crystal structure. Atoms in solid polonium sit at the corners of a simple cubic unit cell and no where else. Polonium has a valence electron configuration 6s{sup 2}6p{sup 4} (Z = 84). The low temperature {alpha}-phase transforms into the rhombohedral (trigonal) {beta} structure at {approx}348 K. The sc {alpha}-Po unit cell constant is a = 3.345 A. The beta form of polonium ({beta}-Po) has the lattice parameters, a{sub R} = 3.359 A and a rhombohedral angle 98 deg. 13'. We have performed an ab initio electronic structure calculation by using the density functional theory. We have performed the calculation with and without spin-orbit (SO) coupling by using both the LDA and the GGA for the exchange-correlations. The k-points in a simple cubic BZ are determined by R (0.5, 0.5, 0.5), {gamma} (0, 0, 0), X (0.5, 0, 0), M (0.5, 0.5, 0) and {gamma} (0, 0, 0). Other directions of k-points are {gamma} (0, 0, 0), X (0.5, 0, 0), R (0.5, 0.5, 0.5) and {gamma} (0, 0, 0). The SO splittings of p states at the {gamma} point in the GGA+SO scheme for {alpha}-Po are 0.04 eV and 0.02 eV while for the {beta}-Po these are 0.03 eV and 0.97 eV. We have also calculated the vibrational spectra for the unit cells in both the structures. We find that exchanging of a Po atom by Pb atom produces several more bands and destabilizes the {beta} phase.

  7. Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator

    SciTech Connect

    Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

    2009-05-15

    In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+{alpha}xx+{beta}x{sup 3}+{gamma}x=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+{alpha}x{sup q}x+{beta}x{sup 2q+1}=0, where {alpha}, {beta}, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.

  8. Simple model for deriving [ital sdg] interacting boson model Hamiltonians: [sup 150]Nd example

    SciTech Connect

    Devi, Y.D.; Kota, V.K.B. )

    1993-07-01

    A simple and yet useful model for deriving [ital sdg] interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle ([ital pp] and [ital nn]) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from [ital pn] interaction, with an IBM-2 to IBM-1 projection of the resulting [ital p]-[ital n] [ital sdg] IBM Hamiltonian. The applicability of this model in generating [ital sdg] IBM Hamiltonians is demonstrated, using a single-[ital j]-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, [ital B]([ital E]2)'s, and [ital E]4 strength distribution in the example of [sup 150]Nd.

  9. Ground State Properties of the 1/2 Flux Harper Hamiltonian

    NASA Astrophysics Data System (ADS)

    Kennedy, Colin; Burton, William Cody; Chung, Woo Chang; Ketterle, Wolfgang

    2015-05-01

    The Harper Hamiltonian describes the motion of charged particles in an applied magnetic field - the spectrum of which exhibits the famed Hofstadter's butterfly. Recent advances in driven optical lattices have made great strides in simulating nontrivial Hamiltonians, such as the Harper model, in the time-averaged sense. We report on the realization of the ground state of bosons in the Harper Hamiltonian for 1/2 flux per plaquette utilizing a tilted two-dimensional lattice with laser assisted tunneling. We detail progress in studying various ground state properties of the 1/2 flux Harper Hamiltonian including ground state degeneracies, gauge-dependent observables, effects of micromotion, adiabatic loading schemes, and emergence and decay of coherence. Additionally, we describe prospects for flux rectification using a period-tripled superlattice and generalizations to three dimensions. MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology.

  10. Quantum Simulation via Filtered Hamiltonian Engineering: Application to Perfect Quantum Transport in Spin Networks

    NASA Astrophysics Data System (ADS)

    Ajoy, Ashok; Cappellaro, Paola

    2013-05-01

    We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.

  11. Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks.

    PubMed

    Ajoy, Ashok; Cappellaro, Paola

    2013-05-31

    We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions. PMID:23767705

  12. Complete Hamiltonian analysis of cosmological perturbations at all orders II: non-canonical scalar field

    NASA Astrophysics Data System (ADS)

    Nandi, Debottam; Shankaranarayanan, S.

    2016-10-01

    In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.

  13. Positive-operator-valued measures in the Hamiltonian formulation of quantum mechanics

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

    In the Hilbert space formulation of quantum mechanics, ideal measurements of physical variables are discussed using the spectral theory of Hermitian operators and the corresponding projector-valued measures (PVMs). However, more general types of measurements require the treatment in terms of positive-operator-valued measures (POVMs). In the Hamiltonian formulation of quantum mechanics, canonical coordinates are related to PVM. In this paper the results of an analysis of various aspects of applications of POVMs in the Hamiltonian formulation are reported. Several properties of state parameters and quantum observables given by POVMs or represented in an overcomplete basis, including the general Hamiltonian treatment of the Neumark extension, are presented. An analysis of the phase operator, given by the corresponding POVMs, in the Hilbert space and the Hamiltonian frameworks is also given.

  14. Effective Hamiltonian for surface states of topological insulator thin films with hexagonal warping

    NASA Astrophysics Data System (ADS)

    Siu, Zhuo Bin; Tan, Seng Ghee; Jalil, Mansoor B. A.

    2016-05-01

    The effective Hamiltonian of the surface states on semi-infinite slabs of the topological insulators (TI) Bi2Te3 and Bi2Se3 require the addition of a cubic momentum hexagonal warping term on top of the usual Dirac fermion Hamiltonian in order to reproduce the experimentally measured constant energy contours at intermediate values of Fermi energy. In this work, we derive the effective Hamiltonian for the surface states of a Bi2Se3 thin film incorporating the corresponding hexagonal warping terms. We then calculate the dispersion relation of the effective Hamiltonian and show that the hexagonal warping leads distorts the equal energy contours from the circular cross sections of the Dirac cones.

  15. On an application of the intermediate Hamiltonian method for molecular systems

    SciTech Connect

    Seto, R.; Stankevich, I.V.

    1999-04-01

    An application of the intermediate Hamiltonian method is reported in estimation of the lower bounds to the potential energy curve of the hydrogen molecule ion. An improvement of the method and its limitation are also discussed.

  16. Hamiltonian Formulation for Wave-Current Interactions in Stratified Rotational Flows

    NASA Astrophysics Data System (ADS)

    Constantin, A.; Ivanov, R. I.; Martin, C.-I.

    2016-09-01

    We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.

  17. Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

    SciTech Connect

    Longhi, Stefano

    2014-06-15

    Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -hat} (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for the Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.

  18. Spin orbit coupling for molecular ab initio density matrix renormalization group calculations: Application to g-tensors

    SciTech Connect

    Roemelt, Michael

    2015-07-28

    Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.

  19. Modeling study of the ABS relay valve

    NASA Astrophysics Data System (ADS)

    Lei, Ming; Lin, Min; Guo, Bin; Luo, Zai; Xu, Weidong

    2011-05-01

    The ABS (anti-lock braking system) relay valve is the key component of anti-lock braking system in most commercial vehicles such as trucks, tractor-trailers, etc. In this paper, structure of ABS relay valve and its work theory were analyzed. Then a mathematical model of ABS relay valve, which was investigated by dividing into electronic part, magnetic part, pneumatic part and mechanical part, was set up. The displacement of spools and the response of pressure increasing, holding, releasing of ABS relay valve were simulated and analyzed under conditions of control pressure 500 KPa, braking pressure 600 KPa, atmospheric pressure 100 KPa and air temperature 310 K. Thisarticle provides reliable theory for improving the performance and efficiency of anti-lock braking system of vehicles.

  20. Modeling study of the ABS relay valve

    NASA Astrophysics Data System (ADS)

    Lei, Ming; Lin, Min; Guo, Bin; Luo, Zai; Xu, Weidong

    2010-12-01

    The ABS (anti-lock braking system) relay valve is the key component of anti-lock braking system in most commercial vehicles such as trucks, tractor-trailers, etc. In this paper, structure of ABS relay valve and its work theory were analyzed. Then a mathematical model of ABS relay valve, which was investigated by dividing into electronic part, magnetic part, pneumatic part and mechanical part, was set up. The displacement of spools and the response of pressure increasing, holding, releasing of ABS relay valve were simulated and analyzed under conditions of control pressure 500 KPa, braking pressure 600 KPa, atmospheric pressure 100 KPa and air temperature 310 K. Thisarticle provides reliable theory for improving the performance and efficiency of anti-lock braking system of vehicles.

  1. Hamiltonian structure of the higher-order corrections to the Korteweg-de Vries equation

    NASA Astrophysics Data System (ADS)

    Menyuk, C. R.; Chen, H.-H.

    1985-10-01

    Higher-order corrections to the Korteweg-de Vries equation are examined by Hamiltonian methods. Starting from the underlying Hamiltonian systems (e.g., the two-fluid equations in the case of ion-acoustic waves), one finds that the corrected equations have the same Poisson bracket as the Korteweg-de Vries equation at every order. One also finds that the underlying equations become nonlocal at sufficiently high order.

  2. Generalized velocity-gauge form of the light-matter interaction Hamiltonian beyond the dipole approximation

    NASA Astrophysics Data System (ADS)

    Førre, Morten; Simonsen, Aleksander Skjerlie

    2016-01-01

    The exact velocity-gauge minimal-coupling Hamiltonian describing the laser-matter interaction is transformed into another form by means of a series of gauge transformations. The Hamiltonian corresponding to this point of view is valid for an arbitrary time- and space-dependent laser field, also known as a nondipole field. In effect, the Hamiltonian represents a generalization of the original velocity-gauge minimal-coupling Hamiltonian in the sense that the particle's (classical) velocity in the laser propagation direction is also explicitly accounted for by a new operator term. Imposing the so-called long-wavelength approximation (LWA) on the field, i.e., assuming the laser wavelength being much larger than the extent of the atomic system, the spatial dependence of the field can be neglected and the interaction Hamiltonian reduces to a simpler form. Nevertheless, the resulting LWA Hamiltonian includes the effect of the magnetic-field component of the laser, which is in clear contrast with the usual dipole approximation Hamiltonian derived by imposing the LWA directly on the initial velocity-gauge minimal-coupling Hamiltonian. As such, the weak-field condition necessary to justify neglecting the magnetic field, and the LWA condition, can be considered independently in this formalism, making it an attractive alternative for a broad range of applications in strong-field physics. We demonstrate that, from a numerical perspective, this form of the light-matter interaction is advantageous compared to its standard velocity-gauge counterpart as it gives rise to faster convergence properties when describing ionization dynamics in superintense fields beyond the dipole approximation.

  3. Symmetries, pseudosymmetries and conservation laws in Lagrangian and Hamiltonian k-symplectic formalisms

    NASA Astrophysics Data System (ADS)

    Munteanu, Florian

    2016-01-01

    In this paper, we will present Lagrangian and Hamiltonian k-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will obtain new kinds of conservation laws for k-symplectic Hamiltonian systems and k-symplectic Lagrangian systems.

  4. Non-integrable character of Hamiltonian systems with global and symmetric coupling

    NASA Astrophysics Data System (ADS)

    Umeno, Ken

    A new sufficient condition to prove non-integrability of Hamiltonian systems with symmetric variational equations is proposed. Though the present condition is taken as an extension of Ziglin and Yoshida's “non-resonant condition”, the algorithmic bottle-neck proving non-integrability in high dimensional cases can be removed here. As a result, the non-existence of additional integrals of various symmetric Hamiltonian systems with an arbitrary number of degrees of freedom is proven.

  5. On the time evolution operator for time-dependent quadratic Hamiltonians

    SciTech Connect

    Fernandez, F. M.

    1989-07-01

    The Schr/umlt o/dinger equation with a time-dependent quadratic Hamiltonian isinvestigated. The time-evolution operator is written as a product of exponentialoperators determined by the Heisenberg equations of motion. This productoperator is shown to be global in the occupation number representation when theHamiltonian is Hermitian. The success of some physical applications of theproduct-form representation is explained.

  6. Algebraic expression of the IBM3 hamiltonian in terms of various quantum numbers

    NASA Astrophysics Data System (ADS)

    Hasegawa, M.

    1991-04-01

    The properties of the IBM3 hamiltonian are algebraically studied. The IBM3 hamiltonian determined microscopically has as characteristic that the isospin T, rmrather than the spin J, is essential to classifying the energy spectra. The T-dependence of the two-body boson interactions is expressed in terms of the Casimir operators or quantum numbers of various groups. This algebraic approach makes preparations for phenomenological understanding of light nuclei with definite isospin.

  7. Quantum dynamics on a three-sheeted six-dimensional ab initio potential-energy surface of the phosphine cation: Simulation of the photoelectron spectrum and the ultrafast radiationless decay dynamics

    SciTech Connect

    Bhattacharyya, Swarnendu Domcke, Wolfgang; Dai, Zuyang

    2015-11-21

    A diabatic three-sheeted six-dimensional potential-energy surface has been constructed for the ground state and the lowest excited state of the PH{sub 3}{sup +} cation. Coupling terms of Jahn-Teller and pseudo-Jahn-Teller origin up to eighth order had to be included to describe the pronounced anharmonicity of the surface due to multiple conical intersections. The parameters of the diabatic Hamiltonian have been optimized by fitting the eigenvalues of the potential-energy matrix to ab initio data calculated at the CASSCF/MRCI level employing the correlation-consistent triple-ζ basis. The theoretical photoelectron spectrum of phosphine and the non-adiabatic nuclear dynamics of the phosphine cation have been computed by propagating nuclear wave packets with the multiconfiguration time-dependent Hartree method. The theoretical photoelectron bands obtained by Fourier transformation of the autocorrelation function agree well with the experimental results. It is shown that the ultrafast non-radiative decay dynamics of the first excited state of PH{sub 3}{sup +} is dominated by the exceptionally strong Jahn-Teller coupling of the asymmetric bending vibrational mode together with a hyperline of conical intersections with the electronic ground state induced by the umbrella mode. Time-dependent population probabilities have been computed for the three adiabatic electronic states. The non-adiabatic Jahn-Teller dynamics within the excited state takes place within ≈5 fs. Almost 80% of the excited-state population decay to the ground state within about 10 fs. The wave packets become highly complex and delocalized after 20 fs and no further significant transfer of electronic population seems to occur up to 100 fs propagation time.

  8. An ab initio MO study of butalene

    NASA Astrophysics Data System (ADS)

    Ohta, Katsuhisa; Shima, Toru

    1994-01-01

    Butalene as a structural isomer of p-benzyne has been studied by using an ab initio GVB wavefunction. The geometry of butalene, which is shown to be almost rectangular, is first optimized as a local minimum on the energy surface at the ab initio level. However, the energy barrier of conversion to p-benzyne is as small as 1.6 kcal/mol, and experimental isolation of butalene is predicted to be difficult from a force-constant analysis.

  9. Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions

    NASA Astrophysics Data System (ADS)

    Lloyd, Seth; Terhal, Barbara M.

    2016-02-01

    We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent two-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space-time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.

  10. Symplectic structure of post-Newtonian Hamiltonian for spinning compact binaries

    SciTech Connect

    Wu Xin; Xie Yi

    2010-04-15

    The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum, and spin variables [X,P,S{sub 1},S{sub 2}] compose its phase space. This may give a convenient application of perturbation theory to the derivation of the post-Newtonian formulation, but also makes classic theories of a symplectic Hamiltonian system a serious obstacle in application, especially in diagnosing integrability and nonintegrability from a dynamical system theory perspective. To completely understand the dynamical characteristic of the integrability or nonintegrability for the binary system, we construct a set of conjugate spin variables and reexpress the spin Hamiltonian part so as to make the complete Hamiltonian formulation symplectic. As a result, it is directly shown with the least number of independent isolating integrals that a conservative Hamiltonian compact binary system with both one spin and the pure orbital part to any post-Newtonian order is typically integrable and not chaotic. And a conservative binary system consisting of two spins restricted to the leading order spin-orbit interaction and the pure orbital part at all post-Newtonian orders is also integrable, independently on the mass ratio. For all other various spinning cases, the onset of chaos is possible.

  11. Multiple Time-Step Dual-Hamiltonian Hybrid Molecular Dynamics — Monte Carlo Canonical Propagation Algorithm

    PubMed Central

    Weare, Jonathan; Dinner, Aaron R.; Roux, Benoît

    2016-01-01

    A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method. PMID:26918826

  12. An ab Initio Benchmark and DFT Validation Study on Gold(I)-Catalyzed Hydroamination of Alkynes.

    PubMed

    Ciancaleoni, Gianluca; Rampino, Sergio; Zuccaccia, Daniele; Tarantelli, Francesco; Belanzoni, Paola; Belpassi, Leonardo

    2014-03-11

    High level ab initio calculations have been carried out on an archetypal gold(I)-catalyzed reaction: hydroamination of ethyne. We studied up to 12 structures of possible gold(I)-coordinated species modeling different intermediates potentially present in a catalytic cycle for the addition of a protic nucleophile to an alkyne. The benchmark is used to evaluate the performances of some popular density functionals for describing geometries and relative energies of stationary points along the reaction profile. Most functionals (including hybrid or meta-hybrid) give accurate structures but large nonsystematic errors (4-12 kcal/mol) along the reaction energy profile. The double hybrid functional B2PLYP outperforms all considered functionals and compares very nicely with our reference ab initio benchmark energies. Moreover, we present an assessment of the accuracy of commonly used approaches to include relativistic effects, such as relativistic effective potentials and a scalar ZORA Hamiltonian, by a comparison with the results obtained using a relativistic all-electron four-component Dirac-Kohn-Sham method. The contribution of nonscalar relativistic effects in gold(I)-catalyzed reactions, as we investigated here, is expected to be on the order of 1 kcal/mol. PMID:26580180

  13. On the spin separation of algebraic two-component relativistic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Li, Zhendong; Xiao, Yunlong; Liu, Wenjian

    2012-10-01

    The separation of the spin-free and spin-dependent terms of a given relativistic Hamiltonian is usually facilitated by the Dirac identity. However, this is no longer possible for the recently developed exact two-component relativistic Hamiltonians derived from the matrix representation of the Dirac equation in a kinetically balanced basis. This stems from the fact that the decoupling matrix does not have an explicit form. To resolve this formal difficulty, we first define the spin-dependent term as the difference between a two-component Hamiltonian corresponding to the full Dirac equation and its one-component counterpart corresponding to the spin-free Dirac equation. The series expansion of the spin-dependent term is then developed in two different ways. One is in the spirit of the Douglas-Kroll-Hess (DKH) transformation and the other is based on the perturbative expansion of a two-component Hamiltonian of fixed structure, either the two-step Barysz-Sadlej-Snijders (BSS) or the one-step exact two-component (X2C) form. The algorithms for constructing arbitrary order terms are proposed for both schemes and their convergence patterns are assessed numerically. Truncating the expansions to finite orders leads naturally to a sequence of novel spin-dependent Hamiltonians. In particular, the order-by-order distinctions among the DKH, BSS, and X2C approaches can nicely be revealed. The well-known Pauli, zeroth-order regular approximation, and DKH1 spin-dependent Hamiltonians can also be recovered naturally by appropriately approximating the decoupling and renormalization matrices. On the practical side, the sf-X2C+so-DKH3 Hamiltonian, together with appropriately constructed generally contracted basis sets, is most promising for accounting for relativistic effects in two steps, first spin-free and then spin-dependent, with the latter applied either perturbatively or variationally.

  14. Serum PDGF-AB in pleural mesothelioma.

    PubMed

    Filiberti, Rosa; Marroni, Paola; Neri, Monica; Ardizzoni, Andrea; Betta, Pier Giacomo; Cafferata, Mara A; Canessa, Pier Aldo; Puntoni, Riccardo; Ivaldi, Giovanni Paolo; Paganuzzi, Michela

    2005-01-01

    Overexpression of platelet-derived growth factor (PDGF) has been observed in lung and pleural tumors. The aim of this study was to evaluate the diagnostic and prognostic role of serum PDGF in pleural mesothelioma (PM). Four groups of subjects were studied: 93 malignant PM patients, 33 primary non small cell lung cancer patients, 51 subjects exposed to asbestos, defined as high-risk controls, and 24 healthy controls. PDGF-AB mean concentration was higher in PM patients (45.8 ng/ml) than in high-risk controls (33.1 ng/ml) and healthy controls (26.8 ng/ml). Using the cut-off level of 49.8 ng/ml, corresponding to the mean+2SD of PDGF-AB in healthy controls, 43% of PM patients showed positive PDGF-AB levels. Survival was evaluated in 82 PM patients. At the end of the follow-up (median 9.8 months) 80.5% of patients had died. Median survival was 13.1 and 7.9 months for patients with PDGF-AB lower and higher than the cut-off, respectively. Adjusting for age, sex, histology and platelet count, positive PDGF-AB levels were associated with lower survival (OR=1.2, 95%CI: 0.9-1.6), even if not significantly so. In conclusion, serum PDGF may represent a useful additional parameter to prognostic factors already available for PM.

  15. Ab initio dynamics of the cytochrome P450 hydroxylation reaction

    SciTech Connect

    Elenewski, Justin E.; Hackett, John C

    2015-02-14

    The iron(IV)-oxo porphyrin π-cation radical known as Compound I is the primary oxidant within the cytochromes P450, allowing these enzymes to affect the substrate hydroxylation. In the course of this reaction, a hydrogen atom is abstracted from the substrate to generate hydroxyiron(IV) porphyrin and a substrate-centered radical. The hydroxy radical then rebounds from the iron to the substrate, yielding the hydroxylated product. While Compound I has succumbed to theoretical and spectroscopic characterization, the associated hydroxyiron species is elusive as a consequence of its very short lifetime, for which there are no quantitative estimates. To ascertain the physical mechanism underlying substrate hydroxylation and probe this timescale, ab initio molecular dynamics simulations and free energy calculations are performed for a model of Compound I catalysis. Semiclassical estimates based on these calculations reveal the hydrogen atom abstraction step to be extremely fast, kinetically comparable to enzymes such as carbonic anhydrase. Using an ensemble of ab initio simulations, the resultant hydroxyiron species is found to have a similarly short lifetime, ranging between 300 fs and 3600 fs, putatively depending on the enzyme active site architecture. The addition of tunneling corrections to these rates suggests a strong contribution from nuclear quantum effects, which should accelerate every step of substrate hydroxylation by an order of magnitude. These observations have strong implications for the detection of individual hydroxylation intermediates during P450 catalysis.

  16. Emergence of quasi-one-dimensional physics in a nearly-isotropic three-dimensional molecular crystal: Ab initio modeling of Mo3S7(dmit) 3

    NASA Astrophysics Data System (ADS)

    Jacko, A. C.; Janani, C.; Koepernik, Klaus; Powell, B. J.

    2015-03-01

    We report density functional theory calculations for Mo3S7(dmit) 3 . We derive an ab initio tight-binding model from overlaps of Wannier orbitals; finding a layered model with interlayer hopping terms ˜3 /4 the size of the in-plane terms. The in-plane Hamiltonian interpolates the kagomé and honeycomb lattices. It supports states localized to dodecahedral rings within the plane, which populate one-dimensional (1D) bands and lead to a quasi-1D spin-one model on a layered honeycomb lattice once interactions are included. Two lines of Dirac cones also cross the Fermi energy.

  17. Deuteron distribution in nuclear matter

    NASA Astrophysics Data System (ADS)

    Benhar, O.; Fabrocini, A.; Fantoni, S.; Illarionov, A. Yu.; Lykasov, G. I.

    2002-05-01

    We analyze the properties of deuteron-like structures in infinite, correlated nuclear matter, described by a realistic hamiltonian containing the Urbana v14 two-nucleon and the Urbana TNI many-body potentials. The distribution of neutron-proton pairs, carrying the deuteron quantum numbers, is obtained as a function of the total momentum by computing the overlap between the nuclear matter in its ground state and the deuteron wave functions in correlated basis functions theory. We study the differences between the S- and D-wave components of the deuteron and those of the deuteron-like pair in the nuclear medium. The total number of deuteron type pairs is computed and compared with the predictions of Levinger's quasideuteron model. The resulting Levinger's factor in nuclear matter at equilibrium density is 11.63. We use the local density approximation to estimate the Levinger's factor for heavy nuclei, obtaining results which are consistent with the available experimental data from photoreactions.

  18. Ab interno trabeculectomy: patient selection and perspectives.

    PubMed

    Vinod, Kateki; Gedde, Steven J

    2016-01-01

    Ab interno trabeculectomy is one among several recently introduced minimally invasive glaucoma surgeries that avoid a conjunctival incision and full-thickness sclerostomy involved in traditional glaucoma surgery. Ablation of the trabecular meshwork and inner wall of Schlemm's canal is performed in an arcuate fashion via a clear corneal incision, alone or in combination with phacoemulsification cataract surgery. Intraocular pressure reduction following ab interno trabeculectomy is limited by resistance in distal outflow pathways and generally stabilizes in the mid-to-high teens. Relief of medication burden has been demonstrated by some studies. A very low rate of complications, most commonly transient hyphema and intraocular pressure elevations in the immediate postoperative period, have been reported. However, available data are derived from small retrospective and prospective case series. Randomized, controlled trials are needed to better elucidate the potential merits of ab interno trabeculectomy in the combined setting versus phacoemulsification cataract surgery alone and to compare it with other minimally invasive glaucoma surgeries. PMID:27574396

  19. Full Dimensional Vibrational Calculations for Methane Using AN Accurate New AB Initio Based Potential Energy Surface

    NASA Astrophysics Data System (ADS)

    Majumder, Moumita; Dawes, Richard; Wang, Xiao-Gang; Carrington, Tucker; Li, Jun; Guo, Hua; Manzhos, Sergei

    2014-06-01

    New potential energy surfaces for methane were constructed, represented as analytic fits to about 100,000 individual high-level ab initio data. Explicitly-correlated multireference data (MRCI-F12(AE)/CVQZ-F12) were computed using Molpro [1] and fit using multiple strategies. Fits with small to negligible errors were obtained using adaptations of the permutation-invariant-polynomials (PIP) approach [2,3] based on neural-networks (PIP-NN) [4,5] and the interpolative moving least squares (IMLS) fitting method [6] (PIP-IMLS). The PESs were used in full-dimensional vibrational calculations with an exact kinetic energy operator by representing the Hamiltonian in a basis of products of contracted bend and stretch functions and using a symmetry adapted Lanczos method to obtain eigenvalues and eigenvectors. Very close agreement with experiment was produced from the purely ab initio PESs. References 1- H.-J. Werner, P. J. Knowles, G. Knizia, 2012.1 ed. 2012, MOLPRO, a package of ab initio programs. see http://www.molpro.net. 2- Z. Xie and J. M. Bowman, J. Chem. Theory Comput 6, 26, 2010. 3- B. J. Braams and J. M. Bowman, Int. Rev. Phys. Chem. 28, 577, 2009. 4- J. Li, B. Jiang and Hua Guo, J. Chem. Phys. 139, 204103 (2013). 5- S Manzhos, X Wang, R Dawes and T Carrington, JPC A 110, 5295 (2006). 6- R. Dawes, X-G Wang, A.W. Jasper and T. Carrington Jr., J. Chem. Phys. 133, 134304 (2010).

  20. Effective Hamiltonian for surface states of Bi2Te3 nanocylinders with hexagonal warping

    NASA Astrophysics Data System (ADS)

    Siu, Zhuo Bin; Jalil, Mansoor B. A.; Ghee Tan, Seng

    2016-06-01

    The three-dimensional topological insulator \\text{B}{{\\text{i}}2}\\text{T}{{\\text{e}}3} differs from other topological insulators in the \\text{B}{{\\text{i}}2}\\text{S}{{\\text{e}}3} family in that the effective Hamiltonian of its surface states on a flat semi-infinite slab requires the addition of a cubic momentum hexagonal warping term in order to reproduce the experimentally measured constant energy contours. In this work, we derive the appropriate effective Hamiltonian for the surface states of a \\text{B}{{\\text{i}}2}\\text{T}{{\\text{e}}3} cylinder incorporating the corresponding hexagonal warping terms in a cylindrical geometry. We show that at the energy range where the surface states dominate, the effective Hamiltonian adequately reproduces the dispersion relation obtained from a full four-band Hamiltonian which describes both the bulk and surface states. As an example application of our effective Hamiltonian, we study the transmission between two collinear \\text{B}{{\\text{i}}2}\\text{T}{{\\text{e}}3} cylinders magnetized in different directions perpendicular to their axes. We show that the hexagonal warping term results in a transmission profile between the cylinders which may be of utility in a multiple state magnetic memory bit.