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Sample records for nuclear hamiltonian ab

  1. The nuclear monopole Hamiltonian

    NASA Astrophysics Data System (ADS)

    Duflo, J.; Zuker, A. P.

    1999-05-01

    The monopole Hamiltonian Hm is defined as the part of the interaction that reproduces the average energies of configurations. After separating the bulk contributions, we propose a minimal form for Hm containing six parameters adjusted to reproduce the spectra of particle and hole states on doubly magic cores. The mechanism of shell formation is then explained. The reliability of the parametrization is checked by showing that the predicted particle-hole gaps are consistent with experimental data, and that the monopole matrix elements obtained provide the phenomenological cure made necessary by the bad saturation and shell properties of the realistic NN interaction. Predictions are made for the yet unobserved levels around 132Sn, 22O, 34,42Si, 68,78Ni, and 100Sn and for the particle-hole gaps in these nuclei.

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

    PubMed

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

    2013-04-25

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

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

    SciTech Connect

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

    2009-12-17

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

  4. 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.

  5. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

  7. Relativistic k .p Hamiltonians for centrosymmetric topological insulators from ab initio wave functions

    NASA Astrophysics Data System (ADS)

    Nechaev, I. A.; Krasovskii, E. E.

    2016-11-01

    We present a method to microscopically derive a small-size k .p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three- and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3 , Bi2Te3 , and Sb2Te3 . It turns out that the effective continuous k .p models with open boundary conditions often incorrectly predict the topological character of thin films.

  8. 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.

  9. Unified ab initio approaches to nuclear structure and reactions

    DOE PAGES

    Navratil, Petr; Quaglioni, Sofia; Hupin, Guillaume; ...

    2016-04-13

    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 7Bemore » $${({\\rm{p}},\\gamma )}^{8}{\\rm{B}}$$ radiative capture. Lastly, we highlight our efforts to describe transfer reactions including the 3H$${({\\rm{d}},{\\rm{n}})}^{4}$$He fusion.« less

  10. Ab Initio Effective Rovibrational Hamiltonians for Non-Rigid Molecules via Curvilinear VMP2

    NASA Astrophysics Data System (ADS)

    Changala, Bryan; Baraban, Joshua H.

    2017-06-01

    Accurate predictions of spectroscopic constants for non-rigid molecules are particularly challenging for ab initio theory. For all but the smallest systems, ``brute force'' diagonalization of the full rovibrational Hamiltonian is computationally prohibitive, leaving us at the mercy of perturbative approaches. However, standard perturbative techniques, such as second order vibrational perturbation theory (VPT2), are based on the approximation that a molecule makes small amplitude vibrations about a well defined equilibrium structure. Such assumptions are physically inappropriate for non-rigid systems. In this talk, we will describe extensions to curvilinear vibrational Møller-Plesset perturbation theory (VMP2) that account for rotational and rovibrational effects in the molecular Hamiltonian. Through several examples, we will show that this approach provides predictions to nearly microwave accuracy of molecular constants including rotational and centrifugal distortion parameters, Coriolis coupling constants, and anharmonic vibrational and tunneling frequencies.

  11. 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.

  12. Comparison of nuclear Hamiltonians using spectral function sum rules

    NASA Astrophysics Data System (ADS)

    Rios, A.; Carbone, A.; Polls, A.

    2017-07-01

    Background: The energy weighted sum rules of the single-particle spectral functions provide a quantitative understanding of the fragmentation of nuclear states due to short-range and tensor correlations. Purpose: The aim of this paper is to compare on a quantitative basis the single-particle spectral function generated by different nuclear Hamiltonians in symmetric nuclear matter using the first three energy-weighted moments. Method: The spectral functions are calculated in the framework of the self-consistent Green's function approach at finite temperature within a ladder resummation scheme. We analyze the first three moments of the spectral function and connect these to the correlations induced by the interactions between the nucleons in symmetric nuclear matter. In particular, the variance of the spectral function is directly linked to the dispersive contribution of the self-energy. The discussion is centered around two- and three-body chiral nuclear interactions, with and without renormalization, but we also provide results obtained with the traditional phase-shift-equivalent CD-Bonn and Av18 potentials. Results: The variance of the spectral function is particularly sensitive to the short-range structure of the force, with hard-core interactions providing large variances. Chiral forces yield variances which are an order of magnitude smaller and, when tamed using the similarity renormalization group, the variance reduces significantly and in proportion to the renormalization scale. The presence of three-body forces does not substantially affect the results. Conclusions: The first three moments of the spectral function are useful tools in analyzing the importance of correlations in nuclear ground states. In particular, the second-order moment provides a direct insight into dispersive contributions to the self-energy and its value is indicative of the fragmentation of single-particle states.

  13. 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.

  14. 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.

  15. Toward eliminating the electronic structure bottleneck in nonadiabatic dynamics on the fly: An algorithm to fit nonlocal, quasidiabatic, coupled electronic state Hamiltonians based on ab initio electronic structure data

    NASA Astrophysics Data System (ADS)

    Zhu, Xiaolei; Yarkony, David R.

    2010-03-01

    An algorithm for constructing a quasidiabatic, coupled electronic state Hamiltonian, in a localized region of nuclear coordinate space, suitable for determining bound state spectra, is generalized to determine a nonlocal Hamiltonian capable of describing, for example, multichannel nonadiabatic photodissociation. For Nstate coupled electronic states, the Hamiltonian, Hd, is a symmetric Nstate×Nstate matrix whose elements are polynomials involving: decaying exponentials exp(-ari,jn) n =1,2, where ri,j=Ri-Rj, ri,j=|ri,j|, Rj locates the jth nucleus; and scaled dot-cross product coordinates, proportional to ri,j×ri,k•ri,l. The constructed Hamiltonian is constrained to reproduce, exactly, the ab initio data, energies, gradients, and derivative coupling at selected points, or nodes, in nuclear coordinate space. The remainder of the ab initio data is approximated in a least-squares sense using a normal equations approach. The fitting procedure includes a damping term that precludes oscillations due to the nodal constraints or local excesses of parameters. To illustrate the potential of the fitting procedure an Hd is constructed, with the full nuclear permutation-inversion symmetry, which describes portions of the 1,2 A1 potential energy surfaces of NH3, including the minimum energy point on the 1,2 A1 seam of conical intersection and the NH2+H asymptote. Ab initio data at 239 nuclear configurations was used in the construction which was tested at 48 additional nuclear configurations. While the energy range on the ground and excited potential energy surface is each individually ˜45 000 cm-1, the root mean square error for the energies at all points is only 93.6 cm-1. The location and local conical topography of the minimum energy conical intersection is exactly reproduced. The derivative couplings are shown to be well reproduced, justifying the attribute quasidiabatic.

  16. 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.

  17. Dipole and transition moments of SiH, PH and SH by ab initio effective valence shell Hamiltonian method

    NASA Astrophysics Data System (ADS)

    Park, Jong Keun; Sun, Hosung

    1992-07-01

    The ab initio effective valence shell Hamiltonian method, based on quasi-degenerate many-body perturbation theory, is generalized to calculate molecular properties as well as the valence state energies. The procedure requires the evaluation of effective operators for each molecular property. Effective operators are perturbatively expanded in powers of correlation and contain contributions from excitations outside of the multireference valence space. To demonstrate the validity of this method, calculations for dipole moments of and transition moments between several low lying valence states of SiH, SiH +, PH, PH +, SH, and SH + to the lowest nontrivial order in the correlations have been performed and compared with other theoretical calculations.

  18. 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.

  19. Unified ab initio approaches to nuclear structure and reactions

    SciTech Connect

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

    2016-04-13

    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 ${({\\rm{p}},\\gamma )}^{8}{\\rm{B}}$ radiative capture. Lastly, we highlight our efforts to describe transfer reactions including the 3H${({\\rm{d}},{\\rm{n}})}^{4}$He fusion.

  20. Unified ab initio approaches to nuclear structure and reactions

    SciTech Connect

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

    2016-04-13

    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 ${({\\rm{p}},\\gamma )}^{8}{\\rm{B}}$ radiative capture. Lastly, we highlight our efforts to describe transfer reactions including the 3H${({\\rm{d}},{\\rm{n}})}^{4}$He fusion.

  1. Some implications of the Hartree product treatment of the quantum nuclei in the ab initio nuclear-electronic orbital methodology

    NASA Astrophysics Data System (ADS)

    Gharabaghi, Masumeh; Shahbazian, Shant

    2016-12-01

    In this letter the conceptual and computational implications of the Hartree product type nuclear wavefunction introduced recently within the context of the ab initio non-Born-Oppenheimer Nuclear-electronic orbital (NEO) methodology are considered. It is demonstrated that this wavefunction may imply a pseudo-adiabatic separation of the nuclei and electrons and each nucleus is conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian is deduced for electrons. Using the variational principle this Hamiltonian is employed to derive a modified set of single-component Hartree-Fock equations which are equivalent to the multi-component version derived previously within the context of the NEO and, easy to be implemented computationally.

  2. Ab initio relaxation times and time-dependent Hamiltonians within the steepest-entropy-ascent quantum thermodynamic framework

    NASA Astrophysics Data System (ADS)

    Kim, Ilki; von Spakovsky, Michael R.

    2017-08-01

    Quantum systems driven by time-dependent Hamiltonians are considered here within the framework of steepest-entropy-ascent quantum thermodynamics (SEAQT) and used to study the thermodynamic characteristics of such systems. In doing so, a generalization of the SEAQT framework valid for all such systems is provided, leading to the development of an ab initio physically relevant expression for the intrarelaxation time, an important element of this framework and one that had as of yet not been uniquely determined as an integral part of the theory. The resulting expression for the relaxation time is valid as well for time-independent Hamiltonians as a special case and makes the description provided by the SEAQT framework more robust at the fundamental level. In addition, the SEAQT framework is used to help resolve a fundamental issue of thermodynamics in the quantum domain, namely, that concerning the unique definition of process-dependent work and heat functions. The developments presented lead to the conclusion that this framework is not just an alternative approach to thermodynamics in the quantum domain but instead one that uniquely sheds new light on various fundamental but as of yet not completely resolved questions of thermodynamics.

  3. Advances in ab initio theories for nuclear reactions

    NASA Astrophysics Data System (ADS)

    Quaglioni, Sofia

    2016-09-01

    Driven by high-performance computing and new ideas, in recent years ab initio theory has made great strides in achieving a unified description of nuclear structure, clustering and reactions from the constituent nucleons and their strong and electroweak interactions. This is giving access to forefront tools and new fertile grounds to further our understanding of the nuclear force and electroweak currents in nuclei in terms of effective degrees of freedom. A fundamental understanding of nuclear reaction mechanisms and a new capability to accurately compute their properties is also relevant for nuclear astrophysics, terrestrial applications of nuclear fusion, and for using nuclei as probes of fundamental physics through, for example, neutrino-nucleus scattering. In this talk, I will present recent highlights and reflect on future perspectives for this area of nuclear theory. Prepared by LLNL under Contract No. DE-AC52-07NA27344.

  4. Ab initio calculations of nuclear structure and reactions with chiral two- and three-nucleon interactions

    NASA Astrophysics Data System (ADS)

    Navratil, Petr; Langhammer, Joachim; Hupin, Guillaume; Quaglioni, Sofia; Calci, Angelo; Roth, Robert; Soma, Vittorio; Cipollone, Andrea; Barbieri, Carlo; Duguet, T.

    2014-09-01

    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 recent years, a significant progress has been made in developing ab initio many-body approaches capable of describing both bound and scattering states in light and medium mass nuclei based on input from QCD employing Hamiltonians constructed within chiral effective field theory. We will present calculations of proton-10C scattering and resonances of the exotic nuclei 11N and 9He within the no-core shell model with continuum. Also, we will discuss calculations of binding and separation energies of neutron rich isotopes of Ar, K, Ca, Sc and Ti within the self-consistent Gorkov-Green's function approach. 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 recent years, a significant progress has been made in developing ab initio many-body approaches capable of describing both bound and scattering states in light and medium mass nuclei based on input from QCD employing Hamiltonians constructed within chiral effective field theory. We will present calculations of proton-10C scattering and resonances of the exotic nuclei 11N and 9He within the no-core shell model with continuum. Also, we will discuss calculations of binding and separation energies of neutron rich isotopes of Ar, K, Ca, Sc and Ti within the self-consistent Gorkov-Green's function approach. Support from the NSERC Grant No. 401945-2011 is acknowledged. This work was prepared in part by the LLNL under Contract No. DE-AC52-07NA27344.

  5. Study of Nuclear Clustering from an Ab Initio Perspective

    NASA Astrophysics Data System (ADS)

    Kravvaris, Konstantinos; Volya, Alexander

    2017-08-01

    We put forward a new ab initio approach that seamlessly bridges the structure, clustering, and reactions aspects of the nuclear quantum many-body problem. The configuration interaction technique combined with the resonating group method based on a harmonic oscillator basis allows us to treat the reaction and multiclustering dynamics in a translationally invariant way and preserve the Pauli principle. Our presentation includes studies of Be,108 and an exploration of 3 α clustering in 12C.

  6. Ab initio study of the Zener polaron spectrum of half-doped manganites: Comparison of several model Hamiltonians

    NASA Astrophysics Data System (ADS)

    Bastardis, Roland; Guihéry, Nathalie; de Graaf, Coen

    2006-07-01

    The low-energy spectrum of the Zener polaron in half-doped manganite is studied by means of correlated ab initio calculations. It is shown that the electronic structure of the low-energy states results from a subtle interplay between double-exchange configurations and O 2pσ to Mn 3d charge-transfer configurations that obey a Heisenberg logic. The comparison of the calculated spectrum to those predicted by the Zener Hamiltonian reveals that this simple description does not correctly reproduces the Zener polaron physics. A better reproduction of the calculated spectrum is obtained with either a Heisenberg model that considers a purely magnetic oxygen or the Girerd-Papaefthymiou double-exchange model. An additional significant improvement is obtained when different antiferromagnetic contributions are combined with the double-exchange model, showing that the Zener polaron spectrum is actually ruled by a refined double-exchange mechanism where non-Hund atomic states play a non-negligible role. Finally, eight states of a different nature have been found to be intercalated in the double-exchange spectrum. These states exhibit an O to Mn charge transfer, implying a second O 2p orbital of approximate π character instead of the usual σ symmetry. A small mixing of the two families of states occurs, accounting for the final ordering of the states.

  7. 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).

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

    NASA Astrophysics Data System (ADS)

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

    2012-07-01

    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.

  9. 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.

  10. Ab initio calculations of nuclear widths via an integral relation

    NASA Astrophysics Data System (ADS)

    Nollett, Kenneth M.

    2012-10-01

    I describe the computation of energy widths of nuclear states using an integral over the interaction region of ab initio variational Monte Carlo wave functions, and I present calculated widths for many states. I begin by presenting relations that connect certain short-range integrals to widths. I then present predicted widths for 5⩽A⩽9 nuclei, and I compare them against measured widths. They match the data more closely and with less ambiguity than estimates based on spectroscopic factors. I consider the consequences of my results for identification of observed states in 8B, 9He, and 9Li. I also examine failures of the method and conclude that they generally involve broad states and variational wave functions that are not strongly peaked in the interaction region. After examining bound-state overlap functions computed from a similar integral relation, I conclude that overlap calculations can diagnose cases in which computed widths should not be trusted.

  11. 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.

  12. Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules

    NASA Astrophysics Data System (ADS)

    Rey, M.; Nikitin, A. V.; Tyuterev, Vl. G.

    2010-08-01

    A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY3 molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH3 where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)].

  13. Ab initio effective rotational and rovibrational Hamiltonians for non-rigid systems via curvilinear second order vibrational Møller-Plesset perturbation theory

    NASA Astrophysics Data System (ADS)

    Changala, P. Bryan; Baraban, Joshua H.

    2016-11-01

    We present a perturbative method for ab initio calculations of rotational and rovibrational effective Hamiltonians of both rigid and non-rigid molecules. Our approach is based on a curvilinear implementation of second order vibrational Møller-Plesset perturbation theory extended to include rotational effects via a second order contact transformation. Though more expensive, this approach is significantly more accurate than standard second order vibrational perturbation theory for systems that are poorly described to zeroth order by rectilinear normal mode harmonic oscillators. We apply this method to and demonstrate its accuracy on two molecules: Si2C, a quasilinear triatomic with significant bending anharmonicity, and CH3NO2, which contains a completely unhindered methyl rotor. In addition to these two examples, we discuss several key technical aspects of the method, including an efficient implementation of Eckart and quasi-Eckart frame embedding that does not rely on numerical finite differences.

  14. Ab initio effective rotational and rovibrational Hamiltonians for non-rigid systems via curvilinear second order vibrational Møller-Plesset perturbation theory.

    PubMed

    Changala, P Bryan; Baraban, Joshua H

    2016-11-07

    We present a perturbative method for ab initio calculations of rotational and rovibrational effective Hamiltonians of both rigid and non-rigid molecules. Our approach is based on a curvilinear implementation of second order vibrational Møller-Plesset perturbation theory extended to include rotational effects via a second order contact transformation. Though more expensive, this approach is significantly more accurate than standard second order vibrational perturbation theory for systems that are poorly described to zeroth order by rectilinear normal mode harmonic oscillators. We apply this method to and demonstrate its accuracy on two molecules: Si2C, a quasilinear triatomic with significant bending anharmonicity, and CH3NO2, which contains a completely unhindered methyl rotor. In addition to these two examples, we discuss several key technical aspects of the method, including an efficient implementation of Eckart and quasi-Eckart frame embedding that does not rely on numerical finite differences.

  15. 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.

  16. Accurate ab initio tight-binding Hamiltonians: Effective tools for electronic transport and optical spectroscopy from first principles

    NASA Astrophysics Data System (ADS)

    D'Amico, Pino; Agapito, Luis; Catellani, Alessandra; Ruini, Alice; Curtarolo, Stefano; Fornari, Marco; Nardelli, Marco Buongiorno; Calzolari, Arrigo

    2016-10-01

    The calculations of electronic transport coefficients and optical properties require a very dense interpolation of the electronic band structure in reciprocal space that is computationally expensive and may have issues with band crossing and degeneracies. Capitalizing on a recently developed pseudoatomic orbital projection technique, we exploit the exact tight-binding representation of the first-principles electronic structure for the purposes of (i) providing an efficient strategy to explore the full band structure En(k ) , (ii) computing the momentum operator differentiating directly the Hamiltonian, and (iii) calculating the imaginary part of the dielectric function. This enables us to determine the Boltzmann transport coefficients and the optical properties within the independent particle approximation. In addition, the local nature of the tight-binding representation facilitates the calculation of the ballistic transport within the Landauer theory for systems with hundreds of atoms. In order to validate our approach we study the multivalley band structure of CoSb3 and a large core-shell nanowire using the ACBN0 functional. In CoSb3 we point the many band minima contributing to the electronic transport that enhance the thermoelectric properties; for the core-shell nanowire we identify possible mechanisms for photo-current generation and justify the presence of protected transport channels in the wire.

  17. 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.

  18. Ground-state properties of Na2IrO3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

    NASA Astrophysics Data System (ADS)

    Okubo, Tsuyoshi; Shinjo, Kazuya; Yamaji, Youhei; Kawashima, Naoki; Sota, Shigetoshi; Tohyama, Takami; Imada, Masatoshi

    2017-08-01

    We investigate the ground state properties of Na2IrO3 based on numerical calculations of the recently proposed ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study [Y. Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), 10.1103/PhysRevLett.113.107201], we apply a two-dimensional density matrix renormalization group and an infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of Na2IrO3 is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the ab initio value of Na2IrO3 controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in 120 degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a 16-site unit cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in A2IrO3 compounds for A other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contributing to finding a route to realize the Kitaev spin liquid.

  19. 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.

  20. 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.

  1. Extension of the MIRS computer package for the modeling of molecular spectra: From effective to full ab initio ro-vibrational Hamiltonians in irreducible tensor form

    NASA Astrophysics Data System (ADS)

    Nikitin, A. V.; Rey, M.; Champion, J. P.; Tyuterev, Vl. G.

    2012-07-01

    The MIRS software for the modeling of ro-vibrational spectra of polyatomic molecules was considerably extended and improved. The original version [Nikitin AV, Champion JP, Tyuterev VlG. The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules. J Quant Spectrosc Radiat Transf 2003;82:239-49.] was especially designed for separate or simultaneous treatments of complex band systems of polyatomic molecules. It was set up in the frame of effective polyad models by using algorithms based on advanced group theory algebra to take full account of symmetry properties. It has been successfully used for predictions and data fitting (positions and intensities) of numerous spectra of symmetric and spherical top molecules within the vibration extrapolation scheme. The new version offers more advanced possibilities for spectra calculations and modeling by getting rid of several previous limitations particularly for the size of polyads and the number of tensors involved. It allows dealing with overlapping polyads and includes more efficient and faster algorithms for the calculation of coefficients related to molecular symmetry properties (6C, 9C and 12C symbols for C3v, Td, and Oh point groups) and for better convergence of least-square-fit iterations as well. The new version is not limited to polyad effective models. It also allows direct predictions using full ab initio ro-vibrational normal mode Hamiltonians converted into the irreducible tensor form. Illustrative examples on CH3D, CH4, CH3Cl, CH3F and PH3 are reported reflecting the present status of data available. It is written in C++ for standard PC computer operating under Windows. The full package including on-line documentation and recent data are freely available at http://www.iao.ru/mirs/mirs.htm or http://xeon.univ-reims.fr/Mirs/ or http://icb.u-bourgogne.fr/OMR/SMA/SHTDS/MIRS.html and as supplementary data from the online version of the article.

  2. Quantifying statistical uncertainties in ab initio nuclear physics using Lagrange multipliers

    NASA Astrophysics Data System (ADS)

    Carlsson, B. D.

    2017-03-01

    Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating theoretical uncertainties in ab initio nuclear physics, I here present and compare methods for evaluating the statistical part of the uncertainties. A special focus is put on the (for the field) novel method of Lagrange multipliers (LM). Uncertainties from the fit of the nuclear interaction to experimental data are propagated to a few observables in light-mass nuclei to highlight any differences between the presented methods. The main conclusion is that the LM method is more robust, while covariance-based methods are less demanding in their evaluation.

  3. Realistic collective nuclear Hamiltonian

    NASA Astrophysics Data System (ADS)

    Dufour, Marianne; Zuker, Andrés P.

    1996-10-01

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

  4. Nuclear quantum effect on intramolecular hydrogen bond of hydrogen maleate anion: An ab initio path integral molecular dynamics study

    NASA Astrophysics Data System (ADS)

    Kawashima, Yukio; Tachikawa, Masanori

    2013-05-01

    Ab initio path integral molecular dynamics simulation was performed to understand the nuclear quantum effect on the hydrogen bond of hydrogen malonate anion. Static calculation predicted the proton transfer barrier as 0.12 kcal/mol. Conventional ab initio molecular dynamics simulation at 300 K found proton distribution with a double peak on the proton transfer coordinate. Inclusion of thermal effect alone elongates the hydrogen bond length, which increases the barrier height. Inclusion of nuclear quantum effect washes out this barrier, and distributes a single broad peak in the center. H/D isotope effect on the proton transfer is also discussed.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-09-01

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

  10. 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.

  11. 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.

  12. Spectroscopic fingerprints of toroidal nuclear quantum delocalization via ab initio path integral simulations.

    PubMed

    Schütt, Ole; Sebastiani, Daniel

    2013-04-05

    We investigate the quantum-mechanical delocalization of hydrogen in rotational symmetric molecular systems. To this purpose, we perform ab initio path integral molecular dynamics simulations of a methanol molecule to characterize the quantum properties of hydrogen atoms in a representative system by means of their real-space and momentum-space densities. In particular, we compute the spherically averaged momentum distribution n(k) and the pseudoangular momentum distribution n(kθ). We interpret our results by comparing them to path integral samplings of a bare proton in an ideal torus potential. We find that the hydroxyl hydrogen exhibits a toroidal delocalization, which leads to characteristic fingerprints in the line shapes of the momentum distributions. We can describe these specific spectroscopic patterns quantitatively and compute their onset as a function of temperature and potential energy landscape. The delocalization patterns in the projected momentum distribution provide a promising computational tool to address the intriguing phenomenon of quantum delocalization in condensed matter and its spectroscopic characterization. As the momentum distribution n(k) is also accessible through Nuclear Compton Scattering experiments, our results will help to interpret and understand future measurements more thoroughly.

  13. Ab initio statistical mechanics of surface adsorption and desorption. II. Nuclear quantum effects.

    PubMed

    Alfè, D; Gillan, M J

    2010-07-28

    We show how the path-integral formulation of quantum statistical mechanics can be used to construct practical ab initio techniques for computing the chemical potential of molecules adsorbed on surfaces, with full inclusion of quantum nuclear effects. The techniques we describe are based on the computation of the potential of mean force on a chosen molecule and generalize the techniques developed recently for classical nuclei. We present practical calculations based on density functional theory with a generalized-gradient exchange-correlation functional for the case of H(2)O on the MgO (001) surface at low coverage. We note that the very high vibrational frequencies of the H(2)O molecule would normally require very large numbers of time slices (beads) in path-integral calculations, but we show that this requirement can be dramatically reduced by employing the idea of thermodynamic integration with respect to the number of beads. The validity and correctness of our path-integral calculations on the H(2)O/MgO(001) system are demonstrated by supporting calculations on a set of simple model systems for which quantum contributions to the free energy are known exactly from analytic arguments.

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

    PubMed

    Marsalek, Ondrej; Markland, Thomas E

    2016-02-07

    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.

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

    SciTech Connect

    Marsalek, Ondrej; Markland, Thomas E.

    2016-02-07

    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.

  16. Why Dynamic Simulations are Needed to Calculate Thermally Averaged Spin Hamiltonians

    NASA Astrophysics Data System (ADS)

    Weitekamp, Daniel P.; Mueller, Leonard J.

    1998-03-01

    The spin Hamiltonian needed to describe nearly all magnetic resonance experiments is an average over rapidly relaxing spatial degrees of freedom. This has previously been taken to be a Boltzmann average of quantities calculable from the time-independent Hamiltonian describing the system. We show why this approach is conceptually flawed and describe the physics of previously unsuspected, intrinsically dynamic, contributions to the spin Hamiltonian for this ubiquitous situation. Numerical estimates indicate that these new terms are required in order to simulate nuclear magnetic resonance spectra at the resolution with which they are routinely measured. An approach is outlined in which ab initio electronic structures may be combined with a tractable semi-classical description of rovibrational relaxation to give the necessary dynamic corrections, which are described by an average Liouvillian born as the result of spatial susceptibility (ALBATROSS).

  17. Ab initio calculations of the intermolecular chemical shift in nuclear magnetic resonance in the gas phase and for adsorbed species

    NASA Astrophysics Data System (ADS)

    Jameson, Cynthia J.; de Dios, Angel C.

    1992-07-01

    The chemical shifts observed in nuclear magnetic resonance experiments are the differences in shielding of the nuclear spin in different electronic environments. These are known to depend on intermolecular interactions as evidenced by density-dependent chemical shifts in the gas phase, gas-to-liquid shifts, and adsorption shifts on surfaces. We present the results of the first ab initio intermolecular chemical shielding function calculated for a pair of interacting atoms for a wide range of internuclear separations. We used the localized orbital local origin (LORG) approach of Hansen and Bouman and also investigated the second-order electron correlation contributions using second-order LORG (SOLO). The 39Ar shielding in Ar2 passes through zero at some very short distance, going through a minimum, and asymptotically approaches zero at larger separations. The 21Ne shielding function in Ne2 has a similar shape. The Drude model suggests a method of scaling that portion of the shielding function that is weighted most heavily by exp[-V(R)/kT]. The scaling factors, which have been verified in the comparison of 21Ne in Ne2 against 39Ar in Ar2 ab initio results, allows us to project out from the same 39Ar in Ar2 ab initio values the appropriate 129Xe shielding functions in the Xe-Ar, Xe-Kr, and Xe-Xe interacting pairs. These functions lead to temperature-dependent second virial coefficients of chemical shielding which agree with experiments in the gas phase. Ab initio calculations of 39Ar shielding in clusters of argon are used to model the observed 129Xe chemical shifts of Xe, Xe2,...,Xe8 trapped in the cages of zeolite NaA.

  18. Determining quasidiabatic coupled electronic state Hamiltonians using derivative couplings: A normal equations based method.

    PubMed

    Papas, Brian N; Schuurman, Michael S; Yarkony, David R

    2008-09-28

    A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing N(state) coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a least-squares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a least-squares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the 1 (2)A(1) and 1 (2)E states of the 1-propynyl radical, CH(3)CC.

  19. Communication: XFAIMS—eXternal Field Ab Initio Multiple Spawning for electron-nuclear dynamics triggered by short laser pulses

    SciTech Connect

    Mignolet, Benoit; Curchod, Basile F. E.; Martinez, Todd J.

    2016-11-17

    Attoscience is an emerging field where attosecond pulses or few cycle IR pulses are used to pump and probe the correlated electron-nuclear motion of molecules. We present the trajectory-guided eXternal Field Ab Initio Multiple Spawning (XFAIMS) method that models such experiments “on-the-fly,” from laser pulse excitation to fragmentation or nonadiabatic relaxation to the ground electronic state. For the photoexcitation of the LiH molecule, we show that XFAIMS gives results in close agreement with numerically exact quantum dynamics simulations, both for atto- and femtosecond laser pulses. As a result, we then show the ability of XFAIMS to model the dynamics in polyatomic molecules by studying the effect of nuclear motion on the photoexcitation of a sulfine (H2CSO).

  20. Communication: XFAIMS—eXternal Field Ab Initio Multiple Spawning for electron-nuclear dynamics triggered by short laser pulses

    DOE PAGES

    Mignolet, Benoit; Curchod, Basile F. E.; Martinez, Todd J.

    2016-11-17

    Attoscience is an emerging field where attosecond pulses or few cycle IR pulses are used to pump and probe the correlated electron-nuclear motion of molecules. We present the trajectory-guided eXternal Field Ab Initio Multiple Spawning (XFAIMS) method that models such experiments “on-the-fly,” from laser pulse excitation to fragmentation or nonadiabatic relaxation to the ground electronic state. For the photoexcitation of the LiH molecule, we show that XFAIMS gives results in close agreement with numerically exact quantum dynamics simulations, both for atto- and femtosecond laser pulses. As a result, we then show the ability of XFAIMS to model the dynamics inmore » polyatomic molecules by studying the effect of nuclear motion on the photoexcitation of a sulfine (H2CSO).« less

  1. Weakly Hamiltonian actions

    NASA Astrophysics Data System (ADS)

    Martínez Torres, David; Miranda, Eva

    2017-05-01

    In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split into Hamiltonian and non-Hamiltonian factors, and explore generalizations in the Poisson setting.

  2. 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.

  3. The isotropic Hamiltonian formalism

    SciTech Connect

    Vaisman, Izu

    2011-02-10

    A Hamiltonian formalism is a procedure that allows to associate a dynamical system to a function and that includes classical Hamiltonian mechanics as a particular case. The present, expository paper gives a survey of the Hamiltonian formalism defined by an isotropic subbundle of TM+T*M, in particular, by a Dirac structure. We discuss reduction and geometric quantization of the Hamiltonian dynamical systems provided by this formalism.

  4. 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.

  5. Ab initio determination of the nuclear relaxation contribution to the second hyperpolarizability of carbon disulfide

    NASA Astrophysics Data System (ADS)

    Champagne, Benoı̂t

    1998-04-01

    Although basis set saturation, electron correlation and frequency dispersion have been addressed thoroughly, the electronic second hyperpolarizability of carbon disulfide computed by K. Ohta, T. Sakaguchi, K. Kamada and T. Fukumi (Chem. Phys. Lett. 274 (1997) 306) is not in agreement with experiment. In this Letter the potentially substantial nuclear relaxation contribution is evaluated within the Møller-Plesset scheme limited to second order by using the 6-31G * basis set augmented by three diffuse functions (1p and 2d). Within the enhanced approximation, the nuclear relaxation contribution to the static, dc-Kerr and ESHG second hyperpolarizability turns out to amount to 26.5%, 6.8% and -0.8% of the pure static electronic counterpart, respectively. The remaining gap between theory and experiment suggests new experiments should be carried out.

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

    NASA Astrophysics Data System (ADS)

    Watts, Daniel; Finkenstadt, Daniel

    2012-02-01

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

  7. Modelling the local atomic structure of molybdenum in nuclear waste glasses with ab initio molecular dynamics simulations.

    PubMed

    Konstantinou, Konstantinos; Sushko, Peter V; Duffy, Dorothy M

    2016-09-21

    The nature of chemical bonding of molybdenum in high level nuclear waste glasses has been elucidated by ab initio molecular dynamics simulations. Two compositions, (SiO2)57.5-(B2O3)10-(Na2O)15-(CaO)15-(MoO3)2.5 and (SiO2)57.3-(B2O3)20-(Na2O)6.8-(Li2O)13.4-(MoO3)2.5, were considered in order to investigate the effect of ionic and covalent components on the glass structure and the formation of the crystallisation precursors (Na2MoO4 and CaMoO4). The coordination environments of Mo cations and the corresponding bond lengths calculated from our model are in excellent agreement with experimental observations. The analysis of the first coordination shell reveals two different types of molybdenum host matrix bonds in the lithium sodium borosilicate glass. Based on the structural data and the bond valence model, we demonstrate that the Mo cation can be found in a redox state and the molybdate tetrahedron can be connected with the borosilicate network in a way that inhibits the formation of crystalline molybdates. These results significantly extend our understanding of bonding in Mo-containing nuclear waste glasses and demonstrate that tailoring the glass composition to specific heavy metal constituents can facilitate incorporation of heavy metals at high concentrations.

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

    NASA Astrophysics Data System (ADS)

    Walker, Brent; Michaelides, Angelos

    2010-11-01

    The impact of quantum nuclear effects on hydrogen (H-) bond strength has been inferred in earlier work from bond lengths obtained from path integral molecular dynamics (PIMD) simulations. To obtain a direct quantitative assessment of such effects, we use constrained-centroid PIMD simulations to calculate the free energy changes upon breaking the H-bonds in dimers of HF and water. Comparing ab initio simulations performed using PIMD and classical nucleus molecular dynamics (MD), we find smaller dissociation free energies with the PIMD method. Specifically, at 50 K, the H-bond in (HF)2 is about 30% weaker when quantum nuclear effects are included, while that in (H2O)2 is about 15% weaker. In a complementary set of simulations, we compare unconstrained PIMD and classical nucleus MD simulations to assess the influence of quantum nuclei on the structures of these systems. We find increased heavy atom distances, indicating weakening of the H-bond consistent with that observed by direct calculation of the free energies of dissociation.

  10. Significance of symmetry in the nuclear spin Hamiltonian for efficient heteronuclear dipolar decoupling in solid-state NMR: A Floquet description of supercycled rCW schemes.

    PubMed

    Equbal, Asif; Shankar, Ravi; Leskes, Michal; Vega, Shimon; Nielsen, Niels Chr; Madhu, P K

    2017-03-14

    Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient (1)H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (Ix, Iy, Iz) in the interaction frame can lead to complete annihilation of the (1)H-(1)H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of (1)H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme.

  11. Significance of symmetry in the nuclear spin Hamiltonian for efficient heteronuclear dipolar decoupling in solid-state NMR: A Floquet description of supercycled rCW schemes

    NASA Astrophysics Data System (ADS)

    Equbal, Asif; Shankar, Ravi; Leskes, Michal; Vega, Shimon; Nielsen, Niels Chr.; Madhu, P. K.

    2017-03-01

    Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient 1H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (Ix, Iy, Iz) in the interaction frame can lead to complete annihilation of the 1H-1H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of 1H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme.

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

    SciTech Connect

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

    2009-05-15

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

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

    NASA Astrophysics Data System (ADS)

    Gebrerufael, Eskendr; Calci, Angelo; Roth, Robert

    2016-03-01

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

  14. Fitting and using model Hamiltonian in non-adiabatic molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Smale, Jonathan Ross

    In order to study computationally increasingly complex systems using theoretical methods model, Hamiltonians are required to accurately describe the potential energy surface they represent. Also ab-initio methods improve the calculation of the excited states of these complex systems becomes increasingly feasible. One such model Hamiltonian described herein, the Vibronic Coupling Hamiltonian, has previously shown its versatility and ability to describe a variety of non-adiabatic problems. This thesis describes a new method, a genetic algorithm, for the parameterisation of the Vibronic Coupling Hamiltonian to describe both previously calculated potential energy surfaces (allene and pentatetraene) and newly calculated (cyclo-butadiene and toluene) potential energy surfaces. In order to test this genetic algorithm, quantum nuclear dynamics calculations were performed using the multi-configurational time dependent Hartree method and the results compared to experiment..

  15. Ab initio Study of Nuclear Quadrupole Interactions in Selenium and Tellurium

    NASA Astrophysics Data System (ADS)

    Maharjan, N. B.; Paudyal, D. D.; Mishra, D. R.; Byahut, S. P.; Cho, Hwa-Suck; Scheicher, R. H.; Jeong, Junho; Das, T. P.

    2004-03-01

    We are systematically studying the influence of impurities in calcogenide glasses on the glass transition temperature using the first-principles Hartree-Fock cluster method. Results of our calculations on the electronic structures of pure selenium and tellurium chain systems, and with Te and Se impurities respectively, will be reported. By comparing the theoretically obtained nuclear quadrupole interaction (NQI) tensors for ^77Se and ^125Te with available experimental NQI tensors, we were able to test the accuracy of the calculated electronic structures. Good agreement for both the pure and the impurity systems has been found. We have also studied ^125Te NQI tensors in Te-Thiourea and compared our result with experimental data to check on the choice of the ^125Te quadrupole moment used.

  16. MO-AB-207-03: ACR Update in Nuclear Medicine

    SciTech Connect

    Harkness, B.

    2015-06-15

    A goal of an imaging accreditation program is to ensure adequate image quality, verify appropriate staff qualifications, and to assure patient and personnel safety. Currently, more than 35,000 facilities in 10 modalities have been accredited by the American College of Radiology (ACR), making the ACR program one of the most prolific accreditation options in the U.S. In addition, ACR is one of the accepted accreditations required by some state laws, CMS/MIPPA insurance and others. Familiarity with the ACR accreditation process is therefore essential to clinical diagnostic medical physicists. Maintaining sufficient knowledge of the ACR program must include keeping up-to-date as the various modality requirements are refined to better serve the goals of the program and to accommodate newer technologies and practices. This session consists of presentations from authorities in four ACR accreditation modality programs, including magnetic resonance imaging, computed tomography, nuclear medicine, and mammography. Each speaker will discuss the general components of the modality program and address any recent changes to the requirements. Learning Objectives: To understand the requirements of the ACR MR Accreditation program. The discussion will include accreditation of whole-body general purpose magnets, dedicated extremity systems well as breast MRI accreditation. Anticipated updates to the ACR MRI Quality Control Manual will also be reviewed. To understand the requirements of the ACR CT accreditation program, including updates to the QC manual as well as updates through the FAQ process. To understand the requirements of the ACR nuclear medicine accreditation program, and the role of the physicist in annual equipment surveys and the set up and supervision of the routine QC program. To understand the current ACR MAP Accreditation requirement and present the concepts and structure of the forthcoming ACR Digital Mammography QC Manual and Program.

  17. MO-AB-207-00: ACR Update in MR, CT, Nuclear Medicine, and Mammography

    SciTech Connect

    2015-06-15

    A goal of an imaging accreditation program is to ensure adequate image quality, verify appropriate staff qualifications, and to assure patient and personnel safety. Currently, more than 35,000 facilities in 10 modalities have been accredited by the American College of Radiology (ACR), making the ACR program one of the most prolific accreditation options in the U.S. In addition, ACR is one of the accepted accreditations required by some state laws, CMS/MIPPA insurance and others. Familiarity with the ACR accreditation process is therefore essential to clinical diagnostic medical physicists. Maintaining sufficient knowledge of the ACR program must include keeping up-to-date as the various modality requirements are refined to better serve the goals of the program and to accommodate newer technologies and practices. This session consists of presentations from authorities in four ACR accreditation modality programs, including magnetic resonance imaging, computed tomography, nuclear medicine, and mammography. Each speaker will discuss the general components of the modality program and address any recent changes to the requirements. Learning Objectives: To understand the requirements of the ACR MR Accreditation program. The discussion will include accreditation of whole-body general purpose magnets, dedicated extremity systems well as breast MRI accreditation. Anticipated updates to the ACR MRI Quality Control Manual will also be reviewed. To understand the requirements of the ACR CT accreditation program, including updates to the QC manual as well as updates through the FAQ process. To understand the requirements of the ACR nuclear medicine accreditation program, and the role of the physicist in annual equipment surveys and the set up and supervision of the routine QC program. To understand the current ACR MAP Accreditation requirement and present the concepts and structure of the forthcoming ACR Digital Mammography QC Manual and Program.

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  19. Ab initio 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.

  20. 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.

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

    PubMed

    Scherrer, Arne; Vuilleumier, Rodolphe; Sebastiani, Daniel

    2016-08-28

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

  2. Nuclear Quantum Effects in Liquid Water: A Highly Accurate ab initio Path-Integral Molecular Dynamics Study

    NASA Astrophysics Data System (ADS)

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

    2014-03-01

    In this work, we report highly accurate ab initio path-integral molecular dynamics (AI-PIMD) simulations on liquid water at ambient conditions utilizing the recently developed PBE0+vdW(SC) exchange-correlation functional, which accounts for exact exchange and a self-consistent pairwise treatment of van der Waals (vdW) or dispersion interactions, combined with nuclear quantum effects (via the colored-noise generalized Langevin equation). The importance of each of these effects in the theoretical prediction of the structure of liquid water will be demonstrated by a detailed comparative analysis of the predicted and experimental oxygen-oxygen (O-O), oxygen-hydrogen (O-H), and hydrogen-hydrogen (H-H) radial distribution functions as well as other structural properties. In addition, we will discuss the theoretically obtained proton momentum distribution, computed using the recently developed Feynman path formulation, in light of the experimental deep inelastic neutron scattering (DINS) measurements. DOE: DE-SC0008626, DOE: DE-SC0005180.

  3. Modelling the local atomic structure of molybdenum in nuclear waste glasses with ab initio molecular dynamics simulations

    SciTech Connect

    None, None

    2016-01-01

    The nature of chemical bonding of molybdenum in high level nuclear waste glasses has been elucidated by ab initio molecular dynamics simulations. Two compositions, (SiO2)57.5 – (B2O3)10 – (Na2O)15 – (CaO)15 – (MoO3)2.5 and (SiO2)57.3 – (B2O3)20 – (Na2O)6.8 – (Li2O)13.4 – (MoO3)2.5 , were considered in order to investigate the effect of ionic and covalent components on the glass structure and the formation of the crystallisation precursors (Na2MoO4 and CaMoO4). The coordination environments of Mo cations and the corresponding bond lengths calculated from our model are in excellent agreement with experimental observations. The analysis of the first coordination shell reveals two different types of molybdenum host matrix bonds in the lithium sodium borosilicate glass. Based on the structural data and the bond valence model, we demonstrate that the Mo cation can be found in a redox state and the molybdate tetrahedron can be connected with the borosilicate network in a way that inhibits the formation of crystalline molybdates. These results significantly extend our understanding of bonding in Mo-containing nuclear waste glasses and demonstrate that tailoring the glass composition to specific heavy metal constituents can facilitate incorporation of heavy metals at high concentrations. K.K. was supported through the Impact Studentship scheme at UCL co-funded by the IHI Corporation and UCL. P.V.S. thanks the Royal Society, which supported preliminary work on this project, and the Laboratory Directed Research and Development program at PNNL, a multiprogram national laboratory operated by Battelle for the U.S. Department of Energy. Via our membership of the UK's HEC Materials Chemistry Consortium, which is funded by EPSRC (EP/L000202), this work used the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk).

  4. Effective Floquet Hamiltonians for dipolar and quadrupolar coupled N-spin systems in solid state nuclear magnetic resonance under magic angle spinning.

    PubMed

    Pandey, Manoj Kumar; Krishnan, Mangala Sunder

    2010-11-07

    Spin dynamics under magic angle spinning has been studied using different theoretical approaches and also by extensive numerical simulation programs. In this article we present a general theoretical approach that leads to analytic forms for effective Hamiltonians for an N-spin dipolar and quadrupolar coupled system under magic angle spinning (MAS) conditions, using a combination of Floquet theory and van Vleck (contact) transformation. The analytic forms presented are shown to be useful for the study of MAS spin dynamics in solids with the help of a number of simulations in two, three, and four coupled, spin-1/2 systems as well as spins in which quadrupolar interactions are also present.

  5. Path Integrals and Hamiltonians

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2014-03-01

    1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.

  6. Branched Hamiltonians and supersymmetry

    DOE PAGES

    Curtright, Thomas L.; Zachos, Cosmas K.

    2014-03-21

    Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles. In conclusion, a basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail.

  7. Supersymmetry of tridiagonal Hamiltonians

    NASA Astrophysics Data System (ADS)

    Yamani, Hashim A.; Mouayn, Zouhair

    2014-07-01

    A positive semi-definite Hamiltonian H that has a tridiagonal matrix representation in a basis set, allows a definition of forward- and backward-shift operators that can be used to define the matrix representation of its supersymmetric partner Hamiltonian H( + ) with respect to the same basis. We find explicit relationships connecting the matrix elements of both Hamiltonians. We present a method to obtain the orthogonal polynomials in the eigenstate expansion problem attached to H( + ) starting from those polynomials arising in the same problem for H. This connection is established by using the notion of kernel polynomials. We apply the obtained results to two known solvable models with different kinds of spectrum.

  8. Dynamical supersymmetric Dirac Hamiltonians

    SciTech Connect

    Ginocchio, J.N.

    1986-01-01

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

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

    PubMed

    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.

  10. 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.

  11. Ab initio path integral simulations for the fluoride ion-water clusters: competitive nuclear quantum effect between F(-)-water and water-water hydrogen bonds.

    PubMed

    Kawashima, Yukio; Suzuki, Kimichi; Tachikawa, Masanori

    2013-06-20

    Small hydrated fluoride ion complexes, F(-)(H2O)n (n = 1-3), have been studied by ab initio hybrid Monte Carlo (HMC) and ab initio path integral hybrid Monte Carlo (PIHMC) simulations. Because of the quantum effect, our simulation shows that the average hydrogen-bonded F(-)···HO distance in the quantum F(-)(H2O) is shorter than that in the classical one, while the relation inverts at the three water molecular F(-)(H2O)3 cluster. In the case of F(-)(H2O)3, we have found that the nuclear quantum effect enhances the formation of hydrogen bonds between two water molecules. In F(-)(H2O)2 and F(-)(H2O)3, the nuclear quantum effect on two different kinds of hydrogen bonds, F(-)-water and water-water hydrogen bonds, competes against each other. In F(-)(H2O)3, thus, the nuclear quantum effect on the water-water hydrogen bond leads to the elongation of hydrogen-bonded F(-)···HO distance, which we suggest this as the possible origin of the structural inversion from F(-)(H2O) to F(-)(H2O)3.

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

    PubMed

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

    2013-10-04

    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.

  13. Allene and pentatetraene cations as models for intramolecular charge transfer: vibronic coupling Hamiltonian and conical intersections.

    PubMed

    Markmann, Andreas; Worth, Graham A; Cederbaum, Lorenz S

    2005-04-08

    We consider the vibronic coupling effects involving cationic states with degenerate components that can be represented as charge localized at either end of the short cumulene molecules allene and pentatetraene. Our aim is to simulate dynamically the charge transfer process when one component is artificially depopulated. We model the Jahn-Teller vibronic interaction within these states as well as their pseudo-Jahn-Teller coupling with some neighboring states. For the manifold of these states, we have calculated cross sections of the ab initio adiabatic potential energy surfaces along all nuclear degrees of freedom, including points at large distances from the equilibrium to increase the physical significance of our model. Ab initio calculations for the cationic states of allene and pentatetraene were based on the fourth-order Møller-Plesset method and the outer valence Green's function method. In some cases we had to go beyond this method and use the more involved third-order algebraic diagrammatic construction method to include intersections with satellite states. The parameters for a five-state, all-mode diabatic vibronic coupling model Hamiltonian were least-square fitted to these potentials. The coupling parameters for the diabatic model Hamiltonian are such that, in comparison to allene, an enhanced preference for indirect charge transfer is predicted for pentatetraene.

  14. 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.

  15. Stochastic surrogate Hamiltonian

    NASA Astrophysics Data System (ADS)

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

    2008-07-01

    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.

  16. 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.

  17. Experimental quantum Hamiltonian learning

    NASA Astrophysics Data System (ADS)

    Wang, Jianwei; Paesani, Stefano; Santagati, Raffaele; Knauer, Sebastian; Gentile, Antonio A.; Wiebe, Nathan; Petruzzella, Maurangelo; O'Brien, Jeremy L.; Rarity, John G.; Laing, Anthony; Thompson, Mark G.

    2017-06-01

    The efficient characterization of quantum systems, the verification of the operations of quantum devices and the validation of underpinning physical models, are central challenges for quantum technologies and fundamental physics. The computational cost of such studies could be improved by machine learning enhanced by quantum simulators. Here we interface two different quantum systems through a classical channel--a silicon-photonics quantum simulator and an electron spin in a diamond nitrogen-vacancy centre--and use the former to learn the Hamiltonian of the latter via Bayesian inference. We learn the salient Hamiltonian parameter with an uncertainty of approximately 10-5. Furthermore, an observed saturation in the learning algorithm suggests deficiencies in the underlying Hamiltonian model, which we exploit to further improve the model. We implement an interactive version of the protocol and experimentally show its ability to characterize the operation of the quantum photonic device.

  18. Machine-learned approximations to Density Functional Theory Hamiltonians

    PubMed Central

    Hegde, Ganesh; Bowen, R. Chris

    2017-01-01

    Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471

  19. Machine-learned approximations to Density Functional Theory Hamiltonians

    NASA Astrophysics Data System (ADS)

    Hegde, Ganesh; Bowen, R. Chris

    2017-02-01

    Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.

  20. Machine-learned approximations to Density Functional Theory Hamiltonians.

    PubMed

    Hegde, Ganesh; Bowen, R Chris

    2017-02-15

    Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.

  1. Hamiltonian Engineering for High Fidelity Quantum Operations

    NASA Astrophysics Data System (ADS)

    Ribeiro, Hugo; Baksic, Alexandre; Clerk, Aashish

    High-fidelity gates and operations are crucial to almost every aspect of quantum information processing. In recent experiments, fidelity is mostly limited by unwanted couplings with states living out of the logical subspace. This results in both leakage and phase errors. Here, we present a general method to deal simultaneously with both these issues and improve the fidelity of quantum gates and operations. Our method is applicable to a wide variety of systems. As an example, we can correct gates for superconducting qubits, improve coherent state transfer between a single NV centre electronic spin and a single nitrogen nuclear spin, improve control over a nuclear spin ensemble, etc. Our method is intimately linked to the Magnus expansion. By modifying the Magnus expansion of an initially given Hamiltonian Hi, we find analytically additional control Hamiltonians Hctrl such that Hi +Hctrl leads to the desired gate while minimizing both leakage and phase errors.

  2. Which grids are Hamiltonian

    SciTech Connect

    Hedetniemi, S. M.; Hedetniemi, S. T.; Slater, P. J.

    1980-01-01

    A complete grid G/sub m,n/ is a graph having m x n pertices that are connected to form a rectangular lattice in the plane, i.e., all edges of G/sub m,n/ connect vertices along horizontal or vertical lines. A grid is a subgraph of a complete grid. As an illustration, complete grids describe the basic pattern of streets in most cities. This paper examines the existence of Hamiltonian cycles in complete grids and complete grids with one or two vertices removed. It is determined for most values of m,n greater than or equal to 1, which grids G/sub m,n/ - (u) and G/sub m,n/ - (u,v) are Hamiltonian. 12 figures. (RWR)

  3. Hamiltonian spinfoam gravity

    NASA Astrophysics Data System (ADS)

    Wieland, Wolfgang M.

    2014-01-01

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

  4. An electromechanical Ising Hamiltonian

    PubMed Central

    Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi

    2016-01-01

    Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling. PMID:28861469

  5. Approximate symmetries of Hamiltonians

    NASA Astrophysics Data System (ADS)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  6. Chaotic Hamiltonian Dynamics.

    NASA Astrophysics Data System (ADS)

    Bialek, James Mark

    Chaotic behavior may be observed in deterministic Hamiltonian Systems with as few as three dimensions, i.e., X, P, and t. The amount of chaotic behavior depends on the relative influence of the integrable and non-integrable parts of the Hamiltonian. The Standard Map is such a system and the amount of chaotic behavior may be varied by adjusting a single parameter. The global phase space portrait is a complicated mixture of quiescent and chaotic regions. First a new calculational method, characterized by a Fractal Diagram, is presented. This allows the quantitative prediction of the boundaries between regular and chaotic regions in phase space. Where these barriers are located gives qualitative insight into diffusion in phase space. The method is illustrated with the Standard Map but may be applied to any Hamiltonian System. The second phenomenon is the Universal Behavior predicted to occur for all area preserving maps. As a parameter is varied causing the mapping to become more chaotic a pattern is observed in the location and stability of the fixed points of the maps. The fixed points undergo an infinite sequence of period doubling bifurcations in a finite range of the parameter. The relative locations of the fixed point bifurcation and the parameter intervals between bifurcations both asymptotically approach constants which are Universal in that the same constants keep appearing in different problems. Predictions of Universal Behavior have been based on the study of algebraic mappings. The problem we examine has a Hamiltonian given by H = p^2 over {2} - lambda over{2pi}sin(2pi x)sin(2pit). This Hamiltonian describes the motion of a compass needle in a sinusoidally varying magnetic field or, equally well, the one dimensional motion of a particle in a standing wave potential. By treating the magnitude(lambda ) of the time dependent potential as a parameter and by examining the trajectories of the system in a Poincare surface of section, the resulting differential

  7. Hamiltonian cosmology of bigravity

    NASA Astrophysics Data System (ADS)

    Soloviev, V. O.

    2017-03-01

    This article is written as a review of the Hamiltonian formalism for the bigravity with de Rham-Gabadadze-Tolley (dRGT) potential, and also of applications of this formalism to the derivation of the background cosmological equations. It is demonstrated that the cosmological scenarios are close to the standard ΛCDM model, but they also uncover the dynamical behavior of the cosmological term. This term arises in bigravity regardless on the choice of the dRGT potential parameters, and its scale is given by the graviton mass. Various matter couplings are considered.

  8. Ab-initio calculations of electric field gradient in Ru compounds and their implication on the nuclear quadrupole moments of ^{99}Ru and ^{101}Ru

    NASA Astrophysics Data System (ADS)

    Mishra, S. N.

    2017-08-01

    The nuclear quadrupole moments, Q, for the ground and first excited states in ^{99}Ru and ground state of ^{101}Ru have been determined by comparing the experimentally observed quadrupole interaction frequencies ν _Q with calculated electric field gradient (EFG) for a large number of Ru-based compounds. The ab-initio calculations of EFG were performed using the all-electron augmented plane wave + local orbital (APW + lo) method of the density functional theory (DFT). From the slope of the linear correlation between theoretically calculated EFGs and experimentally observed ν _Q, we obtain the quadrupole moment for the (5/2^+) ground state in ^{99}Ru and ^{101}Ru as 0.0734(17) b and 0.431(14) b respectively, showing excellent agreement with the values reported in literature. For 3/2^+, the quadrupole moment of the first excited state in ^{99}Ru is obtained as +0.203(3) b, which is considerably lower than the commonly accepted literature value of +0.231(12) b. The results presented in this paper would be useful for the precise determination of quadrupole moment of high spin states in other Ru isotopes and is likely to stimulate further shell model calculations for an improved understanding of nuclear shape in these nuclei.

  9. 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.

  10. 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.

  11. Ab initio studies of the nuclear magnetic resonance chemical shifts of a rare gas atom in a zeolite

    NASA Astrophysics Data System (ADS)

    Jameson, Cynthia J.; Lim, Hyung-Mi

    1995-09-01

    The intermolecular chemical shift of a rare gas atom inside a zeolite cavity is calculated by ab initio analytical derivative theory using gauge-including atomic orbitals (GIAO) at the Ar atom and the atoms of selected neutral clusters each of which is a 4-, 6-, or 8-ring fragment of the zeolite cage. The Si, Al, O atoms and the charge-balancing counterions (Na+, K+, Ca2+) of the clusters (from 24 to 52 atoms) are at coordinates taken from the refined single crystal x-ray structure of the NaA, KA, and CaA zeolites. Terminating OH groups place the H atom at an appropriate O-H distance along the bond to the next Si or Al atom in the crystal. The chemical shift of the Ar atom located at various positions relative to the cluster is calculated using Boys-Bernardi counterpoise correction at each position. The dependence of the rare gas atom chemical shift on the Al/Si ratio of the clusters is investigated. The resulting shielding values are fitted to a pairwise additive form to elicit effective individual Ar-O, Ar-Na, Ar-K, Ar-Ca intermolecular shielding functions of the form σ(39Ar, Ar...Ozeol)= a6r-6+a8r-8+a10r-10+a12r -12, where r is the distance between the Ar and the O atom. A similar form is used for the counterions. The dependence of the Ar shielding on the Al/Si ratio is established (the greater the Al content, the higher the Ar chemical shift), which is in agreement with the few experimental cases where the dependence of the 129Xe chemical shift on the Al/Si ratio of the zeolite has been observed.

  12. Quantum Dynamics and Spectroscopy of Ab Initio Liquid Water: The Interplay of Nuclear and Electronic Quantum Effects.

    PubMed

    Marsalek, Ondrej; Markland, Thomas E

    2017-04-06

    Understanding the reactivity and spectroscopy of aqueous solutions at the atomistic level is crucial for the elucidation and design of chemical processes. However, the simulation of these systems requires addressing the formidable challenges of treating the quantum nature of both the electrons and nuclei. Exploiting our recently developed methods that provide acceleration by up to 2 orders of magnitude, we combine path integral simulations with on-the-fly evaluation of the electronic structure at the hybrid density functional theory level to capture the interplay between nuclear quantum effects and the electronic surface. Here we show that this combination provides accurate structure and dynamics, including the full infrared and Raman spectra of liquid water. This allows us to demonstrate and explain the failings of lower-level density functionals for dynamics and vibrational spectroscopy when the nuclei are treated quantum mechanically. These insights thus provide a foundation for the reliable investigation of spectroscopy and reactivity in aqueous environments.

  13. 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.

  14. Robust online Hamiltonian learning

    NASA Astrophysics Data System (ADS)

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

    2012-10-01

    In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.

  15. Heterogeneous nuclear ribonucleoprotein A/B and G inhibits the transcription of gonadotropin-releasing-hormone 1

    PubMed Central

    Zhao, Sheng; Korzan, Wayne J.; Chen, Chun-Chun; Fernald, Russell D.

    2008-01-01

    Gonadotropin releasing hormone 1 (GnRH1) causes the release of gonadotropins from the pituitary to control reproduction. Here we report that two heterogeneous nuclear ribonucleoproteins (hnRNP-A/B and hnRNP-G) bind to the GnRH-I upstream promoter region in a cichlid fish, Astatotilapia burtoni. We identified these binding proteins using a newly developed homology based method of mass spectrometric peptide mapping. We show that both hnRNP-A/B and hnRNP-G co-localize with GnRH1 in the pre-optic area of the hypothalamus in the brain. We also demonstrated that these ribonucleoproteins exhibit similar binding capacity in vivo, using immortalized mouse GT1-7 cells where overexpression of either hnRNP-A/B or hnRNP-G significantly down-regulate GnRH1 mRNA levels in GT1-7 cells, suggesting that both act as repressors in GnRH1 transcriptional regulation. PMID:17920292

  16. Ab initio no core shell model

    SciTech Connect

    Barrett, Bruce R.; Navrátil, Petr; Vary, James P.

    2012-11-17

    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

  17. Multistage ab initio quantum wavepacket dynamics for electronic structure and dynamics in open systems: momentum representation, coupled electron-nuclear dynamics, and external fields.

    PubMed

    Pacheco, Alexander B; Iyengar, Srinivasan S

    2011-02-21

    We recently proposed a multistage ab initio wavepacket dynamics (MS-AIWD) treatment for the study of delocalized electronic systems as well as electron transport through donor-bridge-acceptor systems such as those found in molecular-wire/electrode networks. In this method, the full donor-bridge-acceptor open system is treated through a rigorous partitioning scheme that utilizes judiciously placed offsetting absorbing and emitting boundary conditions. In this manner, the electronic coupling between the bridge molecule and surrounding electrodes is accounted. Here, we extend MS-AIWD to include the dynamics of open-electronic systems in conjunction with (a) simultaneous treatment of nuclear dynamics and (b) external electromagnetic fields. This generalization is benchmarked through an analysis of wavepackets propagated on a potential modeled on an Al(27) - C(7) - Al(27) nanowire. The wavepacket results are inspected in the momentum representation and the dependence of momentum of the wavepacket as well as its transmission probabilities on the magnitude of external bias are analyzed.

  18. Multistage ab initio quantum wavepacket dynamics for electronic structure and dynamics in open systems: Momentum representation, coupled electron-nuclear dynamics, and external fields

    NASA Astrophysics Data System (ADS)

    Pacheco, Alexander B.; Iyengar, Srinivasan S.

    2011-02-01

    We recently proposed a multistage ab initio wavepacket dynamics (MS-AIWD) treatment for the study of delocalized electronic systems as well as electron transport through donor-bridge-acceptor systems such as those found in molecular-wire/electrode networks. In this method, the full donor-bridge-acceptor open system is treated through a rigorous partitioning scheme that utilizes judiciously placed offsetting absorbing and emitting boundary conditions. In this manner, the electronic coupling between the bridge molecule and surrounding electrodes is accounted. Here, we extend MS-AIWD to include the dynamics of open-electronic systems in conjunction with (a) simultaneous treatment of nuclear dynamics and (b) external electromagnetic fields. This generalization is benchmarked through an analysis of wavepackets propagated on a potential modeled on an Al27 - C7 - Al27 nanowire. The wavepacket results are inspected in the momentum representation and the dependence of momentum of the wavepacket as well as its transmission probabilities on the magnitude of external bias are analyzed.

  19. Nuclear, Virescent Mutants of Zea mays L. with High Levels of Chlorophyll (a/b) Light-Harvesting Complex during Thylakoid Assembly 1

    PubMed Central

    Polacco, Mary L.; Chang, M. T.; Neuffer, M. Gerald

    1985-01-01

    We have found nuclear, recessive mutants in Zea mays L. where assembly of the major chlorophyll (a/b) light-harvesting complex (LHC) was not delayed relative to most other thylakoid protein complexes during thylakoid biogenesis. This contrasts with the normal development of maize chloroplasts (NR Baker, R Leech 1977 Plant Physiol 60: 640-644). All four mutants examined were allelic and virescent, and displayed visibly higher yields of leaf Chl fluorescence during greening. Fully greened mutants had normal leaf Chl fluorescence yield and normal levels of LHC, and grew to maturity under field conditions. Therefore, delayed LHC assembly is not an obligate feature of thylakoid differentiation. Assigning the molecular basis for the mutation should provide information concerning reguation of LHC assembly. Several possibilities are discussed. The pleiotropic mutant phenotype is not attributable to defects in thylakoid glycerolipid synthesis. Thylakoids isolated from greening mutant leaf sections had elevated glycerolipid/Chl ratios. In addition, both the molar distribution and acyl composition of four major glycerolipids were normal for developing mutant thylakoids. Images Fig. 2 PMID:16664140

  20. Nuclear, Virescent Mutants of Zea mays L. with High Levels of Chlorophyll (a/b) Light-Harvesting Complex during Thylakoid Assembly.

    PubMed

    Polacco, M L; Chang, M T; Neuffer, M G

    1985-04-01

    We have found nuclear, recessive mutants in Zea mays L. where assembly of the major chlorophyll (a/b) light-harvesting complex (LHC) was not delayed relative to most other thylakoid protein complexes during thylakoid biogenesis. This contrasts with the normal development of maize chloroplasts (NR Baker, R Leech 1977 Plant Physiol 60: 640-644). All four mutants examined were allelic and virescent, and displayed visibly higher yields of leaf Chl fluorescence during greening. Fully greened mutants had normal leaf Chl fluorescence yield and normal levels of LHC, and grew to maturity under field conditions. Therefore, delayed LHC assembly is not an obligate feature of thylakoid differentiation.Assigning the molecular basis for the mutation should provide information concerning reguation of LHC assembly. Several possibilities are discussed. The pleiotropic mutant phenotype is not attributable to defects in thylakoid glycerolipid synthesis. Thylakoids isolated from greening mutant leaf sections had elevated glycerolipid/Chl ratios. In addition, both the molar distribution and acyl composition of four major glycerolipids were normal for developing mutant thylakoids.

  1. Effective Hamiltonians for phosphorene and silicene

    DOE PAGES

    Lew Yan Voon, L. C.; Lopez-Bezanilla, A.; Wang, J.; ...

    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

  2. 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.

  3. Effective Hamiltonians of polymethineimine, polyazine and polyazoethene: A density matrix variation approach

    NASA Astrophysics Data System (ADS)

    Chen, GuanHua; Su, ZhongMin; Shen, ZhenWen; Yan, YiJing

    1998-08-01

    A new variation method is proposed to determine the effective Hamiltonians for conjugated π-electron systems. This method is based on the minimization of the difference between the ground state reduced single electron density matrix calculated from the effective Hamiltonian and its ab initio counterpart under a set of well-defined constraints. Applications are made to various oligomers of polymethineimine (PMI), polyazine (PAZ) and polyazoethene (PAE) at the Hartree-Fock level. Calculated are also the optical gaps of these oligomers. The effective Hamiltonians contain electron-electron Coulomb interactions and are suitable for the study of excited state dynamic processes such as nonlinear optical properties in π-conjugated systems.

  4. A partial Hamiltonian approach for current value Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Naz, R.; Mahomed, F. M.; Chaudhry, Azam

    2014-10-01

    We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.

  5. Robust Online Hamiltonian Learning

    NASA Astrophysics Data System (ADS)

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

    2013-05-01

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

  6. 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.

  7. 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.

  8. Collective Hamiltonian for wobbling modes

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

    The simple, longitudinal, and transverse wobblers are systematically studied within the framework of a collective Hamiltonian, where the collective potential and mass parameter included are obtained based on the tilted axis cranking approach. Solving the collective Hamiltonian by diagonalization, the energies and the wave functions of the wobbling states are obtained. The obtained results are compared with those by the harmonic approximation formula and particle rotor model. The wobbling energies calculated by the collective Hamiltonian are closer to the exact solutions by the particle rotor model than the harmonic approximation formula. It is confirmed that the wobbling frequency increases with the rotational frequency in simple and longitudinal wobbling motions while decreases in transverse wobbling motion. These variation trends are related to the stiffness of the collective potential in the collective Hamiltonian.

  9. Time-dependent drift Hamiltonian

    SciTech Connect

    Boozer, A.H.

    1983-03-01

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

  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. 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

  12. 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.

  13. 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.

  14. 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

  15. Can we perturbatively expand the \\Qcirc -box in the Bloch-Horowitz Hamiltonian?

    NASA Astrophysics Data System (ADS)

    Shimizu, Genki; Takayanagi, Kazuo; Otsuka, Takaharu

    2014-09-01

    In nuclear many-body problems, it is impossible to diagonalize the Hamiltonian directly because of the huge Hilbert space. We introduce, therefore, the concept of the effective interaction. We first partition the whole Hilbert space into the model space of tractable size and its complement, and then look for the effective Hamiltonian defined in the model space that reproduces exact eigenenergies and model space projections of the corresponding eigenstates. Effective Hamiltonians are categorized into energy-independent and energy-dependent groups. The energy-independent effective Hamiltonian has been calculated by iterative methods, and has been used widely for a long time. The energy-dependent effective Hamiltonian is known as the Bloch-Horowitz (BH) Hamiltonian. Though it requires a self-consistent solution, it can, in principle, give all the eigenenergies of the Hamiltonian, if provided with the exact BH Hamiltonian. In actual calculations, however, we can calculate the \\Qcirc -box only up to a finite order of perturbation expansion. In this work, we clarify its convergence condition and examine what we can obtain with the approximate BH Hamiltonian, and what we cannot.

  16. 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.

  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. Hamiltonians defined by biorthogonal sets

    NASA Astrophysics Data System (ADS)

    Bagarello, Fabio; Bellomonte, Giorgia

    2017-04-01

    In some recent papers, studies on biorthogonal Riesz bases have found renewed motivation because of their connection with pseudo-Hermitian quantum mechanics, which deals with physical systems described by Hamiltonians that are not self-adjoint but may still have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed in some previous papers. However, in many physical models, one has to deal not with orthonormal bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of G -quasi basis, and we show a series of conditions under which a definition of non-self-adjoint Hamiltonian with purely point real spectra is still possible.

  20. 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.

  1. Generalized James' effective Hamiltonian method

    NASA Astrophysics Data System (ADS)

    Shao, Wenjun; Wu, Chunfeng; Feng, Xun-Li

    2017-03-01

    James' effective Hamiltonian method has been extensively adopted to investigate largely detuned interacting quantum systems. This method only corresponds to the second-order perturbation theory and cannot be exploited to treat problems which should be solved by using the third- or higher-order perturbation theory. In this paper, we generalize James' effective Hamiltonian method to the higher-order case. Using the method developed here, we reexamine two recently published examples [L. Garziano et al., Phys. Rev. Lett. 117, 043601 (2016), 10.1103/PhysRevLett.117.043601; Ken K. W. Ma and C. K. Law, Phys. Rev. A 92, 023842 (2015), 10.1103/PhysRevA.92.023842]; our results turn out to be the same as the original ones derived from the third-order perturbation theory and adiabatic elimination method, respectively. For some specific problems, this method can simplify the calculating procedure and the resultant effective Hamiltonian is more general.

  2. Ab initio calculation of the potential bubble nucleus 34Si

    NASA Astrophysics Data System (ADS)

    Duguet, T.; Somà, V.; Lecluse, S.; Barbieri, C.; Navrátil, P.

    2017-03-01

    the many-body correlations included in the calculation, is studied in detail. We eventually compare our predictions to state-of-the-art multireference energy density functional and shell model calculations. Results: The prediction regarding the (non)existence of the bubble structure in 34Si varies significantly with the nuclear Hamiltonian used. However, demanding that the experimental charge density distribution and the root-mean-square radius of 36S be well reproduced, along with 34Si and 36S binding energies, only leaves the NNLOsat Hamiltonian as a serious candidate to perform this prediction. In this context, a bubble structure, whose fingerprint should be visible in an electron scattering experiment of 34Si, is predicted. Furthermore, a clear correlation is established between the occurrence of the bubble structure and the weakening of the 1 /2--3 /2- splitting in the spectrum of 35Si as compared to 37S. Conclusions: The occurrence of a bubble structure in the charge distribution of 34Si is convincingly established on the basis of state-of-the-art ab initio calculations. This prediction will have to be reexamined in the future when improved chiral nuclear Hamiltonians are constructed. On the experimental side, present results act as a strong motivation to measure the charge density distribution of 34Si in future electron scattering experiments on unstable nuclei. In the meantime, it is of interest to perform one-neutron removal on 34Si and 36S in order to further test our theoretical spectral strength distributions over a wide energy range.

  3. Collective Hamiltonian for chiral modes

    NASA Astrophysics Data System (ADS)

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

    2013-02-01

    A collective model is proposed to describe the chiral rotation and vibration and applied to a system with one h11/2 proton particle and one h11/2 neutron hole coupled to a triaxial rigid rotor. The collective Hamiltonian is constructed from the potential energy and mass parameter obtained in the tilted axis cranking approach. By diagonalizing the collective Hamiltonian with a box boundary condition, it is found that for the chiral rotation, the partner states become more degenerate with the increase of the cranking frequency, and for the chiral vibrations, their important roles for the collective excitation are revealed at the beginning of the chiral rotation region.

  4. 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.

  5. Lowest eigenvalues of random Hamiltonians

    SciTech Connect

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

    2008-05-15

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

  6. Remembering AB

    NASA Astrophysics Data System (ADS)

    Belyayev, S. T.

    2013-06-01

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

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

    DOE PAGES

    Schuster, Micah D.; Quaglioni, Sofia; Johnson, Calvin W.; ...

    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

  8. 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…

  9. Derivation of Hamiltonians for accelerators

    SciTech Connect

    Symon, K.R.

    1997-09-12

    In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.

  10. 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…

  11. On third order integrable vector Hamiltonian equations

    NASA Astrophysics Data System (ADS)

    Meshkov, A. G.; Sokolov, V. V.

    2017-03-01

    A complete list of third order vector Hamiltonian equations with the Hamiltonian operator Dx having an infinite series of higher conservation laws is presented. A new vector integrable equation on the sphere is found.

  12. 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.

    The recent progresses of the collective Hamiltonian for chiral and wobbling modes are briefly introduced. The collective Hamiltonian is constructed from the collective potential and mass parameter obtained in the tilted axis cranking approach. The collective Hamiltonian can reproduce the exact solutions by the particle rotor model very well for both chiral and wobbling modes.

  13. Systematic method for deriving effective Hamiltonians

    NASA Astrophysics Data System (ADS)

    Swain, S.

    1994-04-01

    A systematic procedure for deriving effective Hamiltonians to any order is presented, which is applicable to any time-independent Hamiltonian. The method is based on a continued-fraction approach and avoids the singularities which may occur with perturbation theory. It is illustrated by deriving the effective Hamiltonian for the one-photon, dressed-state laser to second order.

  14. 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…

  15. 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.

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

    SciTech Connect

    Tronko, Natalia; Brizard, Alain J.

    2015-11-15

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

  17. Hamiltonian formulation of teleparallel gravity

    NASA Astrophysics Data System (ADS)

    Ferraro, Rafael; Guzmán, María José

    2016-11-01

    The Hamiltonian formulation of the teleparallel equivalent of general relativity is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudoinverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first-class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms and the (local) Lorentz transformations of the vielbein. In particular, the Arnowitt, Deser, and Misner algebra of general relativity is recovered as a subalgebra.

  18. A Hamiltonian approach to Thermodynamics

    SciTech Connect

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

    2016-10-15

    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. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.

  19. Computational power of symmetric Hamiltonians

    NASA Astrophysics Data System (ADS)

    Kay, Alastair

    2008-07-01

    The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the computational complexity of simulating Hamiltonian dynamics; the problem is still bounded error, quantum polynomial time complete, and is believed to be hard on a classical computer. This is achieved by designing a system to implement a universal quantum interface, a device which enables control of an arbitrary computation through the control of a fixed number of spins, and using it as a building block to entirely remove the need for control, except in the system initialization. Finally, it is shown that cooling such Hamiltonians to their ground states in the presence of random magnetic fields solves a Quantum-Merlin-Arthur-complete problem.

  20. Core polarization and modern realistic shell-model Hamiltonians

    NASA Astrophysics Data System (ADS)

    Coraggio, L.; Covello, A.; Gargano, A.; Itaco, N.

    The understanding of the convergence properties of the shell-model effective Hamiltonian, within the framework of the many-body perturbation theory, is a long-standing problem. The infinite summation of a certain class of diagrams, the so-called "bubble diagrams," may be provided calculating the Kirson-Babu-Brown induced interaction, and provides a valid instrument to study whether or not the finite summation of the perturbative series is well-grounded. Here, we perform an application of the calculation of the Kirson-Babu-Brown induced interaction to derive the shell-model effective Hamiltonian for p-shell nuclei starting from a modern nucleon-nucleon potential, obtained by way of the chiral perturbation theory. The outcome of our calculation is compared with a standard calculation of the shell-model Hamiltonian, where the core-polarization effects are calculated only up to third-order in perturbation theory. The results of the two calculations are very close to each other, evidencing that the perturbative approach to the derivation of the shell-model Hamiltonian is still a valid tool for nuclear structure studies.

  1. Core polarization and modern realistic shell-model Hamiltonians

    NASA Astrophysics Data System (ADS)

    Coraggio, L.; Covello, A.; Gargano, A.; Itaco, N.

    The understanding of the convergence properties of the shell-model effective Hamiltonian, within the framework of the many-body perturbation theory, is a long-standing problem. The infinite summation of a certain class of diagrams, the so-called “bubble diagrams,” may be provided calculating the Kirson-Babu-Brown induced interaction, and provides a valid instrument to study whether or not the finite summation of the perturbative series is well-grounded. Here, we perform an application of the calculation of the Kirson-Babu-Brown induced interaction to derive the shell-model effective Hamiltonian for p-shell nuclei starting from a modern nucleon-nucleon potential, obtained by way of the chiral perturbation theory. The outcome of our calculation is compared with a standard calculation of the shell-model Hamiltonian, where the core-polarization effects are calculated only up to third-order in perturbation theory. The results of the two calculations are very close to each other, evidencing that the perturbative approach to the derivation of the shell-model Hamiltonian is still a valid tool for nuclear structure studies.

  2. Higher-dimensional Wannier functions of multiparameter Hamiltonians

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

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

  3. 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.

  4. Ab Initio and Ab Exitu No-Core Shell Model

    SciTech Connect

    Vary, J P; Navratil, P; Gueorguiev, V G; Ormand, W E; Nogga, A; Maris, P; Shirokov, A

    2007-10-02

    We outline two complementary approaches based on the no core shell model (NCSM) and present recent results. In the ab initio approach, nuclear properties are evaluated with two-nucleon (NN) and three-nucleon interactions (TNI) derived within effective field theory (EFT) based on chiral perturbation theory (ChPT). Fitting two available parameters of the TNI generates good descriptions of light nuclei. In a second effort, an ab exitu approach, results are obtained with a realistic NN interaction derived by inverse scattering theory with off-shell properties tuned to fit light nuclei. Both approaches produce good results for observables sensitive to spin-orbit properties.

  5. Ab initio calculations of ^12C and neutron drops

    NASA Astrophysics Data System (ADS)

    Pieper, Steven C.

    2009-10-01

    Ab initio calculations of nuclei, which treat a nucleus as a system of A nucleons interacting by realistic two- and three-nucleon forces, have made tremendous progress in the last 15 years. This is a result of better Hamiltonians, rapidly increasing computer power, and new or improved many-body methods. Three methods are principally being used: Green's function Monte Carlo (GFMC), no-core shell model, and coupled cluster. In the limit of large computer resources, all three methods produce exact eigenvalues of a given nuclear Hamiltonian. With DOE SciDAC and INCITE support, all three methods are using the largest computers available today. Under the UNEDF SciDAC grant, the Argonne GFMC program was modified to efficiently use more than 2000 processors. E. Lusk (Argonne), R.M. Butler (Middle Tennessee State U.) and I have developed an Asynchronous Dynamic Load-Balancing (ADLB) library. In addition all the cores in a node are used via OpenMP as one ADLB/MPI client. In this way we obtain very good scalability up to 30,000 processors on Argonne's IBM Blue Gene/P. Two systems of particular interest that require this computer power are ^12C and neutron drops. V.R. Pandharipande (UIUC, deceased), J. Carlson (LANL), R.B. Wiringa (Argonne), and I have developed new trial wave functions that explicitly contain the three-alpha particle structure of ^12C. These are being used with the Argonne V18 and Illinois-7 potentials which reproduce the energies of 51 states in 3<=A<=12 nuclei with an rms error of 600,eV. Neutron drops are collections of neutrons confined in an artificial external well and interacting with realistic NN and NNN potentials. Their properties can be used as ``experimental data'' for developing energy-density functionals.

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

    SciTech Connect

    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 NNLO${}_{{\\rm{sat}}}$ 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.

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

    SciTech Connect

    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 NNLO${}_{{\\rm{sat}}}$ 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.

  8. 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. ).

  9. Killing symmetries as Hamiltonian constraints

    NASA Astrophysics Data System (ADS)

    Lusanna, Luca

    2016-02-01

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

  10. Staggered quantum walks with Hamiltonians

    NASA Astrophysics Data System (ADS)

    Portugal, R.; de Oliveira, M. C.; Moqadam, J. K.

    2017-01-01

    Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties similar to the ones for quantum computers, though. Therefore, there is a strong motivation to develop new quantum-walk models which might be easier to implement. In this work we present an extension of the staggered quantum walk model that is fitted for physical implementations in terms of time-independent Hamiltonians. We demonstrate that this class of quantum walk includes the entire class of staggered quantum walk model, Szegedy's model, and an important subset of the coined model.

  11. Canonical form of Hamiltonian matrices

    NASA Astrophysics Data System (ADS)

    Zuker, A. P.; Waha Ndeuna, L.; Nowacki, F.; Caurier, E.

    2001-08-01

    On the basis of shell model simulations, it is conjectured that the Lanczos construction at fixed quantum numbers defines-within fluctuations and behavior very near the origin-smooth canonical matrices whose forms depend on the rank of the Hamiltonian, dimensionality of the vector space, and second and third moments. A framework emerges that amounts to a general Anderson model capable of dealing with ground state properties and strength functions. The smooth forms imply binomial level densities. A simplified approach to canonical thermodynamics is proposed.

  12. Chasing Hamiltonian structure in gyrokinetic theory

    SciTech Connect

    Burby, J. W.

    2015-09-01

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

  13. Hamiltonian thermostats fail to promote heat flow

    NASA Astrophysics Data System (ADS)

    Hoover, Wm. G.; Hoover, Carol G.

    2013-12-01

    Hamiltonian mechanics can be used to constrain temperature simultaneously with energy. We illustrate the interesting situations that develop when two different temperatures are imposed within a composite Hamiltonian system. The model systems we treat are ϕ4 chains, with quartic tethers and quadratic nearest-neighbor Hooke's-law interactions. This model is known to satisfy Fourier's law. Our prototypical problem sandwiches a Newtonian subsystem between hot and cold Hamiltonian reservoir regions. We have characterized four different Hamiltonian reservoir types. There is no tendency for any of these two-temperature Hamiltonian simulations to transfer heat from the hot to the cold degrees of freedom. Evidently steady heat flow simulations require energy sources and sinks, and are therefore incompatible with Hamiltonian mechanics.

  14. Aharonov-Bohm Hamiltonians, isospectrality and minimal partitions

    NASA Astrophysics Data System (ADS)

    Bonnaillie-Noël, V.; Helffer, B.; Hoffmann-Ostenhof, T.

    2009-05-01

    The spectral analysis of Aharonov-Bohm Hamiltonians with flux \\frac12 leads surprisingly to a new insight on some questions of isospectrality appearing for example in Jakobson et al (2006 J. Comput. Appl. Math. 194 141-55) and Levitin et al (J. Phys. A: Math. Gen. 39 2073-82) and of minimal partitions (Helffer et al 2009 Ann. Inst. H. Poincaré Anal. Non Linéaire 26 101-38). We will illustrate this point of view by discussing the question of spectral minimal 3-partitions for the rectangle \\big]{-}\\frac a2,\\frac a2\\big[\\times \\big]{-}\\frac b2,\\frac b2\\big[ , with 0 < a <= b. It has been observed in Helffer et al (2009 Ann. Inst. H. Poincaré Anal. Non Linéaire 26 101-38) that when 0<\\frac ab < \\sqrt{\\vphantom{A^A}\\smash{\\\\frac 38}} the minimal 3-partition is obtained by the three nodal domains of the third eigenfunction corresponding to the three rectangles \\big]{-}\\frac a2,\\frac a2\\big[\\times \\big] {-}\\frac b2,-\\frac b6\\big[, \\big]{-}\\frac a2,\\frac a2\\big[\\times \\big]{-}\\frac b6,\\frac b6\\big[ and \\big]{-}\\frac a2,\\frac a2\\big[\\times \\big] \\frac b6, \\frac b2\\big[ . We will describe a possible mechanism of transition for increasing \\frac ab between these nodal minimal 3-partitions and non-nodal minimal 3-partitions at the value \\sqrt{\\vphantom{A^A}\\smash{\\\\frac 38}} and discuss the existence of symmetric candidates for giving minimal 3-partitions when \\sqrt{\\vphantom{A^A}\\smash{\\\\frac 38}} <\\frac ab \\leq 1 . Numerical analysis leads very naturally to nice questions of isospectrality which are solved by the introduction of Aharonov-Bohm Hamiltonians or by going on the double covering of the punctured rectangle.

  15. Hamiltonian approach to slip-stacking dynamics

    DOE PAGES

    Lee, S. Y.; Ng, K. Y.

    2017-06-29

    Hamiltonian dynamics has been applied to study the slip-stacking dynamics. The canonical-perturbation method is employed to obtain the second-harmonic correction term in the slip-stacking Hamiltonian. The Hamiltonian approach provides a clear optimal method for choosing the slip-stacking parameter and improving stacking efficiency. The dynamics are applied specifically to the Fermilab Booster-Recycler complex. As a result, the dynamics can also be applied to other accelerator complexes.

  16. Local bulk physics from intersecting modular Hamiltonians

    NASA Astrophysics Data System (ADS)

    Kabat, Daniel; Lifschytz, Gilad

    2017-06-01

    We show that bulk quantities localized on a minimal surface homologous to a boundary region correspond in the CFT to operators that commute with the modular Hamiltonian associated with the boundary region. If two such minimal surfaces intersect at a point in the bulk then CFT operators which commute with both extended modular Hamiltonians must be localized at the intersection point. We use this to construct local bulk operators purely from CFT considerations, without knowing the bulk metric, using intersecting modular Hamiltonians. For conformal field theories at zero and finite temperature the appropriate modular Hamiltonians are known explicitly and we recover known expressions for local bulk observables.

  17. Hamiltonian decomposition for bulk and surface states.

    PubMed

    Sasaki, Ken-Ichi; Shimomura, Yuji; Takane, Yositake; Wakabayashi, Katsunori

    2009-04-10

    We demonstrate that a tight-binding Hamiltonian with nearest- and next-nearest-neighbor hopping integrals can be decomposed into bulk and boundary parts for honeycomb lattice systems. The Hamiltonian decomposition reveals that next-nearest-neighbor hopping causes sizable changes in the energy spectrum of surface states even if the correction to the energy spectrum of bulk states is negligible. By applying the Hamiltonian decomposition to edge states in graphene systems, we show that the next-nearest-neighbor hopping stabilizes the edge states. The application of Hamiltonian decomposition to a general lattice system is discussed.

  18. Moment methods and nuclear level densities

    SciTech Connect

    Johnson, Calvin W.

    2008-04-17

    Working in a shell-model framework, I use moments of the nuclear many-body Hamiltonian to illustrate the importance of the residual interaction to microscopic calculations of the nuclear level density.

  19. Ab initio excited states from the in-medium similarity renormalization group

    NASA Astrophysics Data System (ADS)

    Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K.

    2017-04-01

    We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.

  20. 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.

  1. Hamiltonian tomography of photonic lattices

    NASA Astrophysics Data System (ADS)

    Ma, Ruichao; Owens, Clai; LaChapelle, Aman; Schuster, David I.; Simon, Jonathan

    2017-06-01

    In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from Sα β(ω ) , the (suitably normalized) two-port measurement between sites α and β at frequency ω . This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.

  2. Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian

    NASA Astrophysics Data System (ADS)

    Ripoche, J.; Lacroix, D.; Gambacurta, D.; Ebran, J.-P.; Duguet, T.

    2017-01-01

    internucleon coupling defining the pairing Hamiltonian and driving the normal-to-superfluid quantum phase transition. The presently proposed method offers the advantage of automatic access to the low-lying spectroscopy, which it does with high accuracy. Conclusions: The numerical cost of the newly designed variational method is polynomial (N6) in system size. This method achieves unprecedented accuracy for the ground-state correlation energy, effective pairing gap, and one-body entropy as well as for the excitation energy of low-lying states of the attractive pairing Hamiltonian. This constitutes a sufficiently strong motivation to envision its application to realistic nuclear Hamiltonians in view of providing a complementary, accurate, and versatile ab initio description of mid-mass open-shell nuclei in the future.

  3. 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.

  4. Implicit variational principle for contact Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Wang, Kaizhi; Wang, Lin; Yan, Jun

    2017-02-01

    We establish an implicit variational principle for the contact Hamiltonian systems generated by the Hamiltonian H(x, u, p) with respect to the contact 1-form α =\\text{d}u-p\\text{d}x under Tonelli and Lipschitz continuity conditions.

  5. 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.

  6. Generalized seniority from random Hamiltonians

    SciTech Connect

    Johnson, C. W.; Bertsch, G. F.; Dean, D. J.; Talmi, I.

    2000-01-01

    We investigate the generic pairing properties of shell-model many-body Hamiltonians drawn from ensembles of random two-body matrix elements. Many features of pairing that are commonly attributed to the interaction are in fact seen in a large part of the ensemble space. Not only do the spectra show evidence of pairing with favored J=0 ground states and an energy gap, but the relationship between ground-state wave functions of neighboring nuclei shows signatures of pairing as well. Matrix elements of pair creation-annihilation operators between ground states tend to be strongly enhanced. Furthermore, the same or similar pair operators connect several ground states along an isotopic chain. This algebraic structure is reminiscent of the generalized seniority model. Thus pairing may be encoded to a certain extent in the Fock space connectivity of the interacting shell model even without specific features of the interaction required. (c) 1999 The American Physical Society.

  7. Dynamical manifestations of Hamiltonian monodromy

    SciTech Connect

    Delos, J.B. Dhont, G. Sadovskii, D.A. Zhilinskii, B.I.

    2009-09-15

    Monodromy is the simplest obstruction to the existence of global action-angle variables in integrable Hamiltonian dynamical systems. We consider one of the simplest possible systems with monodromy: a particle in a circular box containing a cylindrically symmetric potential-energy barrier. Systems with monodromy have nontrivial smooth connections between their regular Liouville tori. We consider a dynamical connection produced by an appropriate time-dependent perturbation of our system. This turns studying monodromy into studying a physical process. We explain what aspects of this process are to be looked upon in order to uncover the interesting and somewhat unexpected dynamical behavior resulting from the nontrivial properties of the connection. We compute and analyze this behavior.

  8. Universal two-body-Hamiltonian quantum computing

    NASA Astrophysics Data System (ADS)

    Nagaj, Daniel

    2012-03-01

    We present a Hamiltonian quantum-computation scheme universal for quantum computation. Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) of constant-norm, time-independent, two-body interaction terms. Furthermore, each qubit in the system interacts only with a constant number of other qubits in a three-layer, geometrically local layout. The computer runs in three steps—it starts in a simple initial product state, evolves according to a time-independent Hamiltonian for time of order L2 (up to logarithmic factors), and finishes with a two-qubit measurement. Our model improves previous universal two-local-Hamiltonian constructions, as it avoids using perturbation gadgets and large energy-penalty terms in the Hamiltonian, which would result in a large required run time.

  9. 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.

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

    PubMed

    Mananga, Eugene Stephane

    2013-01-01

    This work presents the possibility of applying the Floquet-Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented. © 2013 Elsevier Inc. All rights reserved.

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

    PubMed Central

    Mananga, Eugene Stephane

    2015-01-01

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

  12. Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene

    NASA Astrophysics Data System (ADS)

    Morrison, Adrian F.; Herbert, John M.

    2017-06-01

    Recently, we introduced an ab initio version of the Frenkel-Davydov exciton model for computing excited-state properties of molecular crystals and aggregates. Within this model, supersystem excited states are approximated as linear combinations of excitations localized on molecular sites, and the electronic Hamiltonian is constructed and diagonalized in a direct-product basis of non-orthogonal configuration state functions computed for isolated fragments. Here, we derive and implement analytic derivative couplings for this model, including nuclear derivatives of the natural transition orbital and symmetric orthogonalization transformations that are part of the approximation. Nuclear derivatives of the exciton Hamiltonian's matrix elements, required in order to compute the nonadiabatic couplings, are equivalent to the "Holstein" and "Peierls" exciton/phonon couplings that are widely discussed in the context of model Hamiltonians for energy and charge transport in organic photovoltaics. As an example, we compute the couplings that modulate triplet exciton transport in crystalline tetracene, which is relevant in the context of carrier diffusion following singlet exciton fission.

  13. Ab Initio Infrared and Raman Spectra.

    DTIC Science & Technology

    1982-08-01

    tions. For parameters not depending on momenta, a parallel ab fhti Monte Carlo approach would use electronic energies and other parameters of... Monte Carlo approach. Specifically, as one of us has suggested,t I classical molecular dynamics may be integrated with ab iniHo quan- tum force...alternative approach, for phenomena which are not explicitly time dependent, is a Monte Carlo procedure in which at each trial nuclear configuration

  14. Periodic ab initio calculation of nuclear quadrupole parameters as an assignment tool in solid-state NMR spectroscopy: applications to 23Na NMR spectra of crystalline materials.

    PubMed

    Johnson, Clive; Moore, Elaine A; Mortimer, Michael

    2005-05-01

    Periodic ab initio HF calculations using the CRYSTAL code have been used to calculate (23)Na NMR quadrupole parameters for a wide range of crystalline sodium compounds including Na(3)OCl. An approach is developed that can be used routinely as an alternative to point-charge modelling schemes for the assignment of distinct lines in (23)Na NMR spectra to specific crystallographic sodium sites. The calculations are based on standard 3-21 G and 6-21 G molecular basis sets and in each case the same modified basis set for sodium is used for all compounds. The general approach is extendable to other quadrupolar nuclei. For the 3-21 G calculations a 1:1 linear correlation between experimental and calculated values of C(Q)((23)Na) is obtained. The 6-21 G calculations, including the addition of d-polarisation functions, give better accuracy in the calculation of eta((23)Na). The sensitivity of eta((23)Na) to hydrogen atom location is shown to be useful in testing the reported hydrogen-bonded structure of Na(2)HPO(4).

  15. Gauge-invariant hydrogen-atom Hamiltonian

    SciTech Connect

    Sun Weimin; Wang Fan; Chen Xiangsong; Lue Xiaofu

    2010-07-15

    For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this puzzle was recently provided by us [X.-S. Chen et al., Phys. Rev. Lett. 100, 232002 (2008)]. Based on the separation of the electromagnetic potential into pure-gauge and gauge-invariant parts, we have proposed a new set of momentum and Hamiltonian operators which satisfy both the requirement of gauge invariance and the relevant commutation relations. In this paper we report a check for the case of the hydrogen-atom problem: Starting from the Hamiltonian of the coupled electron, proton, and electromagnetic field, under the infinite proton mass approximation, we derive the gauge-invariant hydrogen-atom Hamiltonian and verify explicitly that this Hamiltonian is different from the Dirac Hamiltonian, which is the time translation generator of the system. The gauge-invariant Hamiltonian is the energy operator, whose eigenvalue is the energy of the hydrogen atom. It is generally time dependent. In this case, one can solve the energy eigenvalue equation at any specific instant of time. It is shown that the energy eigenvalues are gauge independent, and by suitably choosing the phase factor of the time-dependent eigenfunction, one can ensure that the time-dependent eigenfunction satisfies the Dirac equation.

  16. WE-AB-204-11: Development of a Nuclear Medicine Dosimetry Module for the GPU-Based Monte Carlo Code ARCHER

    SciTech Connect

    Liu, T; Lin, H; Xu, X; Stabin, M

    2015-06-15

    Purpose: To develop a nuclear medicine dosimetry module for the GPU-based Monte Carlo code ARCHER. Methods: We have developed a nuclear medicine dosimetry module for the fast Monte Carlo code ARCHER. The coupled electron-photon Monte Carlo transport kernel included in ARCHER is built upon the Dose Planning Method code (DPM). The developed module manages the radioactive decay simulation by consecutively tracking several types of radiation on a per disintegration basis using the statistical sampling method. Optimization techniques such as persistent threads and prefetching are studied and implemented. The developed module is verified against the VIDA code, which is based on Geant4 toolkit and has previously been verified against OLINDA/EXM. A voxelized geometry is used in the preliminary test: a sphere made of ICRP soft tissue is surrounded by a box filled with water. Uniform activity distribution of I-131 is assumed in the sphere. Results: The self-absorption dose factors (mGy/MBqs) of the sphere with varying diameters are calculated by ARCHER and VIDA respectively. ARCHER’s result is in agreement with VIDA’s that are obtained from a previous publication. VIDA takes hours of CPU time to finish the computation, while it takes ARCHER 4.31 seconds for the 12.4-cm uniform activity sphere case. For a fairer CPU-GPU comparison, more effort will be made to eliminate the algorithmic differences. Conclusion: The coupled electron-photon Monte Carlo code ARCHER has been extended to radioactive decay simulation for nuclear medicine dosimetry. The developed code exhibits good performance in our preliminary test. The GPU-based Monte Carlo code is developed with grant support from the National Institute of Biomedical Imaging and Bioengineering through an R01 grant (R01EB015478)

  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. 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.

  19. Hamiltonian and Lagrangian theory of viscoelasticity

    NASA Astrophysics Data System (ADS)

    Hanyga, A.; Seredyńska, M.

    2008-03-01

    The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.

  20. 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.

  1. The gravity duals of modular Hamiltonians

    SciTech Connect

    Jafferis, Daniel L.; Suh, S. Josephine

    2016-09-12

    In this study, 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.

  2. Symmetries and regular behavior of Hamiltonian systems.

    PubMed

    Kozlov, Valeriy V.

    1996-03-01

    The behavior of the phase trajectories of the Hamilton equations is commonly classified as regular and chaotic. Regularity is usually related to the condition for complete integrability, i.e., a Hamiltonian system with n degrees of freedom has n independent integrals in involution. If at the same time the simultaneous integral manifolds are compact, the solutions of the Hamilton equations are quasiperiodic. In particular, the entropy of the Hamiltonian phase flow of a completely integrable system is zero. It is found that there is a broader class of Hamiltonian systems that do not show signs of chaotic behavior. These are systems that allow n commuting "Lagrangian" vector fields, i.e., the symplectic 2-form on each pair of such fields is zero. They include, in particular, Hamiltonian systems with multivalued integrals. (c) 1996 American Institute of Physics.

  3. Compressed quantum metrology for the Ising Hamiltonian

    NASA Astrophysics Data System (ADS)

    Boyajian, W. L.; Skotiniotis, M.; Dür, W.; Kraus, B.

    2016-12-01

    We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on N spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., O (N-2) precision, and derive the explicit circuit that accomplishes the simulation.

  4. Quasi-Hamiltonian structure and Hojman construction

    NASA Astrophysics Data System (ADS)

    Carinena, Jose F.; Guha, Partha; Ranada, Manuel F.

    2007-08-01

    Given a smooth vector field [Gamma] and assuming the knowledge of an infinitesimal symmetry X, Hojman [S. Hojman, The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system, J. Phys. A Math. Gen. 29 (1996) 667-674] proposed a method for finding both a Poisson tensor and a function H such that [Gamma] is the corresponding Hamiltonian system. In this paper, we approach the problem from geometrical point of view. The geometrization leads to the clarification of several concepts and methods used in Hojman's paper. In particular, the relationship between the nonstandard Hamiltonian structure proposed by Hojman and the degenerate quasi-Hamiltonian structures introduced by Crampin and Sarlet [M. Crampin, W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys. 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction.

  5. Momentum and Hamiltonian in Complex Action Theory

    NASA Astrophysics Data System (ADS)

    Nagao, Keiichi; Nielsen, Holger Bech

    In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.

  6. Quantum mechanical hamiltonian models of turing machines

    NASA Astrophysics Data System (ADS)

    Benioff, Paul

    1982-11-01

    Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both time-independent and time-dependent Hamiltonian models are constructed here. The time-independent models do not dissipate energy or degrade the system state as they evolve. They operate close to the quantum limit in that the total system energy uncertainty/computation speed is close to the limit given by the time-energy uncertainty relation. However, the model evolution is time global and the Hamiltonian is more complex. The time-dependent models do not degrade the system state. Also they are time local and the Hamiltonian is less complex.

  7. 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.

  8. Hamiltonian surface charges using external sources

    SciTech Connect

    Troessaert, Cédric

    2016-05-15

    In this work, we interpret part of the boundary conditions as external sources in order to partially solve the integrability problem present in the computation of surface charges associated to gauge symmetries in the hamiltonian formalism. We start by describing the hamiltonian structure of external symmetries preserving the action up to a transformation of the external sources of the theory. We then extend these results to the computation of surface charges for field theories with non-trivial boundary conditions.

  9. 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.

  10. Hamiltonian formulation of string field theory

    NASA Astrophysics Data System (ADS)

    Siopsis, George

    1987-09-01

    Witten's string field theory is quantized in the hamiltonian formalism. The constraints are solved and the hamiltonian is expressed in terms of only physical degrees of freedom. Thus, no Faddeev-Popov ghosts are introduced. Instead, the action contains terms of arbitrarily high order in the string functionals. Agreement with the standard results is demonstrated by an explicit calculation of the residues of the first few poles of the four-tachyon tree amplitude.

  11. Hamiltonian vector fields on almost symplectic manifolds

    NASA Astrophysics Data System (ADS)

    Vaisman, Izu

    2013-09-01

    Let (M, ω) be an almost symplectic manifold (ω is a nondegenerate, not closed, 2-form). We say that a vector field X of M is locally Hamiltonian if LXω = 0, d(i(X)ω) = 0, and it is Hamiltonian if, furthermore, the 1-form i(X)ω is exact. Such vector fields were considered in Fassò and Sansonetto ["Integrable almost-symplectic Hamiltonian systems," J. Math. Phys. 48, 092902 (2007)], 10.1063/1.2783937, under the name of strongly Hamiltonian, and a corresponding action-angle theorem was proven. Almost symplectic manifolds may have few, nonzero, Hamiltonian vector fields, or even none. Therefore, it is important to have examples and it is our aim to provide such examples here. We also obtain some new general results. In particular, we show that the locally Hamiltonian vector fields generate a Dirac structure on M and we state a reduction theorem of the Marsden-Weinstein type. A final section is dedicated to almost symplectic structures on tangent bundles.

  12. Reaction Hamiltonian and state-to-state description of chemical reactions

    SciTech Connect

    Ruf, B.A.; Kresin, V.Z.; Lester, W.A. Jr.

    1985-08-01

    A chemical reaction is treated as a quantum transition from reactants to products. A specific reaction Hamiltonian (in second quantization formalism) is introduced. The approach leads to Franck-Condon-like factor, and adiabatic method in the framework of the nuclear motion problems. The influence of reagent vibrational state on the product energy distribution has been studied following the reaction Hamiltonian method. Two different cases (fixed available energy and fixed translational energy) are distinguished. Results for several biomolecular reactions are presented. 40 refs., 5 figs.

  13. Geometric Construction of Quantum Hall Clustering Hamiltonians

    NASA Astrophysics Data System (ADS)

    Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny

    2015-10-01

    Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain "pseudopotential" Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU (n ) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.

  14. Hamiltonian Description of Multi-fluid Streaming

    NASA Astrophysics Data System (ADS)

    Valls, C.; de La Llave, R.; Morrison, P. J.

    2001-10-01

    The general noncanonical Hamiltonian description of interpenetrating fluids coupled by electrostatic, gravitational, or other forces is presented. This formalism is used to describe equilibrium and nonlinear stability using techniques of Hamiltonian dynamics theory. For example, we study the stability of two warm counter-streaming electron beams in a neutralizing ion background. The normal modes are obtained from an energy functional by computing the lowest-order expression for the perturbed energy about an equilibrium, and transforming the corresponding system into action-angle variables. Higher-order terms in the Hamiltonian provide coupling between normal modes and can lead to instability because of the presence of negative energy modes (NEM's). (The signature of the NEM's is determined by the signature of the Hamiltonian, Moser's bracket definition, or the conventional plasma definition in terms of the dielectric function, all of which are shown to be equivalent.) The possible nonlinear behavior is discovered by constructing the Birkhoff normal form. Accounting for resonances, we transform away terms in the Hamiltonian to address the question of long-time stability for such systems.

  15. Geometric construction of quantum hall clustering Hamiltonians

    DOE PAGES

    Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny

    2015-10-08

    In this study, many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-bodymore » interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.« less

  16. Generalized index for Hamiltonian systems with applications

    NASA Astrophysics Data System (ADS)

    Zevin, Alexandr A.

    2005-09-01

    Some classes of linear Hamiltonian equations with periodic coefficients (nondegenerate, strongly stable, completely unstable) are determined by the disposition of the Floquet multipliers. Periodic solutions of nonlinear equations (e.g. elliptic or hyperbolic solutions) are also defined by the multipliers of the corresponding variational equation. In this paper, we consider a general set M of linear Hamiltonian equations with multipliers satisfying some arbitrary conditions and a specific condition on the multiplier lying at some point of the unit circle (all known sets admit such a definition). We show that the set M consists of a finite number of subsets Mi which comprise a countable number of domains M_q^i within which any two Hamiltonians can be continuously deformed into each other. The corresponding integer index q is expressed through the eigenvalues of some self-adjoint problem. It is shown that this index (and, therefore, the known indices relating to specific sets) increases on increasing the Hamiltonian. Using the obtained results, some known and new sets are studied from the unified point of view. It is shown that for the sets of nondegenerate and completely unstable equations, the domains M_q^i are directionally convex; for strongly stable equations, necessary and sufficient conditions for directional convexity are found. The results are applied to problems of existence and stability of periodic solutions of nonlinear Hamiltonian equations.

  17. Rovibrational molecular hamiltonian in mixed bond-angle and umbrella-like coordinates.

    PubMed

    Makarewicz, Jan; Skalozub, Alexander

    2007-08-16

    A new exact quantum mechanical rovibrational Hamiltonian operator for molecules exhibiting large amplitude inversion and torsion motions is derived. The derivation is based on a division of a molecule into two parts: a frame and a top. The nuclei of the frame only are used to construct a molecular system of axes. The inversion motion of the frame is described in the umbrella-like coordinates, whereas the torsion motion of the top is described by the nonstandard torsion angle defined in terms of the nuclear vectors and one of the molecular axes. The internal coordinates chosen take into account the properties of the inversion and torsion motions. Vibrational s and rotational Omega vectors obtained for the introduced internal coordinates determine the rovibrational tensor G defined by simple scalar products of these vectors. The Jacobian of the transformation from the Cartesian to the internal coordinates considered and the G tensor specify the rovibrational Hamiltonian. As a result, the Hamiltonian for penta-atomic molecules like NH2OH with one inverter is presented and a complete set of the formulas necessary to write down the Hamiltonian of more complex molecules, like NH2NH2 with two inverters, is reported. The approach considered is essentially general and sufficiently simple, as demonstrated by derivation of a polyatomic molecule Hamiltonian in polyspherical coordinates, obtained by other methods with much greater efforts.

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

    DOE PAGES

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

    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

  19. Geometric Hamiltonian quantum mechanics and applications

    NASA Astrophysics Data System (ADS)

    Pastorello, Davide

    2016-08-01

    Adopting a geometric point of view on Quantum Mechanics is an intriguing idea since, we know that geometric methods are very powerful in Classical Mechanics then, we can try to use them to study quantum systems. In this paper, we summarize the construction of a general prescription to set up a well-defined and self-consistent geometric Hamiltonian formulation of finite-dimensional quantum theories, where phase space is given by the Hilbert projective space (as Kähler manifold), in the spirit of celebrated works of Kibble, Ashtekar and others. Within geometric Hamiltonian formulation quantum observables are represented by phase space functions, quantum states are described by Liouville densities (phase space probability densities), and Schrödinger dynamics is induced by a Hamiltonian flow on the projective space. We construct the star-product of this phase space formulation and some applications of geometric picture are discussed.

  20. Hamiltonian boundary term and quasilocal energy flux

    SciTech Connect

    Chen, C.-M.; Nester, James M.; Tung, R.-S.

    2005-11-15

    The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant.

  1. Equivalent Hamiltonians with additional discrete states

    NASA Astrophysics Data System (ADS)

    Chinn, C. R.; Thaler, R. M.

    1991-01-01

    Given a particular Hamiltonian H, we present a method to generate a new Hamiltonian H~, which has the same discrete energy eigenvalues and the same continuum phase shifts as H, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian h1, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.

  2. Gravitational surface Hamiltonian and entropy quantization

    NASA Astrophysics Data System (ADS)

    Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav

    2017-02-01

    The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

  3. The gravity duals of modular Hamiltonians

    DOE PAGES

    Jafferis, Daniel L.; Suh, S. Josephine

    2016-09-12

    In this study, 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-likemore » to the causal completion of the region.« less

  4. 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.

  5. Charge transfer in strongly correlated systems: an exact diagonalization approach to model Hamiltonians.

    PubMed

    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.

  6. The Legendre transformations in Hamiltonian optics

    NASA Astrophysics Data System (ADS)

    Gitin, A. V.

    2010-04-01

    The Legendre transformations are an important tool in theoretical physics. They play a critical role in mechanics, optics, and thermodynamics. In Hamiltonian optics the Legendre transformations appear twice: as the connection between the Lagrangian and the Hamiltonian and as relations among eikonals. In this article interconnections between these two types of Legendre transformations have been investigated. Using the method of "transition to the centre and difference coordinates'' it is shown that four Legendre transformations which connect point, point-angle, angle-point, and angle eikonals of an optical system correspond to four Legendre transformations which connect four systems of equations: Euler's equations, Hamilton's equations, and two unknown before pairs of equations.

  7. Exploring Hamiltonian dielectric solvent molecular dynamics

    NASA Astrophysics Data System (ADS)

    Bauer, Sebastian; Tavan, Paul; Mathias, Gerald

    2014-09-01

    Hamiltonian dielectric solvent (HADES) is a recent method [7,25], which enables Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric continua. Sample simulations of an α-helical decapeptide with and without explicit solvent demonstrate the high efficiency of HADES-MD. Addressing the folding of this peptide by replica exchange MD we study the properties of HADES by comparing melting curves, secondary structure motifs and salt bridges with explicit solvent results. Despite the unoptimized ad hoc parametrization of HADES, calculated reaction field energies correlate well with numerical grid solutions of the dielectric Poisson equation.

  8. 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.

  9. 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.

  10. Reduction of pre-Hamiltonian actions

    NASA Astrophysics Data System (ADS)

    De Nicola, Antonio; Esposito, Chiara

    2017-05-01

    We prove a reduction theorem for the tangent bundle of a Poisson manifold (M , π) endowed with a pre-Hamiltonian action of a Poisson-Lie group (G ,πG) . In the special case of a Hamiltonian action of a Lie group, we are able to compare our reduction to the classical Marsden-Ratiu reduction of M. If the manifold M is symplectic and simply connected, the reduced tangent bundle is integrable and its integral symplectic groupoid is the Marsden-Weinstein reduction of the pair groupoid M × M ¯ .

  11. Hamiltonians generating optimal-speed evolutions

    NASA Astrophysics Data System (ADS)

    Mostafazadeh, Ali

    2009-01-01

    We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric (inner product) dependence of the lower bound on the travel time and the universality (metric independence) of the upper bound on the speed of unitary evolutions.

  12. Hamiltonian mechanics and planar fishlike locomotion

    NASA Astrophysics Data System (ADS)

    Kelly, Scott; Xiong, Hailong; Burgoyne, Will

    2007-11-01

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

  13. Surface terms and the Gauss Bonnet Hamiltonian

    NASA Astrophysics Data System (ADS)

    Padilla, Antonio

    2003-07-01

    We derive the gravitational Hamiltonian starting from the Gauss Bonnet action, keeping track of all surface terms. This is done using the language of orthonormal frames and forms to keep things as tidy as possible. The surface terms in the Hamiltonian give a remarkably simple expression for the total energy of a spacetime. This expression is consistent with energy expressions found in Preprint hep-th/0212292. However, we can apply our results whatever the choice of background and whatever the symmetries of the spacetime.

  14. 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.

  15. 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.

  16. Convergence to equilibrium under a random Hamiltonian.

    PubMed

    Brandão, Fernando G S L; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K; Mozrzymas, Marek

    2012-09-01

    We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

  17. 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.

  18. 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

  19. Hamiltonian Approach to Nonlinear Travelling Whistler Waves

    SciTech Connect

    Webb, G.M.; McKenzie, J.F.; Dubinin, E.; Sauer, K.

    2005-08-01

    A Hamiltonian formulation of nonlinear, parallel propagating, travelling whistler waves is discussed. The model is based on the equations of two-fluid electron-proton plasmas. In the cold gas limit, the complete system of equations reduces to two coupled differential equations for the transverse electron speed u and a phase variable {phi} = {phi}p - {phi}e representing the difference in the phases of the transverse complex velocities of the protons and the electrons. Two integrals of the equations are obtained. The Hamiltonian integral H, is used to classify the trajectories in the ({phi}, w) phase plane, where {phi} and w = u2 are the canonical coordinates. Periodic, oscillation solitary wave and compacton solutions are obtained, depending on the value of the Hamiltonian integral H and the Alfven Mach number M of the travelling wave. The individual electron and proton phase variables {phi}e and {phi}p are determined in terms of {phi} and w. An alternative Hamiltonian formulation in which {phi}-tilde = {phi}p + {phi}e is the new independent variable replacing x is used to write the travelling wave solutions parametrically in terms of {phi}-tilde.

  20. Mapping between dissipative and Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Xing, Jianhua

    2010-09-01

    Theoretical studies of nonequilibrium systems are complicated by the lack of a general framework. In this work we first show that a transformation recently introduced by Ao (2004 J. Phys. A: Math. Gen. 37 L25) is related to previous works of Graham (1977 Z. Phys. B 26 397) and Eyink et al (1996 J. Stat. Phys. 83 385), which can also be viewed as the generalized application of the Helmholtz theorem in vector calculus. We then show that systems described by ordinary stochastic differential equations with white noise can be mapped to thermostated Hamiltonian systems. A steady-state of a dissipative system corresponds to the equilibrium state of the corresponding Hamiltonian system. These results provide a solid theoretical ground for corresponding studies on nonequilibrium dynamics, especially on nonequilibrium steady state. Mapping permits the application of established techniques and results for Hamiltonian systems to dissipative non-Hamiltonian systems, those for thermodynamic equilibrium states to nonequilibrium steady states. We discuss several implications of this work.

  1. Periodic Solutions of Hamiltonian Systems: A Survey.

    DTIC Science & Technology

    1980-12-01

    auto - nomous Hamiltonian system has the form: (0.) aH 8Hp -S-(p,q) q ( where d denotes This system can be represented more concisely as (HS) z = ZHz(Z...oscillazioni periodiche d’une sistema dinamico, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 19, (1934), 234-237. [15] Arnold, V. I

  2. An underlying geometrical manifold for Hamiltonian mechanics

    NASA Astrophysics Data System (ADS)

    Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.

    2017-02-01

    We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.

  3. Lagrangian tetragons and instabilities in Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    Entov, Michael; Polterovich, Leonid

    2017-01-01

    We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.

  4. From Nonlinear to Hamiltonian via Feedback1

    DTIC Science & Technology

    2002-01-01

    distribution unlimited. 13. Abstract Mechanical control systems are a very important class of nonlinear control systems . They posses a rich mathematical...methodologies developed for mechanical control systel logically rendering nonlinear control systems , mechanical by a proper choice of feedback. In particular, w...OF PA Nonlinear mechanical control systems , Hamiltonian Control Systems x 16. PRICE CODE 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19

  5. Eigenfunction expansions for time dependent hamiltonians

    NASA Astrophysics Data System (ADS)

    Jauslin, H. R.; Guerin, S.; Deroussiaux, A.

    We describe a generalization of Floquet theory for non periodic time dependent Hamiltonians. It allows to express the time evolution in terms of an expansion in eigenfunctions of a generalized quasienergy operator. We discuss a conjecture on the extension of the adiabatic theorem to this type of systems, which gives a procedure for the physical preparation of Floquet states. *** DIRECT SUPPORT *** A3418380 00004

  6. Hamiltonian constraint in polymer parametrized field theory

    NASA Astrophysics Data System (ADS)

    Laddha, Alok; Varadarajan, Madhavan

    2011-01-01

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

  7. Hamiltonian constraint in polymer parametrized field theory

    SciTech Connect

    Laddha, Alok; Varadarajan, Madhavan

    2011-01-15

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

  8. 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.

  9. Incomplete integrable Hamiltonian systems with complex polynomial Hamiltonian of small degree

    SciTech Connect

    Lepskii, Timur A

    2010-12-07

    Complex Hamiltonian systems with one degree of freedom on C{sup 2} with the standard symplectic structure {omega}C=dz and dw and a polynomial Hamiltonian function f=z{sup 2}+P{sub n}(w), n=1,2,3,4, are studied. Two Hamiltonian systems (M{sub i}, Re{omega}{sub C,i}, H{sub i}=Ref{sub i}), i=1,2, are said to be Hamiltonian equivalent if there exists a complex symplectomorphism M{sub 1}{yields}M{sub 2} taking the vector field sgradH{sub 1} to sgradH{sub 2}. Hamiltonian equivalence classes of systems are described in the case n=1,2,3,4, a completed system is defined for n=3,4, and it is proved that it is Liouville integrable as a real Hamiltonian system. By restricting the real action-angle coordinates defined for the completed system in a neighbourhood of any nonsingular leaf, real canonical coordinates are obtained for the original system. Bibliography: 9 titles.

  10. The 2-alkyl-2H-indazole regioisomers of synthetic cannabinoids AB-CHMINACA, AB-FUBINACA, AB-PINACA, and 5F-AB-PINACA are possible manufacturing impurities with cannabimimetic activities.

    PubMed

    Longworth, Mitchell; Banister, Samuel D; Mack, James B C; Glass, Michelle; Connor, Mark; Kassiou, Michael

    2016-01-01

    Indazole-derived synthetic cannabinoids (SCs) featuring an alkyl substituent at the 1-position and l-valinamide at the 3-carboxamide position (e.g., AB-CHMINACA) have been identified by forensic chemists around the world, and are associated with serious adverse health effects. Regioisomerism is possible for indazole SCs, with the 2-alkyl-2H-indazole regioisomer of AB-CHMINACA recently identified in SC products in Japan. It is unknown whether this regiosiomer represents a manufacturing impurity arising as a synthetic byproduct, or was intentionally synthesized as a cannabimimetic agent. This study reports the synthesis, analytical characterization, and pharmacological evaluation of commonly encountered indazole SCs AB-CHMINACA, AB-FUBINACA, AB-PINACA, 5F-AB-PINACA and their corresponding 2-alkyl-2H-indazole regioisomers. Both regioisomers of each SC were prepared from a common precursor, and the physical properties, (1)H and (13)C nuclear magnetic resonance spectroscopy, gas chromatography-mass spectrometry, and ultraviolet-visible spectroscopy of all SC compounds are described. Additionally, AB-CHMINACA, AB-FUBINACA, AB-PINACA, and 5F-AB-PINACA were found to act as high potency agonists at CB1 (EC50 = 2.1-11.6 nM) and CB2 (EC50 = 5.6-21.1 nM) receptors in fluorometric assays, while the corresponding 2-alkyl-2H-indazole regioisomers demonstrated low potency (micromolar) agonist activities at both receptors. Taken together, these data suggest that 2-alkyl-2H-indazole regioisomers of AB-CHMINACA, AB-FUBINACA, AB-PINACA, and 5F-AB-PINACA are likely to be encountered by forensic chemists and toxicologists as the result of improper purification during the clandestine synthesis of 1-alkyl-1H-indazole regioisomers, and can be distinguished by differences in gas chromatography-mass spectrometry fragmentation pattern.

  11. Hamiltonian time integrators for Vlasov-Maxwell equations

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  12. 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.

  13. 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.

  14. Tangent lifts of bi-Hamiltonian structures

    NASA Astrophysics Data System (ADS)

    Dobrogowska, Alina; Jakimowicz, Grzegorz

    2017-08-01

    We construct two Poisson structures πT M and π˜ T M on the tangent bundle TM to a Poisson manifold (M ,π ) using Lie algebroid (T*M, qM, M). Next, we construct the Poisson manifold (T M ,πT M ,λ ) from a bi-Hamiltonian manifold (M ,π1,π2 ) . This structure can be considered as a deformation of the Poisson structure related to an algebroid structure. We show that the bi-Hamiltonian structure from M can be transferred to the manifold TM. Moreover we present how to construct the Casimir functions for structures πT M, πT M ,λ, π˜ T g*, and π˜ T g*,λ from the Casimir functions for π1 and π2 and discuss some particular examples.

  15. Hamiltonian deformations of Gabor frames: First steps.

    PubMed

    de Gosson, Maurice A

    2015-03-01

    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.

  16. 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

  17. General formalism for singly thermostated Hamiltonian dynamics.

    PubMed

    Ramshaw, John D

    2015-11-01

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

  18. Diffusion in very chaotic hamiltonian systems

    SciTech Connect

    Abarbanel, Henry D. I.; Crawford, John David

    1981-04-20

    In this paper, we study nonintegrable hamiltonian dynamics: H(I,θ) = H0(I) + kH1(I,θ), for large k, that is, far from integrability. An integral representation is given for the conditional probability P(I,θ, t¦I0, θ0, t0) that the system is at I, θ at t, given it was at I0, θ0 at t0. By discretizing time into steps of size ϵ, we show how to evaluate physical observables for large k, fixed ϵ. An explicit calculation of a diffusion coefficient in a two degrees of freedom problem is reported. Finally, passage to ϵ = 0, the original hamiltonian flow, is discussed.

  19. 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.

  20. Hamiltonian Approach To Dp-Brane Noncommutativity

    NASA Astrophysics Data System (ADS)

    Nikolic, B.; Sazdovic, B.

    2010-07-01

    In this article we investigate Dp-brane noncommutativity using Hamiltonian approach. We consider separately open bosonic string and type IIB superstring which endpoints are attached to the Dp-brane. From requirement that Hamiltonian, as the time translation generator, has well defined derivatives in the coordinates and momenta, we obtain boundary conditions directly in the canonical form. Boundary conditions are treated as canonical constraints. Solving them we obtain initial coordinates in terms of the effective ones as well as effective momenta. Presence of momenta implies noncommutativity of the initial coordinates. Effective theory, defined as initial one on the solution of boundary conditions, is its Ω even projection, where Ω is world-sheet parity transformation Ω:σ→-σ. The effective background fields are expressed in terms of Ω even and squares of the Ω odd initial background fields.

  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. Controlling Hamiltonian chaos via Gaussian curvature.

    PubMed

    Oloumi, A; Teychenné, D

    1999-12-01

    We present a method allowing one to partly stabilize some chaotic Hamiltonians which have two degrees of freedom. The purpose of the method is to avoid the regions of V(q(1),q(2)) where its Gaussian curvature becomes negative. We show the stabilization of the Hénon-Heiles system, over a wide area, for the critical energy E=1/6. Total energy of the system varies only by a few percent.

  3. 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.

  4. 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.

  5. 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.

  6. mAbs

    PubMed Central

    2009-01-01

    The twenty two monoclonal antibodies (mAbs) currently marketed in the U.S. have captured almost half of the top-20 U.S. therapeutic biotechnology sales for 2007. Eight of these products have annual sales each of more than $1 B, were developed in the relatively short average period of six years, qualified for FDA programs designed to accelerate drug approval, and their cost has been reimbursed liberally by payers. With growth of the product class driven primarily by advancements in protein engineering and the low probability of generic threats, mAbs are now the largest class of biological therapies under development. The high cost of these drugs and the lack of generic competition conflict with a financially stressed health system, setting reimbursement by payers as the major limiting factor to growth. Advances in mAb engineering are likely to result in more effective mAb drugs and an expansion of the therapeutic indications covered by the class. The parallel development of biomarkers for identifying the patient subpopulations most likely to respond to treatment may lead to a more cost-effective use of these drugs. To achieve the success of the current top-tier mAbs, companies developing new mAb products must adapt to a significantly more challenging commercial environment. PMID:20061824

  7. Room temperature line lists for CO2 symmetric isotopologues with ab initio computed intensities

    NASA Astrophysics Data System (ADS)

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

    2017-03-01

    Remote sensing experiments require high-accuracy, preferably sub-percent, line intensities and in response to this need we present computed room temperature line lists for six symmetric isotopologues of carbon dioxide: 13C16O2, 14C16O2, 12C17O2, 12C18O2, 13C17O2 and 13C18O2, covering the range 0-8000 cm-1. Our calculation scheme is based on variational nuclear motion calculations and on a reliability analysis of the generated line intensities. Rotation-vibration wavefunctions and energy levels are computed using the DVR3D software suite and a high quality semi-empirical potential energy surface (PES), followed by computation of intensities using an ab initio dipole moment surface (DMS). Four line lists are computed for each isotopologue to quantify sensitivity to minor distortions of the PES/DMS. Reliable lines are benchmarked against recent state-of-the-art measurements and against the HITRAN2012 database, supporting the claim that the majority of line intensities for strong bands are predicted with sub-percent accuracy. Accurate line positions are generated using an effective Hamiltonian. We recommend the use of these line lists for future remote sensing studies and their inclusion in databases.

  8. 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.

  9. Optimal Hamiltonian Simulation by Quantum Signal Processing

    NASA Astrophysics Data System (ADS)

    Low, Guang Hao; Chuang, Isaac L.

    2017-01-01

    The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d -sparse Hamiltonian H ^ for time-interval t with error ɛ is O [t d ∥H ^ ∥max+log (1 /ɛ ) /log log (1 /ɛ ) ] , which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H ^ into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.

  10. Invariants for time-dependent Hamiltonian systems.

    PubMed

    Struckmeier, J; Riedel, C

    2001-08-01

    An exact invariant is derived for n-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special Ansatz for the invariant and determine its time-dependent coefficients. In the second approach, we perform a two-step canonical transformation of the initially time-dependent Hamiltonian to a time-independent one. The invariant is found to contain a function of time f(2)(t), defined as a solution of a linear third-order differential equation whose coefficients depend in general on the explicitly known configuration space trajectory that follows from the system's time evolution. It is shown that the invariant can be interpreted as the time integral of an energy balance equation. Our result is applied to a one-dimensional, time-dependent, damped non-linear oscillator, and to a three-dimensional system of Coulomb-interacting particles that are confined in a time-dependent quadratic external potential. We finally show that our results can be used to assess the accuracy of numerical simulations of time-dependent Hamiltonian systems.

  11. Effective Hamiltonian for edge states in graphene.

    DOE PAGES

    Deshpande, H.; Winkler, R.

    2017-06-03

    Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Lambda in the Brillouin zone (BZ) with protected degeneracies at Lambda. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for bothmore » zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. We show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Lambda for the edge states without affecting the bulk spectrum.« less

  12. Numerical Continuation of Hamiltonian Relative Periodic Orbits

    NASA Astrophysics Data System (ADS)

    Wulff, Claudia; Schebesch, Andreas

    2008-08-01

    The bifurcation theory and numerics of periodic orbits of general dynamical systems is well developed, and in recent years, there has been rapid progress in the development of a bifurcation theory for dynamical systems with structure, such as symmetry or symplecticity. But as yet, there are few results on the numerical computation of those bifurcations. The methods we present in this paper are a first step toward a systematic numerical analysis of generic bifurcations of Hamiltonian symmetric periodic orbits and relative periodic orbits (RPOs). First, we show how to numerically exploit spatio-temporal symmetries of Hamiltonian periodic orbits. Then we describe a general method for the numerical computation of RPOs persisting from periodic orbits in a symmetry breaking bifurcation. Finally, we present an algorithm for the numerical continuation of non-degenerate Hamiltonian relative periodic orbits with regular drift-momentum pair. Our path following algorithm is based on a multiple shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincaré section and a tangential continuation method with implicit reparametrization. We apply our methods to continue the famous figure eight choreography of the three-body system. We find a relative period doubling bifurcation of the planar rotating eight family and compute the rotating choreographies bifurcating from it.

  13. Redesign of the DFT/MRCI Hamiltonian

    SciTech Connect

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

    2016-01-21

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

  14. Cylindrical coordinate representation for multiband Hamiltonians

    NASA Astrophysics Data System (ADS)

    Takhtamirov, Eduard

    2012-10-01

    Rotationally invariant combinations of the Brillouin zone-center Bloch functions are used as basis function to express in cylindrical coordinates the valence-band and Kane envelope-function Hamiltonians for wurtzite and zinc-blende semiconductor heterostructures. For cylindrically symmetric systems, this basis allows to treat the envelope functions as eigenstates of the operator of projection of total angular momentum on the symmetry axis, with the operator's eigenvalue conventionally entering the Hamiltonians as a parameter. Complementing the Hamiltonians with boundary conditions for the envelope functions on the symmetry axis, we present for the first time a complete formalism for efficient modeling and description of multiband electron states in low-dimensional semiconductor structures with cylindrical symmetry. To demonstrate the potency of the cylindrical symmetry approximation and establish a criterion of its applicability for actual structures, we map the ground and several excited valence-band states in an isolated wurtzite GaN quantum wire of a hexagonal cross-section to the states in an equivalent quantum wire of a circular cross-section.

  15. Dynamics of Hamiltonian Systems and Memristor Circuits

    NASA Astrophysics Data System (ADS)

    Itoh, Makoto; Chua, Leon

    In this paper, we show that any n-dimensional autonomous systems can be regarded as subsystems of 2n-dimensional Hamiltonian systems. One of the two subsystems is identical to the n-dimensional autonomous system, which is called the driving system. Another subsystem, called the response system, can exhibit interesting behaviors in the neighborhood of infinity. That is, the trajectories approach infinity with complicated nonperiodic (chaotic-like) behaviors, or periodic-like behavior. In order to show the above results, we project the trajectories of the Hamiltonian systems onto n-dimensional spheres, or n-dimensional balls by using the well-known central projection transformation. Another interesting behavior is that the transient regime of the subsystems can exhibit Chua corsage knots. We next show that generic memristors can be used to realize the above Hamiltonian systems. Finally, we show that the internal state of two-element memristor circuits can have the same dynamics as n-dimensional autonomous systems.

  16. 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.

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

    SciTech Connect

    Newton, M. D.

    1980-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2009-11-01

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

  19. 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.

  20. Ab initio infrared and Raman spectra

    NASA Astrophysics Data System (ADS)

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

    1983-06-01

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

  1. 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).

  2. Erythema ab igne.

    PubMed

    Miller, Kristen; Hunt, Raegan; Chu, Julie; Meehan, Shane; Stein, Jennifer

    2011-10-15

    Erythema ab igne is a reticulated, erythematous or hyperpigmented dermatosis that results from chronic and repeated exposure to low levels of infrared radiation. Multiple heat sources have been reported to cause this condition, which include heated reclining chairs, heating pads, hot water bottles, car heaters, electric space heaters, and, more recently, laptop computers. Treatment consists of withdrawing the inciting heat source. Although erythema ab igne carries a good prognosis, it is not necessarily a self-limited diagnosis as patients are at long-term risk of developing subsequent cutaneous malignant conditions, which include squamous cell and merkel-cell carcinomas.

  3. The quantization of the Rabi Hamiltonian

    NASA Astrophysics Data System (ADS)

    Vandaele, Eva R. J.; Arvanitidis, Athanasios; Ceulemans, Arnout

    2017-03-01

    The Rabi Hamiltonian addresses the proverbial paradigmatic case of a two-level fermionic system coupled to a single bosonic mode. It is expressed by a system of two coupled first-order differential equations in the complex field, which may be rewritten in a canonical form under the Birkhoff transformation. The transformation gives rise to leapfrog recurrence relations, from which the eigenvalues and eigenvectors could be obtained. The interesting feature of this approach is that it generates integer quantum numbers, which rationalize the spectrum by relating the solutions to the Juddian baselines. The relationship with Braak’s integrability claim (Braak 2011 Phys. Rev. Lett. 107 100401) is discussed.

  4. Quantum Hamiltonian Identification from Measurement Time Traces

    NASA Astrophysics Data System (ADS)

    Zhang, Jun; Sarovar, Mohan

    2014-08-01

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

  5. Hamiltonian analysis of BHT massive gravity

    NASA Astrophysics Data System (ADS)

    Blagojević, M.; Cvetković, B.

    2011-01-01

    We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants ( Λ 0, m 2), our canonical analysis reveals the special role of the condition Λ 0/ m 2 ≠ -1. In this sector, the dimension of the physical phase space is found to be N ∗ = 4, which corresponds to two Lagrangian degree of freedom. When applied to the AdS asymptotic region, the canonical approach yields the conserved charges of the BTZ black hole, and central charges of the asymptotic symmetry algebra.

  6. Forced Oscillations of Nonlinear Hamiltonian Systems, II.

    DTIC Science & Technology

    1979-12-01

    Rabinowitz (J8], 9]). The author obtained similar results ([6]), by using a variational method devised b.: F. Clarke and himself for convex subquadratic...and satisfying, for some constants bl > a’ > 0 and 5 > 2: (39) a’ ixi-21Y 2 _< (V"(x)yy) < b’ lxiy-21yj 2, all x ev , y c ip Then for any T > 0, there is...34Linear operators", Wiley. [6] I. Ekeland, "Periodic Hamiltonian trajectories and a theorem of P. Rabinowitz ", 1978, to appear in Journal of Differential

  7. Exact two-component Hamiltonians revisited.

    PubMed

    Liu, Wenjian; Peng, Daoling

    2009-07-21

    Two routes for deriving the exact two-component Hamiltonians are compared. In the first case, as already known, we start directly from the matrix representation of the Dirac operator in a restricted kinetically balanced basis and make a single block diagonalization. In the second case, not considered before, we start instead from the Foldy-Wouthuysen operator and make proper use of resolutions of the identity. The expressions are surprisingly different. It turns out that a mistake was made in the former formulation when going from the Dirac to the Schrodinger picture. The two formulations become equivalent after the mistake is corrected.

  8. Exact two-component Hamiltonians revisited

    SciTech Connect

    Liu Wenjian; Peng Daoling

    2009-07-21

    Two routes for deriving the exact two-component Hamiltonians are compared. In the first case, as already known, we start directly from the matrix representation of the Dirac operator in a restricted kinetically balanced basis and make a single block diagonalization. In the second case, not considered before, we start instead from the Foldy-Wouthuysen operator and make proper use of resolutions of the identity. The expressions are surprisingly different. It turns out that a mistake was made in the former formulation when going from the Dirac to the Schroedinger picture. The two formulations become equivalent after the mistake is corrected.

  9. Hamiltonian Description of Convective-cell Generation

    SciTech Connect

    J.A. Krommes and R.A. Kolesnikov

    2004-03-11

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

  10. 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).

  11. Wigner quantization of some one-dimensional Hamiltonians

    SciTech Connect

    Regniers, G.; Van der Jeugt, J.

    2010-12-15

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

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

    SciTech Connect

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

    2015-10-28

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-10-01

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

  14. 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.

  15. Nucleus-Dependent Valence-Space Approach to Nuclear Structure

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

    We present a nucleus-dependent valence-space approach for calculating ground and excited states of nuclei, which generalizes the shell-model in-medium similarity renormalization group to an ensemble reference with fractionally filled orbitals. Because the ensemble is used only as a reference, and not to represent physical states, no symmetry restoration is required. This allows us to capture three-nucleon (3 N ) forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space ab initio methods, generally to the 1% level. In addition, we show that this new approach is required in order to obtain convergence for nuclei in the upper p and s d shells. Finally, we address the 1+/3+ inversion problem in 22Na and 46V. This approach extends the reach of ab initio nuclear structure calculations to essentially all light- and medium-mass nuclei.

  16. Norm-square localization for Hamiltonian LG-spaces

    NASA Astrophysics Data System (ADS)

    Loizides, Yiannis

    2017-04-01

    We prove a formula for twisted Duistermaat-Heckman distributions associated to a Hamiltonian LG-space. The terms of the formula are localized at the critical points of the norm-square of the moment map, and can be computed in cross-sections. Our main tools are the theory of quasi-Hamiltonian G-spaces, as well as the Hamiltonian cobordism approach to norm-square localization introduced recently by Harada and Karshon.

  17. Hamiltonian and non-Hamiltonian perturbation theory for nearly periodic motion

    NASA Astrophysics Data System (ADS)

    Larsson, Jonas

    1986-02-01

    Kruskal's asymptotic theory of nearly period motion [M. Kruskal, J. Math. Phys. 4, 806 (1962)] (with applications to nonlinear oscillators, guiding center motion, etc.) is generalized and modified. A new more natural recursive formula, with considerable advantages in applications, determining the averaging transformations and the drift equations is derived. Also almost quasiperiodic motion is considered. For a Hamiltonian system, a manifestly Hamiltonian extension of Kruskal's theory is given by means of the phase-space Lagrangian formulation of Hamiltonian mechanics. By performing an averaging transformation on the phase-space Lagrangian for the system (L → L¯) and adding a total derivative dS/dτ, a nonoscillatory Lagrangian Λ=L¯+dS/dτ is obtained. The drift equations and the adiabatic invariant are now obtained from Λ. By truncating Λ to some finite order in the small parameter ɛ, manifestly Hamiltonian approximating systems are obtained. The utility of the method for treating the guiding-center motion is demonstrated in a separate paper.

  18. 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.

  19. 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.

  20. Entanglement Hamiltonians for Chiral Fermions with Zero Modes

    NASA Astrophysics Data System (ADS)

    Klich, Israel; Vaman, Diana; Wong, Gabriel

    2017-09-01

    In this Letter, we study the effect of topological zero modes on entanglement Hamiltonians and the entropy of free chiral fermions in (1 +1 )D . We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain exact expressions for entanglement Hamiltonians. In the absence of the zero mode, the resulting entanglement Hamiltonians consist of local and bilocal terms. In the periodic sector, the presence of a zero mode leads to an additional nonlocal contribution to the entanglement Hamiltonian. We derive an exact expression for this term and for the resulting change in the entanglement entropy.

  1. 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.

  2. 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.

  3. How is Lorentz invariance encoded in the Hamiltonian?

    NASA Astrophysics Data System (ADS)

    Kajuri, Nirmalya

    2016-07-01

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

  4. Hamiltonian theory of nonlinear waves in planetary rings

    NASA Technical Reports Server (NTRS)

    Stewart, G. R.

    1987-01-01

    The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.

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

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2013-10-01

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

  6. 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.

  7. Classical Hamiltonian structures in wave packet dynamics

    NASA Astrophysics Data System (ADS)

    Gray, Stephen K.; Verosky, John M.

    1994-04-01

    The general, N state matrix representation of the time-dependent Schrödinger equation is equivalent to an N degree of freedom classical Hamiltonian system. We describe how classical mechanical methods and ideas can be applied towards understanding and modeling exact quantum dynamics. Two applications are presented. First, we illustrate how qualitative insights may be gained by treating the two state problem with a time-dependent coupling. In the case of periodic coupling, Poincaré surfaces of section are used to view the quantum dynamics, and features such as the Floquet modes take on interesting interpretations. The second application illustrates computational implications by showing how Liouville's theorem, or more generally the symplectic nature of classical Hamiltonian dynamics, provides a new perspective for carrying out numerical wave packet propagation. We show how certain simple and explicit symplectic integrators can be used to numerically propagate wave packets. The approach is illustrated with an application to the problem of a diatomic molecule interacting with a laser, although it and related approaches may be useful for describing a variety of problems.

  8. Strong coupling expansions for nonintegrable hamiltonian systems

    SciTech Connect

    Abarbanel, Henry D. I.; Crawford, John David

    1982-09-01

    In this paper, we present a method for studying nonintegrable Hamiltonian systems H(I,θ) = H0(I) + kH1(I,θ) (I, θ are action-angle variables) in the regime of large k. Our central tool is the conditional probability P(I,θ,t | I00,t0) that the system is at I. θ at time t given that it resided at I0, θ0 at t0. An integral representation is given for this conditional probability. By discretizing the Hamiltonian equations of motion in small time steps, ϵ, we arrive at a phase volume-preserving mapping which replaces the actual flow. When the motion on the energy surface E = H(I,θ) is bounded we are able to evaluate physical quantities of interest for large k and fixed ϵ. We also discuss the representation of P (I,θ,t | I00t0) when an external random forcing is added in order to smooth the singular functions associated with the deterministic flow. Explicit calculations of a “diffusion” coefficient are given for a non-integrable system with two degrees of freedom. Finally, the limit ϵ → 0, which returns us to the actual flow, is subtle and is discussed.

  9. Thermalization Time Bounds for Pauli Stabilizer Hamiltonians

    NASA Astrophysics Data System (ADS)

    Temme, Kristan

    2017-03-01

    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.

  10. 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.

  11. AB initio infrared and Raman spectra

    NASA Astrophysics Data System (ADS)

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

    1982-08-01

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

  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. 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

  14. Spectral Properties of Fractional Quantum Hall Hamiltonians

    NASA Astrophysics Data System (ADS)

    Weerasinghe, Amila

    The fractional quantum Hall (FQH) effect plays a prominent role in the study of topological phases of matter and of strongly correlated electron systems in general. FQH systems have been demonstrated to show many interesting novel properties such as fractional charges, and are believed to harbor even more intriguing phenomena such as fractional statistics. However, there remain many interesting questions to be addressed in this regime. The work reported in this thesis aims to push the envelope of our understanding of the low-energy properties of FQH states using microscopic principles. In the first part of the thesis, we present a systematic perturbative approach to study excitations in the thin cylinder/torus limit of the quantum Hall states. The approach is applied to the Haldane-Rezayi and Gaffnian quantum Hall states, which are both expected to have gapless excitations in the usual two-dimensional thermodynamic limit. For the Haldane-Rezayi state, we confirm that gapless excitations are present also in the "one-dimensional" thermodynamic limit of an infinite thin cylinder, in agreement with earlier considerations based on the wave functions alone. In contrast, we identify the lowest excitations of the Gaffnian state in the thin cylinder limit, and conclude that they are gapped, using a combination of perturbative and numerical means. We discuss possible scenarios for the cross-over between the two-dimensional and the one-dimensional thermodynamic limit in this case. In the second part of the thesis, we study the low energy spectral properties of positive center-of-mass conserving two-body Hamiltonians as they arise in models of FQH states. Starting from the observation that positive many-body Hamiltonians must have ground state energies that increase monotonously in particle number, we explore what general additional constraints can be obtained for two-body interactions with "center-of-mass conservation" symmetry, both in the presence and absence of particle

  15. New relativistic Hamiltonian: the angular magnetoelectric coupling

    NASA Astrophysics Data System (ADS)

    Paillard, Charles; Mondal, Ritwik; Berritta, Marco; Dkhil, Brahim; Singh, Surendra; Oppeneer, Peter M.; Bellaiche, Laurent

    2016-10-01

    Spin-Orbit Coupling (SOC) is a ubiquitous phenomenon in the spintronics area, as it plays a major role in allowing for enhancing many well-known phenomena, such as the Dzyaloshinskii-Moriya interaction, magnetocrystalline anisotropy, the Rashba effect, etc. However, the usual expression of the SOC interaction ħ/4m2c2 [E×p] • σ (1) where p is the momentum operator, E the electric field, σ the vector of Pauli matrices, breaks the gauge invariance required by the electronic Hamiltonian. On the other hand, very recently, a new phenomenological interaction, coupling the angular momentum of light and magnetic moments, has been proposed based on symmetry arguments: ξ/2 [r × (E × B)] M, (2) with M the magnetization, r the position, and ξ the interaction strength constant. This interaction has been demonstrated to contribute and/or give rise, in a straightforward way, to various magnetoelectric phenomena,such as the anomalous Hall effect (AHE), the anisotropic magnetoresistance (AMR), the planar Hall effect and Rashba-like effects, or the spin-current model in multiferroics. This last model is known to be the origin of the cycloidal spin arrangement in bismuth ferrite for instance. However, the coupling of the angular momentum of light with magnetic moments lacked a fundamental theoretical basis. Starting from the Dirac equation, we derive a relativistic interaction Hamiltonian which linearly couples the angular momentum density of the electromagnetic (EM) field and the electrons spin. We name this coupling the Angular MagnetoElectric (AME) coupling. We show that in the limit of uniform magnetic field, the AME coupling yields an interaction exactly of the form of Eq. (2), thereby giving a firm theoretical basis to earlier works. The AME coupling can be expressed as: ξ [E × A] • σ (3) with A being the vector potential. Interestingly, the AME coupling was shown to be complementary to the traditional SOC, and together they restore the gauge invariance of the

  16. On the physical applications of hyper-Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    Gaeta, Giuseppe; Rodríguez, Miguel A.

    2008-05-01

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

  17. Higher-order Hamiltonian fluid reduction of Vlasov equation

    SciTech Connect

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

    2014-09-15

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

  18. Boson Hamiltonians and stochasticity for the vorticity equation

    NASA Technical Reports Server (NTRS)

    Shen, Hubert H.

    1990-01-01

    The evolution of the vorticity in time for two-dimensional inviscid flow and in Lagrangian time for three-dimensional viscous flow is written in Hamiltonian form by introducing Bose operators. The addition of the viscous and convective terms, respectively, leads to an interpretation of the Hamiltonian contribution to the evolution as Langevin noise.

  19. 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.

  20. 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.

  1. Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

    NASA Astrophysics Data System (ADS)

    de León, Manuel; Jiménez, Fernando; Martín de Diego, David

    2012-05-01

    The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to the geometrical integration of Hamiltonian systems are obtained.

  2. 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.

  3. 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

  4. 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.

  5. 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.

  6. Hamiltonian formalism and path entropy maximization

    NASA Astrophysics Data System (ADS)

    Davis, Sergio; González, Diego

    2015-10-01

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

  7. Hamiltonian formulations and symmetries in rod mechanics

    SciTech Connect

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

    1996-12-31

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

  8. 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

  9. Using Hamiltonian control to desynchronize Kuramoto oscillators

    NASA Astrophysics Data System (ADS)

    Gjata, Oltiana; Asllani, Malbor; Barletti, Luigi; Carletti, Timoteo

    2017-02-01

    Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model.

  10. Discrete variable representation for singular Hamiltonians

    NASA Astrophysics Data System (ADS)

    Schneider, Barry I.; Nygaard, Nicolai

    2004-11-01

    We discuss the application of the discrete variable representation (DVR) to Schrödinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved, the boundary conditions are satisfied, and the calculation is rapidly convergent. The accuracy of the method is demonstrated by applying it to the hydrogen atom. We emphasize that the method is equally capable of describing bound states and continuum solutions.

  11. 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.

  12. Finite Hamiltonian Systems: Linear Transformations and Aberrations

    NASA Astrophysics Data System (ADS)

    Wolf, Kurt Bernardo

    2008-11-01

    In finite Hamiltonian systems, the operators of position, momentum, and energy have a finite number N of eigenvalues. These operators can be naturally realized as generators of the Lie algebra su(2), in a representation of spin j, of dimension N = 2j+1. Time evolution is rotation of a phase space sphere, whose projections perform the harmonic motion of an oscillator. The (centrally extended) group of rigid—linear—motions of this phase space is then U(2). On the other hand, N-point wavefunctions—signals—can be subject to a U(N) group of unitary matrices, containing the linear U(2); aberrations are transformations outside that subgroup. As in geometric optics, we classify the aberration multiplets by order and weight. Their action on phase space is displayed by means of a Wigner function on the sphere, to be compared with the corresponding geometric canonical transformations.

  13. 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.

  14. Discrete variable representation for singular Hamiltonians.

    PubMed

    Schneider, Barry I; Nygaard, Nicolai

    2004-11-01

    We discuss the application of the discrete variable representation (DVR) to Schrödinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved, the boundary conditions are satisfied, and the calculation is rapidly convergent. The accuracy of the method is demonstrated by applying it to the hydrogen atom. We emphasize that the method is equally capable of describing bound states and continuum solutions.

  15. Hamiltonian description of composite fermions: Magnetoexciton dispersions

    NASA Astrophysics Data System (ADS)

    Murthy, Ganpathy

    1999-11-01

    A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in fractional quantum hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the ν=13, 25, and 37 gapped fractions, and find approximate agreement with numerical results. I also analyze the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 25 and 37, and it is shown that the spin-polarized 25 state, in contrast to the spin-polarized 13 state, cannot be described as a simple quantum ferromagnet.

  16. Hamiltonian Approach to the Dynamical Casimir Effect

    SciTech Connect

    Haro, Jaume; Elizalde, Emilio

    2006-09-29

    A Hamiltonian approach is introduced in order to address some severe problems associated with the physical description of the dynamical Casimir effect at all times. For simplicity, the case of a neutral scalar field in a one-dimensional cavity with partially transmitting mirrors (an essential proviso) is considered, but the method can be extended to fields of any kind and higher dimensions. The motional force calculated in our approach contains a reactive term--proportional to the mirrors' acceleration - which is fundamental in order to obtain (quasi)particles with a positive energy all the time during the movement of the mirrors - while always satisfying the energy conservation law. Comparisons with other approaches and a careful analysis of the interrelations among the different results previously obtained in the literature are carried out.

  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. Modal decomposition of Hamiltonian variational equations

    NASA Technical Reports Server (NTRS)

    Wiesel, William E.

    1994-01-01

    Over any finite arc of trajectory, the variational equations of a Hamiltonian system can be separated into 'normal' modes. This transformation is canonical, and the Lyapunov exponents over the trajectory arc occur as positive/negative pairs for conjugate modes, while the modal vectors remain unit vectors. This decomposition effectively solves the variational equations for any canonical, linear-dependent system. As an example, we study the Voyager I trajectory. In an interplanetary flyby, some of the modal variables increase by very large multiplicative factors, but this means that their conjugate modal variables decrease by those same very large multiplicative vectors. Maneuver strategies for this case are explored, and the minimum delta upsilon maneuver is found.

  19. Some remarks about pseudo-Hamiltonian

    SciTech Connect

    Malitsky, N.; Bourianoff, G.; Severgin, Yu.

    1993-11-01

    For the many applied tasks of accelerator physics, the 4D single particle pseudo-Hamiltonian may be presented as the Hamiltonian of the near-integrable system consisting of integrable and perturbed terms. The KAM theorem states that for sufficiently small perturbation the invariant surfaces continue to exist and, for the systems with two degrees of freedom, completely isolate the thin stochastic layers. As the perturbation strength increases, a transition can occur in which these surfaces disappear and the stochastic layers connect, resulting in globally stochastic motion. One of the important problems is to determine this {open_quotes}boundary{close_quotes} invariant surface. There are several approaches that may be used to describe the regular trajectories in the small limited region. The most powerful method is the perturbation theory which allows us to study the combined influence of the different multipoles. The inclusion of Lie operators improved this method and developed it up to high order perturbation. But the perturbation theory failed to describe the change in topology and since the regular trajectories depend discontinuously on choice of initial coordinates, it cannot be used in the whole region of the stable motion. The authors suggest to limit the attention to the study of the {open_quotes}boundary{close_quotes} invariant and implement the additional {open_quotes}local{close_quotes} transformation. The authors briefly review the well known theories, their advantages and imperfections, and the necessity of the {open_quotes}local{close_quotes} transformation. They present the comparison of the map tracking with the invariants determined by the perturbation methods.

  20. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

    SciTech Connect

    Fernández, Francisco M.

    2016-06-15

    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. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.

  1. Simulating typical entanglement with many-body Hamiltonian dynamics

    SciTech Connect

    Nakata, Yoshifumi; Murao, Mio

    2011-11-15

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

  2. Remarks on the Lagrangian representation of bi-Hamiltonian equations

    NASA Astrophysics Data System (ADS)

    Pavlov, M. V.; Vitolo, R. F.

    2017-03-01

    The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2 =LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.

  3. Hamiltonian analysis of higher derivative scalar-tensor theories

    NASA Astrophysics Data System (ADS)

    Langlois, David; Noui, Karim

    2016-07-01

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

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

    NASA Astrophysics Data System (ADS)

    Miao, Yan-Gang; Xu, Zhen-Ming

    2016-05-01

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

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

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2013-10-01

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

  6. Quantum control by means of hamiltonian structure manipulation.

    PubMed

    Donovan, A; Beltrani, V; Rabitz, H

    2011-04-28

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

  7. Optimization of quantum Hamiltonian evolution: From two projection operators to local Hamiltonians

    NASA Astrophysics Data System (ADS)

    Patel, Apoorva; Priyadarsini, Anjani

    Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice among these possibilities can then be made to obtain the best computational complexity and control over errors. It is shown how a construction based on Grover's algorithm scales linearly in time and logarithmically in the error bound, and is exponentially superior in error complexity to the scheme based on the straightforward application of the Lie-Trotter formula. The strategy is then extended first to simulation of any Hamiltonian that is a linear combination of two projection operators, and then to any local efficiently computable Hamiltonian. The key feature is to construct an evolution in terms of the largest possible steps instead of taking small time steps. Reflection operations and Chebyshev expansions are used to efficiently control the total error on the overall evolution, without worrying about discretization errors for individual steps. We also use a digital implementation of quantum states that makes linear algebra operations rather simple to perform.

  8. 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}.

  9. 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.

  10. Ab initio alpha-alpha scattering

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  11. Ab initio alpha-alpha scattering.

    PubMed

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

    2015-12-03

    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

  12. 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

  13. Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

    NASA Astrophysics Data System (ADS)

    Vogl, M.; Pankratov, O.; Shallcross, S.

    2017-07-01

    We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

  14. Low-energy effective Hamiltonians for correlated electron systems beyond density functional theory

    NASA Astrophysics Data System (ADS)

    Hirayama, Motoaki; Miyake, Takashi; Imada, Masatoshi; Biermann, Silke

    2017-08-01

    We propose a refined scheme of deriving an effective low-energy Hamiltonian for materials with strong electronic Coulomb correlations beyond density functional theory (DFT). By tracing out the electronic states away from the target degrees of freedom in a controlled way by a perturbative scheme, we construct an effective Hamiltonian for a restricted low-energy target space incorporating the effects of high-energy degrees of freedom in an effective manner. The resulting effective Hamiltonian can afterwards be solved by accurate many-body solvers. We improve this "multiscale ab initio scheme for correlated electrons" (MACE) primarily in two directions by elaborating and combining two frameworks developed by Hirayama et al. [M. Hirayama, T. Miyake, and M. Imada, Phys. Rev. B 87, 195144 (2013), 10.1103/PhysRevB.87.195144] and Casula et al. [M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake, A. J. Millis, and S. Biermann, Phys. Rev. Lett. 109, 126408 (2012), 10.1103/PhysRevLett.109.126408]: (1) Double counting of electronic correlations between the DFT and the low-energy solver is avoided by using the constrained G W scheme; and (2) the frequency dependent interactions emerging from the partial trace summation are successfully separated into a nonlocal part that is treated following ideas by Hirayama et al. and a local part treated nonperturbatively in the spirit of Casula et al. and are incorporated into the renormalization of the low-energy dispersion. The scheme is favorably tested on the example of SrVO3.

  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. Electronic properties, low-energy Hamiltonian, and superconducting instabilities in CaKFe4As4

    NASA Astrophysics Data System (ADS)

    Lochner, Felix; Ahn, Felix; Hickel, Tilmann; Eremin, Ilya

    2017-09-01

    We analyze the electronic properties of the recently discovered stoichiometric superconductor CaKFe4As4 by combining an ab initio approach and a projection of the band structure to a low-energy tight-binding Hamiltonian, based on the maximally localized Wannier orbitals of the 3 d Fe states. We identify the key symmetries as well as differences and similarities in the electronic structure between CaKFe4As4 and the parent systems CaFe2As2 and KFe2As2 . In particular, we find CaKFe4As4 to have a significantly more quasi-two-dimensional electronic structure than the latter systems. Finally, we study the superconducting instabilities in CaKFe4As4 by employing the leading angular harmonics approximation and find two potential A1 g-symmetry representations of the superconducting gap to be the dominant instabilities in this system.

  17. Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian

    NASA Astrophysics Data System (ADS)

    Wahlen-Strothman, Jacob M.; Henderson, Thomas M.; Hermes, Matthew R.; Degroote, Matthias; Qiu, Yiheng; Zhao, Jinmo; Dukelsky, Jorge; Scuseria, Gustavo E.

    2017-02-01

    Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.

  18. An effective Hamiltonian approach to quantum random walk

    NASA Astrophysics Data System (ADS)

    Sarkar, Debajyoti; Paul, Niladri; Bhattacharya, Kaushik; Ghosh, Tarun Kanti

    2017-03-01

    In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.

  19. Local Hamiltonians for quantitative Green's function embedding methods

    NASA Astrophysics Data System (ADS)

    Rusakov, Alexander A.; Phillips, Jordan J.; Zgid, Dominika

    2014-11-01

    Embedding calculations that find approximate solutions to the Schrödinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective interactions approximating the low energy physics of the initial realistic system, (ii) mapping the model system onto an impurity Hamiltonian, and (iii) solving the impurity problem. We have developed a novel procedure for parametrizing the impurity Hamiltonian that avoids the mathematically uncontrolled step of constructing the low energy model system. Instead, the impurity Hamiltonian is immediately parametrized to recover the self-energy of the realistic system in the limit of high frequencies or short time. The effective interactions parametrizing the fictitious impurity Hamiltonian are local to the embedded regions, and include all the non-local interactions present in the original realistic Hamiltonian in an implicit way. We show that this impurity Hamiltonian can lead to excellent total energies and self-energies that approximate the quantities of the initial realistic system very well. Moreover, we show that as long as the effective impurity Hamiltonian parametrization is designed to recover the self-energy of the initial realistic system for high frequencies, we can expect a good total energy and self-energy. Finally, we propose two practical ways of evaluating effective integrals for parametrizing impurity models.

  20. Nonunitary quantum computation in the ground space of local Hamiltonians

    NASA Astrophysics Data System (ADS)

    Usher, Naïri; Hoban, Matty J.; Browne, Dan E.

    2017-09-01

    A central result in the study of quantum Hamiltonian complexity is that the k -local Hamiltonian problem is quantum-Merlin-Arthur-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection. Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame postselection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are postselecting affects the gap between the ground-state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related by giving a family of circuits where the probability of an event upon which we postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.

  1. Hamiltonian of a spinning test particle in curved spacetime

    SciTech Connect

    Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra

    2009-11-15

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

  2. Hamiltonian of a spinning test-particle in curved spacetime

    NASA Astrophysics Data System (ADS)

    Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra

    2010-02-01

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

  3. Hamiltonian of a spinning test particle in curved spacetime

    NASA Astrophysics Data System (ADS)

    Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra

    2009-11-01

    Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase space algebra in the Newton-Wigner spin supplementary condition, suitably generalized to curved spacetime, and find that the phase space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner canonical Hamiltonian computed in PN theory in the test particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type SKerrS (and SKerr2) through 3PN order, SKerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order.

  4. Enhancing sensitivity in quantum metrology by Hamiltonian extensions

    NASA Astrophysics Data System (ADS)

    Fraïsse, Julien Mathieu Elias; Braun, Daniel

    2017-06-01

    A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form θ G . For such "phase-shift Hamiltonians" it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where the Hamiltonian is not necessarily a phase shift, and show that in this case in general it is possible to increase the quantum channel information and to reach an upper bound. This can be done by adding a term proportional to the derivative of the Hamiltonian, or by subtracting a term from the original Hamiltonian. Neither method makes use of any ancillas, which shows that, for quantum channel estimation with an arbitrary parameter-dependent Hamiltonian, entanglement with an ancillary system is not necessary to reach the best possible sensitivity. By adding an operator to the Hamiltonian we can also modify the time scaling of the channel quantum Fisher information. We illustrate our techniques with nitrogen vacancy center magnetometry and the estimation of the direction of a magnetic field in a given plane using a single spin-1 as probe.

  5. 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.

  6. 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)

  7. Transformation of Hamiltonians to near action-angle form

    SciTech Connect

    Boozer, A.H.

    1985-04-01

    A classical Hamiltonian would be solved by a transformation to action-angle variables I,theta in which the Hamiltonian is H-bar(I). Generally, such a transformation does not exist, and, at best, the Hamiltonian can be transformed to H-bar(I) + H(I,theta,t) with H being a sum of Fourier terms that resonate with H-bar. We give a set of ordinary differential equations in a parameter epsilon that carry out this transformation as the set is integrated from epsilon equal to zero to one. Although the differential equations can be integrated numerically, approximations give classical perturbation theory.

  8. Covariant Hamiltonian for the electromagnetic two-body problem

    NASA Astrophysics Data System (ADS)

    De Luca, Jayme

    2005-09-01

    We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem.

  9. Covariant Hamiltonian for the electromagnetic two-body problem.

    PubMed

    De Luca, Jayme

    2005-09-01

    We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem.

  10. Generic perturbations of linear integrable Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Bounemoura, Abed

    2016-11-01

    In this paper, we investigate perturbations of linear integrable Hamiltonian systems, with the aim of establishing results in the spirit of the KAM theorem (preservation of invariant tori), the Nekhoroshev theorem (stability of the action variables for a finite but long interval of time) and Arnold diffusion (instability of the action variables). Whether the frequency of the integrable system is resonant or not, it is known that the KAM theorem does not hold true for all perturbations; when the frequency is resonant, it is the Nekhoroshev theorem that does not hold true for all perturbations. Our first result deals with the resonant case: we prove a result of instability for a generic perturbation, which implies that the KAM and the Nekhoroshev theorem do not hold true even for a generic perturbation. The case where the frequency is nonresonant is more subtle. Our second result shows that for a generic perturbation the KAM theorem holds true. Concerning the Nekhrosohev theorem, it is known that one has stability over an exponentially long (with respect to some function of ɛ -1) interval of time and that this cannot be improved for all perturbations. Our third result shows that for a generic perturbation one has stability for a doubly exponentially long interval of time. The only question left unanswered is whether one has instability for a generic perturbation (necessarily after this very long interval of time).

  11. Surface Lifshits tails for random quantum Hamiltonians

    NASA Astrophysics Data System (ADS)

    Kirsch, Werner; Raikov, Georgi

    2017-03-01

    We consider Schrödinger operators on L2(ℝd) ⊗L2 (ℝℓ) of the form Hω=H⊥⊗I∥ +I⊥⊗H∥ +Vω , where H⊥ and H∥ are Schrödinger operators on L2(ℝd) and L2(ℝℓ) , respectively, and Vω(x ,y ) :=∑ξ∈ℤdλξ(ω ) v (x -ξ ,y ) ,x ∈ℝd ,y ∈ℝℓ is a random "surface potential." We investigate the behavior of the integrated density of surface states of Hω near the bottom of the spectrum and near internal band edges. The main result of the current paper is that, under suitable assumptions, the behavior of the integrated density of surface states of Hω can be read off from the integrated density of states of a reduced Hamiltonian H⊥+Wω where Wω is a quantum mechanical average of Vω with respect to y ∈ℝℓ . We are particularly interested in cases when H⊥ is a magnetic Schrödinger operator, but we also recover some of the results from Kirsch and Warzel [J. Funct. Anal. 230, 222-250 (2006)] for non-magnetic H⊥.

  12. Hamiltonian chaos in nonlinear optical polarization dynamics

    NASA Astrophysics Data System (ADS)

    David, D.; Holm, D. D.; Tratnik, M. V.

    1990-03-01

    This paper applies Hamiltonian methods to the Stokes representation of the one-beam and two-beam problems of polarized optical pulses propagating as travelling waves in nonlinear media. We treat these two dynamical systems as follows. First, we use the reduction method of Marsden and Weinstein to map each of the systems to the two-dimensional sphere, S 2. The resulting reduced systems are then analyzed from the viewpoints of their stability properties and of bifurcations with symmetry; in particular, several degenerate bifurcations are found and described. We also establish the presence of chaotic dynamics in these systems by demonstrating the existence of Smale horseshoe maps in the three- and four-dimensional cases, as well as Arnold diffusion in the higher-dimensional cases. The method we use to establish such complex dynamics is the Mel'nikov technique, as extended by Holmes and Marsden, and Wiggins for the higher-dimensional cases. These results apply to perturbations of homoclinic and heteroclinic orbits of the reduced integrable problems for static, as well as travelling-wave, solutions describing either a single opt ical beam, or two such beams counterpropagating. Thus, we show that these optics problems exhibit complex dynamics and predict the experimental consequences of this dynamics.

  13. Hamiltonian formalism for Perturbed Black Hole Spacetimes

    NASA Astrophysics Data System (ADS)

    Mihaylov, Deyan; Gair, Jonathan

    2017-01-01

    Present and future gravitational wave observations provide a new mechanism to probe the predictions of general relativity. Observations of extreme mass ratio inspirals with millihertz gravitational wave detectors such as LISA will provide exquisite constraints on the spacetime structure outside astrophysical black holes, enabling tests of the no-hair property that all general relativistic black holes are described by the Kerr metric. Previous work to understand what constraints LISA observations will be able to place has focussed on specific alternative theories of gravity, or generic deviations that preserve geodesic separability. We describe an alternative approach to this problem--a technique that employs canonical perturbations of the Hamiltonian function describing motion in the Kerr metric. We derive this new approach and demonstrate its application to the cases of a slowly rotating Kerr black hole which is viewed as a perturbation of a Schwarzschild black hole, of coupled perturbations of black holes in the second-order Chern-Simons modified gravity theory, and several more indicative scenarios. Deyan Mihaylov is funded by STFC.

  14. Laptop Induced Erythema Ab Igne

    PubMed Central

    Nayak, Sudhir U K; Shenoi, Shrutakirthi D; Prabhu, Smitha

    2012-01-01

    Erythema ab igne is a reticular, pigmented dermatosis caused by prolonged and repeated exposure to infrared radiation that is insufficient to produce a burn. The use of laptop computers has increased manifold in the recent past. Prolonged contact of the laptop with the skin can lead to the development of erythema ab igne. We present a case of erythema ab igne secondary to laptop use in an Indian student. PMID:22615512

  15. Laptop induced erythema ab igne.

    PubMed

    Nayak, Sudhir U K; Shenoi, Shrutakirthi D; Prabhu, Smitha

    2012-03-01

    Erythema ab igne is a reticular, pigmented dermatosis caused by prolonged and repeated exposure to infrared radiation that is insufficient to produce a burn. The use of laptop computers has increased manifold in the recent past. Prolonged contact of the laptop with the skin can lead to the development of erythema ab igne. We present a case of erythema ab igne secondary to laptop use in an Indian student.

  16. The Hamiltonian of Einstein affine-metric formulation of General Relativity

    NASA Astrophysics Data System (ADS)

    Kiriushcheva, N.; Kuzmin, S. V.

    2010-11-01

    It is shown that the Hamiltonian of the Einstein affine-metric (first-order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters as in the case of the second-order formulation. In the second-order formulation of ADM gravity the need for such a redefinition is the result of the non-canonical change of variables ( arXiv:0809.0097 abs/arXiv:0809.0097" TargetType="URL"/> ). For the first-order formulation, the necessity of such a redefinition "to correspond to diffeomorphism invariance" (reported by Ghalati, arXiv:0901.3344 abs/arXiv:0901.3344" TargetType="URL"/> ) is just an artifact of using the Henneaux-Teitelboim-Zanelli ansatz (Nucl. Phys. B 332:169, 1990), which is sensitive to the choice of linear combination of tertiary constraints. This ansatz cannot be used as an algorithm for finding a gauge invariance, which is a unique property of a physical system, and it should not be affected by different choices of linear combinations of non-primary first class constraints. The algorithm of Castellani (Ann. Phys. 143:357, 1982) is free from such a deficiency and it leads directly to four-diffeomorphism invariance for first, as well as for second-order Hamiltonian formulations of GR. The distinct role of primary first class constraints, the effect of considering different linear combinations of constraints, the canonical transformations of phase-space variables, and their interplay are discussed in some detail for Hamiltonians of the second- and first-order formulations of metric GR. The first-order formulation of Einstein-Cartan theory, which is the classical background of Loop Quantum Gravity, is also discussed.

  17. 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

  18. 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.

  19. Estimation of many-body quantum Hamiltonians via compressive sensing

    SciTech Connect

    Shabani, A.; Rabitz, H.; Mohseni, M.; Lloyd, S.; Kosut, R. L.

    2011-07-15

    We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only O(sln(d)) experimental configurations, consisting of random local preparations and measurements, one can estimate the Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly s sparse in a known basis. The classical postprocessing is a convex optimization problem on the total Hilbert space which is generally not scalable. We numerically simulate the performance of this algorithm for three- and four-body interactions in spin-coupled quantum dots and atoms in optical lattices. Furthermore, we apply the algorithm to characterize Hamiltonian fine structure and unknown system-bath interactions.

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

    ERIC Educational Resources Information Center

    Yan, C. C.

    1978-01-01

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

  1. Periodic equatorial water flows from a Hamiltonian perspective

    NASA Astrophysics Data System (ADS)

    Ionescu-Kruse, Delia; Martin, Calin Iulian

    2017-04-01

    The main result of this paper is a Hamiltonian formulation of the nonlinear governing equations for geophysical periodic stratified water flows in the equatorial f-plane approximation allowing for piecewise constant vorticity.

  2. Effective Hamiltonians of 2D Spin Glass Clusters

    NASA Astrophysics Data System (ADS)

    Clement, Colin; Liarte, Danilo; Middleton, Alan; Sethna, James

    2015-03-01

    We have a method for directly identifying the clusters which are thought to dominate the dynamics of spin glasses. We also have a method for generating an effective Hamiltonian treating each cluster as an individual spin. We used these methods on a 2D Ising spin glass with Gaussian bonds. We study these systems by generating samples and correlation functions using a combination of Monte Carlo and high-performance numerically exact Pfaffian methods. With effective cluster Hamiltonians we can calculate the free energy asymmetry of the original clusters and perform a scaling analysis. The scaling exponents found are consistent with Domain-Wall Renormalization Group methods, and probe all length scales. We can also study the flow of these effective Hamiltonians by clustering the clustered spins, and we find that our hard spin Hamiltonians at high temperature retain accurate low-temperature fluctuations when compared to their parent models.

  3. 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.

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

    SciTech Connect

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

    2006-09-25

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

  5. 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.

  6. 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.

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

    NASA Astrophysics Data System (ADS)

    Tuyterev, Vladimir

    2010-06-01

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

  8. Time and a physical Hamiltonian for quantum gravity.

    PubMed

    Husain, Viqar; Pawłowski, Tomasz

    2012-04-06

    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.

  9. 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.

  10. 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.

  11. 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.

  12. Applications of Noether conservation theorem to Hamiltonian systems

    SciTech Connect

    Mouchet, Amaury

    2016-09-15

    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.

  13. 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.

  14. 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.

  15. The rovibrational Hamiltonian for ammonia-like molecules.

    PubMed

    Makarewicz, Jan; Skalozub, Alexander

    2002-03-01

    A new exact quantum mechanical rovibrational Hamiltonian operator for ammonia-like molecules is derived. The Hamiltonian is constructed in a molecular system of axes, such that its z' axis makes a trisection of the pyramidal angle formed by three bond vectors with the vertex on the central atom. The introduced set of the internal rovibrational coordinates is adapted to facilitate a convenient description of the inversion motion. These internal coordinates and the molecular axis system have a remarkable property, namely, the internal vibrational angular momentum of the molecule equals zero. This property significantly reduces the Coriolis coupling and simplifies the form of the Hamiltonian. The correctness of this Hamiltonian is proved by a numerical procedure. The orthogonal Radau vectors allowing us to define a similar molecular axis system and the internal coordinates are considered. The Hamiltonian for the Radau parameterization takes a form simple enough to carry out effectively variational calculations of the molecular rovibrational states. Under the appropriate choice of the variational basis functions, the Hamiltonian matrix elements are fully factorizable and do not have any singularities. A convenient method of symmetrization of the basis functions is proposed.

  16. Ab initio calculation of (hyper)polarizabilities using a sum-over-states formalism.

    NASA Astrophysics Data System (ADS)

    Taylor, Caroline M.; Chaudhuri, Rajat K.; Potts, Davin M.; Freed, Karl F.

    2001-03-01

    Hyperpolarizabilities are relevant to a wide range of non-linear optical properties. Ab initio computations often require a high level of correlation for accurate determination of β and γ , and especially of thier frequency dependence. While sum-over-states methods are widely used within semi-empirical frameworks, they have not been employed with high level ab initio methods because of the computational costs associated with calculating a sufficient number of states. The effective valence shell Hamiltonian method (H^v) is a highly correlated, size-extensive, ab initio, multireference, perturbative (``perturb-then-diagonalize'') method. A single H^v calculation yields a large number of states, making it ideal for use with the sum-over-states fomalism for determination of molecular properties. The method has been used to calculate the (hyper)polarizabilities of small polyene systems.

  17. Leading-order relativistic effects on nuclear magnetic resonance shielding tensors.

    PubMed

    Manninen, Pekka; Ruud, Kenneth; Lantto, Perttu; Vaara, Juha

    2005-03-15

    We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.

  18. Global exploration and inversion of quantum Hamiltonian- Observable relationships

    NASA Astrophysics Data System (ADS)

    Geremia, John Michael

    2001-09-01

    High-precision, quantitative knowledge of quantum Hamiltonians is a crucial prerequisite for accurately predicting and controlling molecular behavior. Understanding the physical connection between the quantum equations of motion and the physical observables measured in the laboratory is fundamental to bridging theory and experiment. However, Hamiltonian-Observable relationships are generally complex and nonlinear, making them difficult to represent, explore, and invert. A functional mapping concept that allows many nonlinear Hamiltonian-Observable relationships to be learned using a relatively small set of representative Hamiltonians is developed. Maps provide rationally organized response information that details how non-perturbative variations in the Hamiltonian affect physical observables. Nonlinear mapping techniques permit the application of global search algorithms to quantum inverse problems, such as Hamiltonian identification and control. The resulting map-facilitated inversion framework provides a new capability for identifying the full family of Hamiltonians consistent with a finite, noise-contaminated molecular objective. As a demonstration, potential energy surfaces for He-Ne, Na2, and Ar-HCl are extracted from spectral and scattering data. A facilitated laboratory control algorithm is introduced and it is demonstrated that maps provide a reliable dynamic analysis of strong-field control mechanisms. The framework of map-facilitated closed-loop inversion unifies the previously distinct fields of quantum Hamiltonian identification and coherent control. It also leads to a hybrid laboratory/computational algorithm that systematically determines the best experiments and data for global Hamiltonian identification. Conventional inversions have been limited to treating available data. Here, it is shown that optimal data, i.e., measurements with maximum information content, provides a superior means for studying molecular Hamiltonians. The concept of optimal

  19. 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)

  20. 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)

  1. 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.

  2. PREFACE: International Symposium on Exotic Nuclear Structure From Nucleons (ENSFN 2012)

    NASA Astrophysics Data System (ADS)

    Honma, Michio; Utsuno, Yutaka; Shimizu, Noritaka

    2013-07-01

    The International Symposium on 'Exotic Nuclear Structure From Nucleons (ENSFN2012)' was held at the Koshiba Hall, the University of Tokyo, Japan, from October 10th to 12th, 2012. This symposium was supported by RIKEN Nishina Center (RNC) and the Center for Nuclear Study (CNS), University of Tokyo. This symposium was devoted to discussing recent achievement and perspectives in the structure of exotic nuclei from the viewpoint of the nuclear force. The following subjects were covered in this symposium from both theoretical and experimental sides: Evolution of shell structure and collectivity in exotic nuclei Ab-initio theory and its application to exotic nuclei Advancement in large-scale nuclear-structure calculations Effective Hamiltonian and energy density functional Spin-isospin responses New aspects of two- and three-body forces Impact on nuclear astrophysics Emphasis was placed on the development of large-scale nuclear-structure calculations and the new experimental information on exotic nuclei. Around 80 participants attended this symposium and we enjoyed 37 excellent invited talks and 9 selected oral presentations. A special talk was presented to celebrate the 60th birthday of professor Takaharu Otsuka, who has made invaluable contribution to the progress in the fields covered in this symposium. The organizing committee consisted of T Abe (Tokyo), M Honma (Aizu; chair), N Itagaki (YITP, Kyoto), T Mizusaki (Senshu), T Nakatsukasa (RIKEN), H Sakurai (Tokyo/RIKEN), N Shimizu (CNS, Tokyo; scientific secretary), S Shimoura (CNS, Tokyo), Y Utsuno (JAEA/CNS, Tokyo; scientific secretary). Finally, we would like to thank all the speakers and the participants as well as the other organizers for their contributions which made the symposium very successful. Michio Honma, Yutaka Utsuno and Noritaka Shimizu Editors Tokyo, April 2013 Sponsors logo1 Sponsors logo2 The PDF also contains the conference program.

  3. Ab initio study of electron-phonon coupling in rubrene

    NASA Astrophysics Data System (ADS)

    Ordejón, P.; Boskovic, D.; Panhans, M.; Ortmann, F.

    2017-07-01

    The use of ab initio methods for accurate simulations of electronic, phononic, and electron-phonon properties of molecular materials such as organic crystals is a challenge that is often tackled stepwise based on molecular properties calculated in gas phase and perturbatively treated parameters relevant for solid phases. In contrast, in this work we report a full first-principles description of such properties for the prototypical rubrene crystals. More specifically, we determine a Holstein-Peierls-type Hamiltonian for rubrene, including local and nonlocal electron-phonon couplings. Thereby, a recipe for circumventing the issue of numerical inaccuracies with low-frequency phonons is presented. In addition, we study the phenyl group motion with a molecular dynamics approach.

  4. Exotic Nuclear Shapes:

    NASA Astrophysics Data System (ADS)

    Dudek, J.; Schunck, N.; Dubray, N.; Góźdź, A.

    After recalling some in principle known but seldom mentioned facts about variety of concepts/notions of the nuclear shapes, we briefly summarize the results of the recent microscopic calculations predicting the existence of the large-elongation (hyper-deformed) nuclear configurations — as well as another series of calculations predicting that some nuclei should exhibit high-rank symmetries: the tetrahedral and the octahedral ones. The latter are associated with 48- and 96- symmetry elements, respectively, of the nuclear mean-field Hamiltonian. Obviously the physics motivations behind the hyper-deformation and the high-rank symmetry studies are not the observations of the new geometrical forms as such; in our opinion these motivations are much deeper and are given in the text.

  5. Probing the symmetries of the Dirac Hamiltonian with axially deformed scalar and vector potentials by similarity renormalization group.

    PubMed

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

    2014-02-14

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

  6. 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.

  7. 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.

  8. 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.

  9. Ab Interno Trabeculectomy

    PubMed Central

    Pantcheva, Mina B.; Kahook, Malik Y.

    2010-01-01

    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

  10. 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.

  11. Many-body ab initio study of antiferromagnetic {Cr7M } molecular rings

    NASA Astrophysics Data System (ADS)

    Chiesa, A.; Carretta, S.; Santini, P.; Amoretti, G.; Pavarini, E.

    2016-12-01

    Antiferromagnetic molecular rings are widely studied both for fundamental quantum-mechanical issues and for technological applications, particularly in the field of quantum information processing. Here we present a detailed first-principles study of two families—purple and green—of {Cr7M } antiferromagnetic rings, where M is a divalent transition metal ion (M =Ni2 + , Mn2 +, and Zn2 +). We employ a recently developed flexible and efficient scheme to build ab initio system-specific Hubbard models. From such many-body models we systematically derive the low-energy effective spin Hamiltonian for the rings. Our approach allows us to calculate isotropic as well as anisotropic terms of the spin Hamiltonian, without any a priori assumption on its form. For each compound we calculate magnetic exchange couplings, zero-field splitting tensors, and gyromagnetic tensors, finding good agreement with experimental results.

  12. 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.

  13. Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

    NASA Astrophysics Data System (ADS)

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

    2016-01-01

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

  14. Limit of small exits in open Hamiltonian systems.

    PubMed

    Aguirre, Jacobo; Sanjuán, Miguel A F

    2003-05-01

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

  15. Distinguishing Lorenz and Chen Systems Based Upon Hamiltonian Energy Theory

    NASA Astrophysics Data System (ADS)

    Cang, Shijian; Wu, Aiguo; Wang, Zenghui; Chen, Zengqiang

    Solving the linear first-order Partial Differential Equations (PDEs) derived from the unified Lorenz system, it is found that there is a unified Hamiltonian (energy function) for the Lorenz and Chen systems, and the unified energy function shows a hyperboloid of one sheet for the Lorenz system and an ellipsoidal surface for the Chen system in three-dimensional phase space, which can be used to explain that the Lorenz system is not equivalent to the Chen system. Using the unified energy function, we obtain two generalized Hamiltonian realizations of these two chaotic systems, respectively. Moreover, the energy function and generalized Hamiltonian realization of the Lü system and a four-dimensional hyperchaotic Lorenz-type system are also discussed.

  16. 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

  17. On the Hamiltonian formalism of the tetrad-connection gravity

    NASA Astrophysics Data System (ADS)

    Lagraa, M. H.; Lagraa, M.; Touhami, N.

    2017-06-01

    We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-connection gravity where the non-dynamic part of the spatial connection is fixed to zero by an adequate gauge transformation. This new action leads to a coherent Hamiltonian formalism where the Lorentz, scalar and vectorial first-class constraints obey a closed algebra in terms of Poisson brackets. This algebra closes with structure constants instead of structure functions resulting from the Hamiltonian formalisms based on the A.D.M. decomposition. The same algebra of the reduced first-class constraints, where the second-class constraints are eliminated as strong equalities, is obtained in terms of Dirac brackets. These first-class constraints lead to the same physical degrees of freedom of the general relativity.

  18. Riemannian geometry of Hamiltonian chaos: Hints for a general theory

    NASA Astrophysics Data System (ADS)

    Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco

    2008-10-01

    We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam β model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.

  19. Effective Hamiltonian for protected edge states in graphene

    NASA Astrophysics Data System (ADS)

    Winkler, R.; Deshpande, H.

    2017-06-01

    Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ . Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. We show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.

  20. Hamiltonian formalism of two-dimensional Vlasov kinetic equation

    PubMed Central

    Pavlov, Maxim V.

    2014-01-01

    In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo–Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo–Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented. PMID:25484603

  1. Hamiltonian formalism of two-dimensional Vlasov kinetic equation.

    PubMed

    Pavlov, Maxim V

    2014-12-08

    In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.

  2. 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.

  3. 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

    2016-07-22

    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.

  4. Riemannian geometry of Hamiltonian chaos: hints for a general theory.

    PubMed

    Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco

    2008-10-01

    We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.

  5. Non-Hermitian Hamiltonians with unitary and antiunitary symmetries

    NASA Astrophysics Data System (ADS)

    Fernández, Francisco M.; Garcia, Javier

    2014-03-01

    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 C2v 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.

  6. Effective Hamiltonians for fastly driven tight-binding chains

    NASA Astrophysics Data System (ADS)

    Itin, A. P.; Neishtadt, A. I.

    2014-02-01

    We consider a single particle tunnelling in a tight-binding model with nearest-neighbour couplings, in the presence of a periodic high-frequency force. An effective Hamiltonian for the particle is derived using an averaging method resembling classical canonical perturbation theory. Three cases are considered: uniform lattice with periodic and open boundary conditions, and lattice with a parabolic potential. We find that in the latter case, interplay of the potential and driving leads to appearance of the effective next-nearest neighbour couplings. In the uniform case with periodic boundary conditions the second- and third-order corrections to the averaged Hamiltonian are completely absent, while in the case with open boundary conditions they have a very simple form, found before in some particular cases by S. Longhi (2008) [10]. These general results may found applications in designing effective Hamiltonian models in experiments with ultracold atoms in optical lattices, e.g. for simulating solid-state phenomena.

  7. 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.

  8. 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.

  9. Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer

    NASA Astrophysics Data System (ADS)

    Ajoy, Ashok; Rao, Rama Koteswara; Kumar, Anil; Rungta, Pranaw

    2012-03-01

    We propose an iterative algorithm to simulate the dynamics generated by any n-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator U (unitary) into a product of different time-step unitaries. The algorithm product-decomposes U in a chosen operator basis by identifying a certain symmetry of U that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the n-qubit quantum state transfer unitary by Di Franco [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.101.230502 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

  10. 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.

  11. Bounded stabilisation of stochastic port-Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Satoh, Satoshi; Saeki, Masami

    2014-08-01

    This paper proposes a stochastic bounded stabilisation method for a class of stochastic port-Hamiltonian systems. Both full-actuated and underactuated mechanical systems in the presence of noise are considered in this class. The proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability. The bounded region and achieving probability are both assignable, and a stochastic Lyapunov function is explicitly provided based on a Hamiltonian structure. Although many conventional stabilisation methods assume that the noise vanishes at the origin, the proposed method is applicable to systems under persistent disturbances.

  12. Evolution-Free Hamiltonian Parameter Estimation through Zeeman Markers

    NASA Astrophysics Data System (ADS)

    Burgarth, Daniel; Ajoy, Ashok

    2017-07-01

    We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. No time-dependent quantities need to be measured; it fully suffices to observe spectral shifts induced by fields applied to local "markers." We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements. Then we generalize the result to show applicability to a wide range of systems, including quantum spin chains, networks of qubits, and coupled harmonic oscillators, and suggest potential experimental implementations.

  13. Evolution-Free Hamiltonian Parameter Estimation through Zeeman Markers.

    PubMed

    Burgarth, Daniel; Ajoy, Ashok

    2017-07-21

    We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. No time-dependent quantities need to be measured; it fully suffices to observe spectral shifts induced by fields applied to local "markers." We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements. Then we generalize the result to show applicability to a wide range of systems, including quantum spin chains, networks of qubits, and coupled harmonic oscillators, and suggest potential experimental implementations.

  14. Hamiltonian and Godunov structures of the Grad hierarchy.

    PubMed

    Grmela, Miroslav; Hong, Liu; Jou, David; Lebon, Georgy; Pavelka, Michal

    2017-03-01

    The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of gradient dynamics guaranteeing the growth of entropy and consequently the approach to equilibrium. We carry all three structures to the Grad reformulation of the Boltzmann equation (to the Grad hierarchy). First, we recognize the structures in the infinite Grad hierarchy and then in several examples of finite hierarchies representing extended hydrodynamic equations. In the context of Grad's hierarchies, we also investigate relations between Hamiltonian and Godunov structures.

  15. Lagrangian-Hamiltonian unified formalism for field theory

    NASA Astrophysics Data System (ADS)

    Echeverría-Enríquez, Arturo; López, Carlos; Marín-Solano, Jesús; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso

    2004-01-01

    The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations.

  16. Continuation of periodic orbits in symmetric Hamiltonian and conservative systems

    NASA Astrophysics Data System (ADS)

    Galan-Vioque, J.; Almaraz, F. J. M.; Macías, E. F.

    2014-12-01

    We present and review results on the continuation and bifurcation of periodic solutions in conservative, reversible and Hamiltonian systems in the presence of symmetries. In particular we show how two-point boundary value problem continuation software can be used to compute families of periodic solutions of symmetric Hamiltonian systems. The technique is introduced with a very simple model example (the mathematical pendulum), justified with a theoretical continuation result and then applied to two non trivial examples: the non integrable spring pendulum and the continuation of the figure eight solution of the three body problem.

  17. Comments on HKT supersymmetric sigma models and their Hamiltonian reduction

    NASA Astrophysics Data System (ADS)

    Fedoruk, Sergey; Smilga, Andrei

    2015-05-01

    Using complex notation, we present new simple expressions for two pairs of complex supercharges in HKT (‘hyper-Kähler with torsion’) supersymmetric sigma models. The second pair of supercharges depends on the holomorphic antisymmetric ‘hypercomplex structure’ tensor {{I}jk} which plays the same role for the HKT models as the complex structure tensor for the Kähler models. When the Hamiltonian and supercharges commute with the momenta conjugate to the imaginary parts of the complex coordinates, one can perform a Hamiltonian reduction. The models thus obtained represent a special class of quasicomplex sigma models introduced recently by Ivanov and Smilga (2013 SIGMA 9 069)

  18. A Geometrical Version of the Maxwell-Vlasov Hamiltonian Structure

    NASA Astrophysics Data System (ADS)

    Vittot, Michel; Morrison, Philip

    2014-10-01

    We present a geometrization of the Hamiltonian approach of classical electrodynamics, via (non-canonical) Poisson structures. This relativistic Hamiltonian framework (introduced by Morrison, Marsden, Weinstein) is a field theory written in terms of differential forms, independently of the gauge potentials. This algebraic and geometric description of the Vlasov kinetics is well suited for a perturbation theory, in a strong inhomogeneous magnetic field (expansion in 1/B, with all the curvature terms...), like in magnetically confined plasmas, and in any coordinates, for instance adapted to a Tokamak (toroidal coordinates, or else...).

  19. Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics.

    PubMed

    Ilinskii, Yurii A; Hamilton, Mark F; Zabolotskaya, Evgenia A

    2007-02-01

    Two models of interacting bubble dynamics are presented, a coupled system of second-order differential equations based on Lagrangian mechanics, and a first-order system based on Hamiltonian mechanics. Both account for pulsation and translation of an arbitrary number of spherical bubbles. For large numbers of interacting bubbles, numerical solution of the Hamiltonian equations provides greater stability. The presence of external acoustic sources is taken into account explicitly in the derivation of both sets of equations. In addition to the acoustic pressure and its gradient, it is found that the particle velocity associated with external sources appears in the dynamical equations.

  20. Phase equilibria in polymer blend thin films: a Hamiltonian approach.

    PubMed

    Souche, M; Clarke, N

    2009-12-28

    We propose a Hamiltonian formulation of the Flory-Huggins-de Gennes theory describing a polymer blend thin film. We then focus on the case of 50:50 polymer blends confined between antisymmetric walls. The different phases of the system and the transitions between them, including finite-size effects, are systematically studied through their relation with the geometry of the Hamiltonian flow in phase space. This method provides an easy and efficient way, with strong graphical insight, to infer the qualitative physical behavior of polymer blend thin films.

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

    NASA Astrophysics Data System (ADS)

    Huber, Felix; Gühne, Otfried

    2016-07-01

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

  2. The Hamilton-Jacobi method and Hamiltonian maps

    NASA Astrophysics Data System (ADS)

    Abdullaev, S. S.

    2002-03-01

    A method for constructing time-step-based symplectic maps for a generic Hamiltonian system subjected to perturbation is developed. Using the Hamilton-Jacobi method and Jacobi's theorem in finite periodic time intervals, the general form of the symplectic maps is established. The generating function of the map is found by the perturbation method in the finite time intervals. The accuracy of the maps is studied for fully integrable and partially chaotic Hamiltonian systems and compared to that of the symplectic integration method.

  3. Effective Hamiltonian for non-minimally coupled scalar fields

    NASA Astrophysics Data System (ADS)

    Meşe, Emine; Pirinççiog˜Lu, Nurettin; Açıkgöz, Irfan; Binbay, Figen

    2009-01-01

    In the post Newtonian limit, a non-relativistic Hamiltonian is derived for scalar fields with quartic self-interaction and non-minimal coupling to the curvature scalar of the background spacetime. These effects are found to contribute to the non-relativistic Hamiltonian by adding nonlinearities and by modifying the gravitational Darwin term. As we discuss briefly in the text, the impact of these novel structures can be sizable in dense media like neutron star core, and can have observable signatures in phase transitions, for example.

  4. Nonclassical degrees of freedom in the Riemann Hamiltonian.

    PubMed

    Srednicki, Mark

    2011-09-02

    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.

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

    NASA Astrophysics Data System (ADS)

    Cornu, F.; Hilhorst, H. J.

    2014-10-01

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

  6. Effective Hamiltonian for a microwave billiard with attached waveguide.

    PubMed

    Stöckmann, H-J; Persson, E; Kim, Y-H; Barth, M; Kuhl, U; Rotter, I

    2002-06-01

    In a recent work the resonance widths in a microwave billiard with attached waveguide were studied in dependence on the coupling strength [E. Persson et al., Phys. Rev. Lett. 85, 2478 (2000)], and resonance trapping was experimentally found. In the present paper an effective Hamiltonian is derived that depends exclusively on billiard and waveguide geometry. Its eigenvalues give the poles of the scattering matrix provided that the system and environment are defined adequately. Further, we present the results of resonance trapping measurements where, in addition to our previous work, the position of the slit aperture within the waveguide was varied. Numerical simulations with the derived Hamiltonian qualitatively reproduce the experimental data.

  7. 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.

  8. 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

  9. Ab initio calculations of light-ion fusion reactions

    SciTech Connect

    Hupin, G.; Quaglioni, S.; Navratil, P.

    2012-10-20

    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. Above all nuclear scattering and reactions, which require the solution of the many-body quantum-mechanical problem in the continuum, represent an extraordinary theoretical as well as computational challenge for ab initio approaches. The ab initio No-Core Shell Model/Resonating-Group Method (NCSM/RGM) complements a microscopic cluster technique with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. This approach is capable of describing simultaneously both bound and scattering states in light nuclei. Recent applications to light nuclei scattering and fusion reactions relevant to energy production in stars and Earth based fusion facilities, such as the deuterium-{sup 3}He fusion, are presented. Progress toward the inclusion of the three nucleon force into the formalism is outlined.

  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. Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians

    NASA Astrophysics Data System (ADS)

    Fring, Andreas; Frith, Thomas

    2017-01-01

    We propose a procedure to obtain exact analytical solutions to the time-dependent Schrödinger equations involving explicit time-dependent Hermitian Hamiltonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation, together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model.

  12. 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.

  13. 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.

  14. 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.

  15. TOPICAL REVIEW: Quadrupole collective states within the Bohr collective Hamiltonian

    NASA Astrophysics Data System (ADS)

    Próchniak, L.; Rohoziński, S. G.

    2009-12-01

    The article reviews the general version of the Bohr collective model for the description of quadrupole collective states, including a detailed discussion of the model's kinematics. The quadrupole coordinates, momenta and angular momenta are defined and the structure of the isotropic tensor fields as functions of the tensor variables is investigated. After a comprehensive discussion of the quadrupole kinematics, the general form of the classical and quantum Bohr Hamiltonian is presented. The electric and magnetic multipole moment operators acting in the collective space are constructed and the collective sum rules are given. A discussion of the tensor structure of the collective wavefunctions and a review of various methods of solving the Bohr Hamiltonian eigenvalue equation are also presented. Next, the methods of derivation of the classical and quantum Bohr Hamiltonian from the microscopic many-body theory are recalled. Finally, the microscopic approach to the Bohr Hamiltonian is applied to interpret collective properties of 12 heavy even-even nuclei in the Hf-Hg region. Calculated energy levels and E2 transition probabilities are compared with experimental data.

  16. A separable shadow Hamiltonian hybrid Monte Carlo method

    NASA Astrophysics Data System (ADS)

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

    2009-11-01

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

  17. A separable shadow Hamiltonian hybrid Monte Carlo method.

    PubMed

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

    2009-11-07

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

  18. 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.

  19. Hamiltonian Noether theorem for gauge systems and two time physics

    NASA Astrophysics Data System (ADS)

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

    2005-08-01

    The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics.

  20. Simulating Hamiltonian Dynamics with a Truncated Taylor Series

    NASA Astrophysics Data System (ADS)

    Somma, Rolando

    2015-03-01

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

  1. 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…

  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. Warped product Finsler manifolds from Hamiltonian point of view

    NASA Astrophysics Data System (ADS)

    Joharinad, Parvaneh

    In this paper, the Finslerian warped product structures are introduced as Hamiltonian formalism without restricting Finsler functions to be absolutely homogeneous. Afterwards, the constituents of the related variational problem and Finslerian connections of this warped product are obtained according to those of its constructing Finsler manifolds.

  4. 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…

  5. Regularization of the Hamiltonian constraint compatible with the spinfoam dynamics

    NASA Astrophysics Data System (ADS)

    Alesci, Emanuele; Rovelli, Carlo

    2010-08-01

    We introduce a new regularization for Thiemann’s Hamiltonian constraint. The resulting constraint can generate the 1-4 Pachner moves and is therefore more compatible with the dynamics defined by the spinfoam formalism. We calculate its matrix elements and observe the appearance of the 15j Wigner symbol in these.

  6. Fractional Hamiltonian analysis of higher order derivatives systems

    SciTech Connect

    Baleanu, Dumitru; Muslih, Sami I.; Tas, Kenan

    2006-10-15

    The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives.

  7. New bi-Hamiltonian systems on the plane

    NASA Astrophysics Data System (ADS)

    Tsiganov, A. V.

    2017-06-01

    We discuss several new bi-Hamiltonian integrable systems on the plane with integrals of motion of third, fourth, and sixth orders in momenta. The corresponding variables of separation, separated relations, compatible Poisson brackets, and recursion operators are also presented in the framework of the Jacobi method.

  8. Estimating equilibrium properties from non-Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    VandeVondele, Joost; Rothlisberger, Ursula

    2001-11-01

    We derive an expression that enables the accurate estimation of equilibrium properties using non-Hamiltonian dynamics. The major advantage of our scheme is that a time average over a single non-Hamiltonian trajectory can be employed instead of an ensemble average. Hence, it can directly be used in standard molecular dynamics simulations. The connection between non-Hamiltonian dynamics and equilibrium properties is established by assigning to the individual frames of the trajectory a weight that is based on the fluctuations of the phase space compression factor. Additionally, a simple scheme that takes into account only fluctuation of a given maximum duration is introduced to reduce the statistical error. By systematically extending the duration of the allowed fluctuations, increasingly accurate results can be obtained. Non-Hamiltonian dynamics schemes that are capable to enhance sampling efficiency are applied to two model systems in order to demonstrate the practical performance of our approach for the calculation of equilibrium free energy differences and probability density profiles.

  9. Model spin-orbit coupling Hamiltonians for graphene systems

    NASA Astrophysics Data System (ADS)

    Kochan, Denis; Irmer, Susanne; Fabian, Jaroslav

    2017-04-01

    We present a detailed theoretical study of effective spin-orbit coupling (SOC) Hamiltonians for graphene-based systems, covering global effects such as proximity to substrates and local SOC effects resulting, for example, from dilute adsorbate functionalization. Our approach combines group theory and tight-binding descriptions. We consider structures with global point group symmetries D6 h, D3 d, D3 h, C6 v, and C3 v that represent, for example, pristine graphene, graphene miniripple, planar boron nitride, graphene on a substrate, and free standing graphone, respectively. The presence of certain spin-orbit coupling parameters is correlated with the absence of the specific point group symmetries. Especially in the case of C6 v—graphene on a substrate, or transverse electric field—we point out the presence of a third SOC parameter, besides the conventional intrinsic and Rashba contributions, thus far neglected in literature. For all global structures we provide effective SOC Hamiltonians both in the local atomic and Bloch forms. Dilute adsorbate coverage results in the local point group symmetries C6 v, C3 v, and C2 v, which represent the stable adsorption at hollow, top and bridge positions, respectively. For each configuration we provide effective SOC Hamiltonians in the atomic orbital basis that respect local symmetries. In addition to giving specific analytic expressions for model SOC Hamiltonians, we also present general (no-go) arguments about the absence of certain SOC terms.

  10. Translation-Invariant Parent Hamiltonians of Valence Bond Crystals

    NASA Astrophysics Data System (ADS)

    Huerga, Daniel; Greco, Andrés; Gazza, Claudio; Muramatsu, Alejandro

    2017-04-01

    We present a general method to construct translation-invariant and SU(2) symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBCs). The method is based on a canonical mapping transforming S =1 /2 spin operators into a bilinear form of a new set of dimer fermion operators. We construct parent Hamiltonians of the columnar and the staggered VBCs on the square lattice, for which the VBC is an eigenstate in all regimes and the exact ground state in some region of the phase diagram. We study the departure from the exact VBC regime upon tuning the anisotropy by means of the hierarchical mean field theory and exact diagonalization on finite clusters. In both Hamiltonians, the VBC phase extends over the exact regime and transits to a columnar antiferromagnet (CAFM) through a window of intermediate phases, revealing an intriguing competition of correlation lengths at the VBC-CAFM transition. The method can be readily applied to construct other VBC parent Hamiltonians in different lattices and dimensions.

  11. 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.

  12. 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.

  13. 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.

  14. Adaptive molecular resolution approach in Hamiltonian form: An asymptotic analysis.

    PubMed

    Zhu, Jinglong; Klein, Rupert; Delle Site, Luigi

    2016-10-01

    Adaptive molecular resolution approaches in molecular dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer (transition) region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined, and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. Such conditions show that molecular simulations in the current computational implementation require systems of large size, and thus a Hamiltonian approach such as the one proposed, at this stage, would not be practical from the numerical point of view. However, the Hamiltonian proposed provides the basis for a simplification and generalization of the numerical implementation of adaptive resolution algorithms to other molecular dynamics codes.

  15. Translation-Invariant Parent Hamiltonians of Valence Bond Crystals.

    PubMed

    Huerga, Daniel; Greco, Andrés; Gazza, Claudio; Muramatsu, Alejandro

    2017-04-21

    We present a general method to construct translation-invariant and SU(2) symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBCs). The method is based on a canonical mapping transforming S=1/2 spin operators into a bilinear form of a new set of dimer fermion operators. We construct parent Hamiltonians of the columnar and the staggered VBCs on the square lattice, for which the VBC is an eigenstate in all regimes and the exact ground state in some region of the phase diagram. We study the departure from the exact VBC regime upon tuning the anisotropy by means of the hierarchical mean field theory and exact diagonalization on finite clusters. In both Hamiltonians, the VBC phase extends over the exact regime and transits to a columnar antiferromagnet (CAFM) through a window of intermediate phases, revealing an intriguing competition of correlation lengths at the VBC-CAFM transition. The method can be readily applied to construct other VBC parent Hamiltonians in different lattices and dimensions.

  16. Hamiltonian evolutions of twisted polygons in {RP}^n

    NASA Astrophysics Data System (ADS)

    Marì Beffa, Gloria; Wang, Jing Ping

    2013-09-01

    In this paper we find a discrete moving frame and their associated invariants along projective polygons in {RP}^n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W3-algebra), its projective realization in {RP}^2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the Wn-algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple.

  17. Integrable Hamiltonian systems on low-dimensional Lie algebras

    SciTech Connect

    Korotkevich, Aleksandr A

    2009-12-31

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

  18. Horseshoes and Arnold Diffusion for Hamiltonian Systems on Lie Groups

    DTIC Science & Technology

    1981-07-28

    478. V. I. Arnold [1964]. Inst"ility of dynamical systenms with several degrees of freedom, Dokl . Akad . Riuk. SSSR 156,9-12. V. I. Ar’nold [1966...a rigid body, Trans, oscow Math. Soc. 41, 287. S.L. Ziglin [1981]. Branching of solutions and nonexistence of integrals in Hamiltonian systems. Doklady Akad . Nauk . SSSR 257, 26-29. - J. I

  19. LETTER TO THE EDITOR: On optimum Hamiltonians for state transformations

    NASA Astrophysics Data System (ADS)

    Brody, Dorje C.; Hook, Daniel W.

    2006-03-01

    For a prescribed pair of quantum states |ψIrang and |ψFrang we establish an elementary derivation of the optimum Hamiltonian, under constraints on its eigenvalues, that generates the unitary transformation |ψIrang → |ψFrang in the shortest duration. The derivation is geometric in character and does not rely on variational calculus.

  20. Evolutionary approach for determining first-principles hamiltonians.

    PubMed

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

    2005-05-01

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

  1. 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.

  2. Evolution of a Spin System Under a Periodic Hamiltonian

    NASA Astrophysics Data System (ADS)

    Goldman, M.

    The expression of the density matrix for a spin system subjected to a periodic Hamiltonian is derived in the form of an expansion in powers of the inverse modulation frequency, an extension of a method devised by Ruishvili and Menabde and by Mehring. Its application to MAS experiments, as regards the contribution of the dipolar interactions to the sideband intensities, is discussed.

  3. Spectral and resonance properties of the Smilansky Hamiltonian

    NASA Astrophysics Data System (ADS)

    Exner, Pavel; Lotoreichik, Vladimir; Tater, Miloš

    2017-02-01

    We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure.

  4. Effective Hamiltonians by optimal control: solid-state NMR double-quantum planar and isotropic dipolar recoupling.

    PubMed

    Tosner, Zdenek; Glaser, Steffen J; Khaneja, Navin; Nielsen, Niels Chr

    2006-11-14

    We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments.

  5. 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.

  6. The (100), (111) and (110) surfaces of diamond: an ab initio B3LYP study

    NASA Astrophysics Data System (ADS)

    De La Pierre, Marco; Bruno, Marco; Manfredotti, Chiara; Nestola, Fabrizio; Prencipe, Mauro; Manfredotti, Claudio

    2014-04-01

    We present an accurate ab initio study of the structure and surface energy of the low-index (100), (111) and (110) diamond faces, by using the hybrid Hartree-Fock/density functional B3LYP Hamiltonian and a localised all-electron Gaussian-type basis set. A two-dimensional periodic slab model has been adopted, for which convergence on both structural and energetic parameters has been thoroughly investigated. For all the three surfaces, possible relaxations and reconstructions have been considered; a detailed geometrical characterisation is provided for the most stable structure of each orientation. Surface energy is discussed for all the investigated faces.

  7. Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Gong, Yuezheng; Wang, Qi; Wang, Zhu

    2017-03-01

    The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian system, a naive application of the POD method can destroy its Hamiltonian structure in the reduced-order model. In this paper, we develop a new reduce-order modeling approach for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but modifies the ROM so that the appropriate Hamiltonian structure is preserved. Since the POD truncation can degrade the approximation of the Hamiltonian function, we propose to use the POD basis from shifted snapshots to improve the Hamiltonian function approximation. We further derive a rigorous a priori error estimate of the structure-preserving ROM and demonstrate its effectiveness in several numerical examples. This approach can be readily extended to dissipative Hamiltonian systems, port-Hamiltonian systems etc.

  8. 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.

  9. 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.

  10. First integrals of generalized Ermakov systems via the Hamiltonian formulation

    NASA Astrophysics Data System (ADS)

    Mahomed, K. S.; Moitsheki, R. J.

    2016-07-01

    We obtain first integrals of the generalized two-dimensional Ermakov systems, in plane polar form, via the Hamiltonian approaches. There are two methods used for the construction of the first integrals, viz. the standard Hamiltonian and the partial Hamiltonian approaches. In the first approach, F(𝜃) and G(𝜃) in the Ermakov system are related as G(𝜃) + F‧(𝜃)/2 = 0. In this case, we deduce four first integrals (three of which are functionally independent) which correspond to the Lie algebra sl(2,R) ⊕ A1 in a direct constructive manner. We recover the results of earlier work that uses the relationship between symmetries and integrals. This results in the complete integrability of the Ermakov system. By use of the partial Hamiltonian method, we discover four new cases: F(𝜃) = G(𝜃)(c1sin 𝜃 + c3cos 𝜃)/(c1cos 𝜃 - c3sin 𝜃) with c2c3 = c1c4, c1≠0, c3≠0; F(𝜃) = G(𝜃)(c2sin 𝜃 + c4cos 𝜃)/(c2cos 𝜃 - c4sin 𝜃) with c1 = c3 = 0, c2≠0, c4≠0; F(𝜃) = -G(𝜃)cot 𝜃 with c1 = c2 = 0, c3, c4 arbitrary and F(𝜃) = G(𝜃)tan 𝜃 with c3 = c4 = 0, c1, c2 arbitrary, where the cis are constants in all cases. In the last two cases, we find that there are three operators each which give rise to three first integrals each. In both these cases, we have complete integrability of the Ermakov system. The first two cases each result in two first integrals each. For every case, both for the standard and partial Hamiltonian, the angular momentum type first integral arises and this is a consequence of the operator which depends on a momentum coordinate which is a generalized symmetry in the Lagrangian context.

  11. 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.

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

    PubMed

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

    2016-06-07

    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.

  13. Moreau-Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

    NASA Astrophysics Data System (ADS)

    Kim, Hwa Kil

    In this paper, we study the stability property of Hamiltonian systems on the Wasserstein space. Let H be a given Hamiltonian satisfying certain properties. We regularize H using the Moreau-Yosida approximation and denote it by Hτ. We show that solutions of the Hamiltonian system for Hτ converge to a solution of the Hamiltonian system for H as τ converges to zero. We provide sufficient conditions on H to carry out this process.

  14. Differential evolution algorithm for global optimizations in nuclear physics

    NASA Astrophysics Data System (ADS)

    Qi, Chong

    2017-04-01

    We explore the applicability of the differential evolution algorithm in finding the global minima of three typical nuclear structure physics problems: the global deformation minimum in the nuclear potential energy surface, the optimization of mass model parameters and the lowest eigenvalue of a nuclear Hamiltonian. The algorithm works very effectively and efficiently in identifying the minima in all problems we have tested. We also show that the algorithm can be parallelized in a straightforward way.

  15. Two integrable Hamiltonian hierarchies in sl(2 ,R ) and so(3 ,R ) with three potentials

    NASA Astrophysics Data System (ADS)

    Gu, Xiang; Ma, Wen-Xiu; Zhang, Wen-Ying

    2017-05-01

    By introducing two specific matrix spectral problems associated with sl(2 ,R ) and so(3 ,R ) matrix Lie algebras, we generate two integrable Hamiltonian hierarchies with three potentials. The computation and analysis on their Hamiltonian structures by means of the trace identity show that the resulting hierarchies are Liouville integrable, namely, that each hierarchy consists of commuting Hamiltonian soliton equations.

  16. 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.

  17. Targeting transcription factor Stat5a/b as a therapeutic strategy for prostate cancer

    PubMed Central

    Liao, Zhiyong; Nevalainen, Marja T

    2011-01-01

    Signal transducer and activator of transcription 5 (Stat5) is critical for the viability and growth of human prostate cancer cells in culture and for prostate xenograft tumors in nude mice. The expression of nuclear active Stat5a/b is associated with high histological grades of clinical prostate cancers, and the presence of active Stat5a/b in prostate cancer predicts early disease recurrence. Stat5a/b and androgen receptor signaling pathways functionally synergize in prostate cancer cells, and recent work suggests that Stat5a/b may be involved in the progression of prostate cancer to metastatic disease. Here, we review the biological functions of Stat5a/b in prostate cancer and potential strategies to target the prolactin receptor (PrlR)/Jak2/Stat5 signaling pathway for therapy development for prostate cancer. PMID:21416055

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

  19. 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.

  20. Astrophysical jet dynamos based on spheromak, dusty plasma, and Hamiltonian concepts

    NASA Astrophysics Data System (ADS)

    Bellan, Paul

    2008-11-01

    Experiments at Caltech demonstrate that spheromak formation physics and astrophysical jets are closely related [1] as both involve toroidal magnetic field pressure inflating poloidal flux surfaces. The use of capacitor banks to power the lab magnetic fields raises the question of what powers the magnetic fields in the astrophysical situation where gravity is presumably the ultimate power source. In answer to this question, the dust grain mass accretion rate is shown to be much greater than previously assumed [2]. Then, by considering Hamiltonian trajectories of charged dust grains in combined gravitational--magnetic fields, dynamos suitable for powering toroidal and poloidal magnetic fields are demonstrated. The toroidal field dynamo is powered by gravitational power liberated by dust grains having zero canonical momentum; these have spiral trajectories towards the central object [3]. The poloidal field dynamo results from dust grains with Speiser-type trajectories; these grains meander back and forth across a toroidal magnetic axis [3]. Supported in part by USDOE [1] P. M. Bellan et al, J. Fusion Energy 10.1007/s10894-006-9048-z (2006) [2] P. M. Bellan, ApJ 678, 1099 (2008) [3] P. M. Bellan, ApJ (in press), http://arxiv.org/abs/0807.1373