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Sample records for nuclear hamiltonian ab

  1. 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.

  2. 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.

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

    NASA Astrophysics Data System (ADS)

    Chibotaru, L. F.; Ungur, L.

    2012-08-01

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

  11. Ab initio 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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).

  19. 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.

  20. 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.

  1. 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)].

  2. 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.

  3. 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.

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

    SciTech Connect

    Lasoroski, Aurélie; Vuilleumier, Rodolphe; Pollet, Rodolphe

    2014-07-07

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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

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

    PubMed

    Marsalek, Ondrej; Markland, Thomas E

    2016-02-07

    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.

  1. 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.

  2. 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.

  3. Ab Initio Calculations Of Light-Ion Reactions

    SciTech Connect

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

    2012-03-12

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

  4. 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. 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.

  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. 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.

  8. 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.

  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. 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.

  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. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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..

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

    NASA Astrophysics Data System (ADS)

    Scherrer, Arne; Vuilleumier, Rodolphe; Sebastiani, Daniel

    2016-08-01

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

  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. 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.

  5. 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.

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

    SciTech Connect

    Kowalewski, Markus Mukamel, Shaul

    2015-07-28

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

  7. 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)

  8. 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.

  9. 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.

  10. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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

  19. 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)

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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

  19. 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.

  20. 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.

  1. 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....

  2. 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.

  3. 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.

  4. 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.

  5. First principles of Hamiltonian medicine

    PubMed Central

    Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

    2014-01-01

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

  6. 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.

  7. Quasilocal Hamiltonians in general relativity

    SciTech Connect

    Anderson, Michael T.

    2010-10-15

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

  8. 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

  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. 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.

  13. 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…

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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. ).

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. Hamiltonian for a restricted isoenergetic thermostat.

    PubMed

    Dettmann, C P

    1999-12-01

    Nonequilibrium molecular dynamics simulations often use mechanisms called thermostats to regulate the temperature. A Hamiltonian is presented for the case of the isoenergetic (constant internal energy) thermostat corresponding to a tunable isokinetic (constant kinetic energy) thermostat, for which a Hamiltonian has recently been given.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. 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).

  14. 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

  15. 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.

  16. 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.

  17. 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)

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  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. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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

  10. 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

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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

    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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. Hamiltonian learning and certification using quantum resources.

    PubMed

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

    2014-05-16

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

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  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. 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.

  2. 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.

  3. 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).

  4. Multipulses in discrete Hamiltonian nonlinear systems.

    PubMed

    Kevrekidis, P G

    2001-08-01

    In this work, the behavior of multipulses in discrete Hamiltonian nonlinear systems is investigated. The discrete nonlinear Schrödinger equation is used as the benchmark system for this study. A singular perturbation methodology as well as a variational approach are implemented in order to identify the dominant factors in the discrete problem. The results of the two methodologies are shown to coincide in assessing the interplay of discreteness and exponential tail-tail pulse interaction. They also allow one to understand why, contrary to what is believed for their continuum siblings, discrete systems can sustain (static) multipulse configurations, a conclusion that is subsequently verified by numerical experiment.

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. 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.

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

    SciTech Connect

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

    2015-10-28

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-10-01

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

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

    PubMed

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

    2015-10-28

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

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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

  7. 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

  8. Ab initio alpha-alpha scattering.

    PubMed

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

    2015-12-03

    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

  9. 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

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. Fourier series expansion for nonlinear Hamiltonian oscillators.

    PubMed

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

    2010-06-01

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

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

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

    SciTech Connect

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

    2008-10-13

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

  16. 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.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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)

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  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. 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).

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  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. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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)

  12. 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

  13. 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.

  14. Autonomous Biological System (ABS) experiments.

    PubMed

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

    1998-12-01

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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  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. 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).

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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)

  19. 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.

  20. 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...).

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  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. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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…

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  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. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. Registration of nine sorghum seed parent (A/B) lines

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Nine sorghum [Sorghum bicolor (L.) Moench] A1 cyto plasmic-genic male sterile seed parent (A) and their maintainer (B) lines [KS 133A/B, KS 134A/B, KS 135A/B, KS 136A/B, KS 137A/B, KS 138A/B, KS 139A/B, KS 140A/B and KS 141A/B] were released by the Kansas State University, Agricultural Research Cent...

  14. 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

  15. 12 CFR Appendixes A-B - [Reserved

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 12 Banks and Banking 6 2014-01-01 2012-01-01 true A Appendixes A-B Banks and Banking OFFICE OF THRIFT SUPERVISION, DEPARTMENT OF THE TREASURY CAPITAL Regulatory Capital Requirements Appendixes A-B...

  16. 12 CFR Appendixes A-B - [Reserved

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 12 Banks and Banking 6 2013-01-01 2012-01-01 true A Appendixes A-B Banks and Banking OFFICE OF THRIFT SUPERVISION, DEPARTMENT OF THE TREASURY CAPITAL Regulatory Capital Requirements Appendixes A-B...

  17. 12 CFR Appendixes A-B - [Reserved

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 12 Banks and Banking 5 2010-01-01 2010-01-01 false A Appendixes A-B Banks and Banking OFFICE OF THRIFT SUPERVISION, DEPARTMENT OF THE TREASURY CAPITAL Regulatory Capital Requirements Appendixes A-B...

  18. 12 CFR Appendixes A-B - [Reserved

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 12 Banks and Banking 5 2011-01-01 2011-01-01 false A Appendixes A-B Banks and Banking OFFICE OF THRIFT SUPERVISION, DEPARTMENT OF THE TREASURY CAPITAL Regulatory Capital Requirements Appendixes A-B...

  19. 12 CFR Appendixes A-B - [Reserved

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 12 Banks and Banking 6 2012-01-01 2012-01-01 false A Appendixes A-B Banks and Banking OFFICE OF THRIFT SUPERVISION, DEPARTMENT OF THE TREASURY CAPITAL Regulatory Capital Requirements Appendixes A-B...

  20. Photorhabdus luminescens PirAB-fusion protein exhibits both cytotoxicity and insecticidal activity.

    PubMed

    Li, Yusheng; Hu, Xiaofeng; Zhang, Xu; Liu, Zhengqiang; Ding, Xuezhi; Xia, Liqiu; Hu, Shengbiao

    2014-07-01

    The binary toxin 'Photorhabdus insect-related' proteins (PirAB) produced by Photorhabdus luminescens have been reported to possess both injectable and oral activities against a range of insects. Here, PirAB-fusion protein was constructed by linking pirA and pirB genes with the flexible linker (Gly4 Ser)3 DNA encoding sequence and then efficiently expressed in Escherichia coli. To better understand the role of PirAB toxin played in the process of invasion, its cytotoxicity against insect midgut CF-203 cells was investigated. Application of purified PirAB-fusion protein as well as PirA/PirB mixture caused loss of viability of CF-203 cells after 24 h incubation. CF-203 cells treated by PirAB-fusion protein displayed morphological changes typical of apoptosis, such as cell shrinkage, cell membrane blebbing, nuclear condensation and DNA fragmentation. Moreover, PirAB-fusion protein also exhibited injectable insecticidal activity against Spodoptera exigua larvae. The bodies of S. exigua fourth-instar larvae injected with PirAB-fusion protein turned completely black. Thus, we concluded that PirAB-fusion protein possessed similar biological activity (cytotoxicity and insecticidal activity) to PirA/PirB mixture, which would enable it to be used as an efficient agent for pest control.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

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

    PubMed

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

    2016-07-07

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  4. Hamiltonian formulation towards minimization of viscous fluid fingering.

    PubMed

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

    2016-07-01

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

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

    SciTech Connect

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

    2013-09-15

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

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

    NASA Astrophysics Data System (ADS)

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

    2013-10-01

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

  7. Reversible folding simulation by hybrid Hamiltonian replica exchange

    NASA Astrophysics Data System (ADS)

    Xu, Weixin; Lai, Tingfeng; Yang, Ye; Mu, Yuguang

    2008-05-01

    Reversible foldings of a β-hairpin peptide, chignolin, by recently invented hybrid Hamiltonian replica exchange molecular dynamics simulations based on Poisson-Boltzmann model in explicit water are demonstrated. Initiated from extended structures the peptide folded and unfolded a couple of times in seven out of eight replica trajectories during 100 nanoseconds simulation. The folded states have the lowest all-atom root mean squared deviation of 1.3Å with respect to the NMR structures. At T =300K the occurrence of folded states was converged to 62% during 80ns simulation which agrees well with experimental data. Especially, a detailed structural evolution map was constructed based on 800 000 structural snapshots and from where a unique folding doorway emerges. Compared with 130ns standard replica exchange simulation using 24 replicas on the same system, the hybrid Hamiltonian replica exchange molecular dynamics simulation presents consistent results.

  8. Hamiltonian formalism for semiflexible molecules in Cartesian coordinates.

    PubMed

    Kneller, G R

    2006-09-21

    The article gives a concise description of Hamiltonian dynamics and thermal averages of semiflexible molecules in Cartesian coordinates. Using the concept of constrained inverse matrices introduced by Bott and Duffin [Trans. Am. Math. Soc. 74, 99 (1953)] explicit expressions are derived for the constrained Hamiltonian, the corresponding equations of motion, and the momentum partition function. In this context Fixman-type corrections of constrained configurational averages are derived for different forms of the constraints. It is shown that the use of mass-weighted coordinates leads to a nonbiased sampling of constrained configurational averages in Cartesian coordinates. The formalism allows moreover to define and to calculate effective masses arising in thermal velocity averages of atoms in semiflexible molecules. These effective masses are identical to the corresponding Sachs-Teller recoil masses, which are here generalized to the case of only partially rigid molecules.

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

    SciTech Connect

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

    2013-08-01

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

  10. Subharmonic Solutions Near an Equilibrium Point for Hamiltonian Systems

    DTIC Science & Technology

    1989-04-01

    Thus A = 0 will be continued as A,(6) = A+ + ... j = 1,2. (2.5) Since the matrix V is invertible, W is nilpotent and, V and W commute, the matrix (eV...Hamiltonian system z JA(t)z + JHt..(z, t) where A(t) is a matrix , fl,(z,t) = o(I z 1) and both A and H are periodic in t. On the linear part of the system we...write the Hamiltonian as H(z, t) = 1(A(t)z, z) + II(z, t) (0.2) where A(t) denotes the Hessian matrix of H at z = 0 and ft(z, t) = o(Iz12) represents the

  11. The envelope Hamiltonian for electron interaction with ultrashort pulses

    NASA Astrophysics Data System (ADS)

    Toyota, Koudai; Saalmann, Ulf; Rost, Jan M.

    2015-07-01

    For ultrashort VUV pulses with a pulse length comparable to the orbital time of the bound electrons they couple to, we propose a simplified envelope Hamiltonian. It is based on the Kramers-Henneberger representation in connection with a Floquet expansion of the strong-field dynamics but keeps the time dependence of the pulse envelope explicit. Thereby, the envelope Hamiltonian captures the essence of the physics—light-induced shifts of bound states, single-photon absorption, and non-adiabatic electronic transitions. It delivers quantitatively accurate ionization dynamics and allows for a physical insight into the processes occurring. Its minimal requirements for construction in terms of laser parameters make it ideally suited for a large class of atomic and molecular problems.

  12. Rapid geometrical chaotization in slow-fast Hamiltonian systems.

    PubMed

    Artemyev, A V; Neishtadt, A I; Zelenyi, L M

    2014-06-01

    In this Rapid Communication we demonstrate effects of a new mechanism of adiabaticity destruction in Hamiltonian systems with a separatrix in the phase space. In contrast to the slow diffusive-like destruction typical for many systems, this new mechanism is responsible for very fast chaotization in a large phase volume. To investigate this mechanism we consider a Hamiltonian system with two degrees of freedom and with a separatrix in the phase plane of fast variables. The fast chaotization is due to an asymmetry of the separatrix and corresponding geometrical jumps of an adiabatic invariant. This system describes the motion of charged particles in a inhomogeneous electromagnetic field with a specific configuration. We show that geometrical jumps of the adiabatic invariant result in a very fast chaotization of particle motion.

  13. Wobbling motion in 135Pr within a collective Hamiltonian

    NASA Astrophysics Data System (ADS)

    Chen, Q. B.; Zhang, S. Q.; Meng, J.

    2016-11-01

    The recently reported wobbling bands in 135Pr are investigated by the collective Hamiltonian, in which the collective parameters, including the collective potential and the mass parameter, are respectively determined from the tilted axis cranking (TAC) model and the harmonic frozen alignment (HFA) formula. It is shown that the experimental energy spectra of both yrast and wobbling bands are well reproduced by the collective Hamiltonian. It is confirmed that the wobbling mode in 135Pr changes from transverse to longitudinal with the rotational frequency. The mechanism of this transition is revealed by analyzing the effective moments of inertia of the three principal axes, and the corresponding variation trend of the wobbling frequency is determined by the softness and shapes of the collective potential.

  14. Entanglement Hamiltonians in two-dimensional conformal field theory

    NASA Astrophysics Data System (ADS)

    Cardy, John; Tonni, Erik

    2016-12-01

    We enumerate the cases in 2d conformal field theory where the logarithm of the reduced density matrix (the entanglement or modular Hamiltonian) may be written as an integral over the energy-momentum tensor times a local weight. These include known examples and new ones corresponding to the time-dependent scenarios of a global and local quench. In these latter cases the entanglement Hamiltonian depends on the momentum density as well as the energy density. In all cases the entanglement spectrum is that of the appropriate boundary CFT. We emphasize the role of boundary conditions at the entangling surface and the appearance of boundary entropies as universal O(1) terms in the entanglement entropy.

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

    NASA Astrophysics Data System (ADS)

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

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

  16. Higher-spin charges in Hamiltonian form. II. Fermi fields

    NASA Astrophysics Data System (ADS)

    Campoleoni, A.; Henneaux, M.; Hörtner, S.; Leonard, A.

    2017-02-01

    We build the asymptotic higher-spin charges associated with "improper" gauge transformations for fermionic higher-spin gauge fields on Anti de Sitter backgrounds of arbitrary dimension. This is achieved within the canonical formalism. We consider massless fields of spin s+1/2, described by a symmetric spinor-tensor of rank s in the Fang-Fronsdal approach. We begin from a detailed analysis of the spin 5/2 example, for which we cast the Fang-Fronsdal action in Hamiltonian form, we derive the charges and we propose boundary conditions on the canonical variables that secure their finiteness. We then extend the computation of charges and the characterisation of boundary conditions to arbitrary half-integer spin. Our construction generalises to higher-spin fermionic gauge fields the known Hamiltonian derivation of supercharges in AdS supergravity.

  17. Hamiltonian identification in presence of large control field perturbations

    NASA Astrophysics Data System (ADS)

    Fu, Ying; Rabitz, Herschel; Turinici, Gabriel

    2016-12-01

    Quantum system inversion concerns learning the characteristics of the underlying Hamiltonian by measuring suitable observables from the responses of the system’s interaction with members of a set of applied fields. Various aspects of inversion have been confirmed in theoretical, numerical and experimental works. Nevertheless, the presence of noise arising from the applied fields may contaminate the quality of the results. In this circumstance, the observables satisfy probability distributions, but often the noise statistics are unknown. Based on a proposed theoretical framework, we present a procedure to recover both the unknown parts of the Hamiltonian and the unknown noise distribution. The procedure is implemented numerically and seen to perform well for illustrative Gaussian, exponential and bi-modal noise distributions.

  18. Comparative index and Sturmian theory for linear Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Šepitka, Peter; Šimon Hilscher, Roman

    2017-01-01

    The comparative index was introduced by J. Elyseeva (2007) as an efficient tool in matrix analysis, which has fundamental applications in the discrete oscillation theory. In this paper we implement the comparative index into the theory of continuous time linear Hamiltonian systems, study its properties, and apply it to obtain new Sturmian separation theorems as well as new and optimal estimates for left and right proper focal points of conjoined bases of these systems on bounded intervals. We derive our results for general possibly abnormal (or uncontrollable) linear Hamiltonian systems. The results turn out to be new even in the case of completely controllable systems. We also provide several examples, which illustrate our new theory.

  19. Effective Hamiltonian and unitarity of the S matrix.

    PubMed

    Rotter, I

    2003-07-01

    The properties of open quantum systems are described well by an effective Hamiltonian H that consists of two parts: the Hamiltonian H of the closed system with discrete eigenstates and the coupling matrix W between discrete states and continuum. The eigenvalues of H determine the poles of the S matrix. The coupling matrix elements W(cc')(k) between the eigenstates k of H and the continuum may be very different from the coupling matrix elements W(cc')(k) between the eigenstates of H and the continuum. Due to the unitarity of the S matrix, the W(cc')(k) depend on energy in a nontrivial manner. This conflicts with the assumptions of some approaches to reactions in the overlapping regime. Explicit expressions for the wave functions of the resonance states and for their phases in the neighborhood of, respectively, avoided level crossings in the complex plane and double poles of the S matrix are given.

  20. Hamiltonian hierarchy and the Hulthén potential

    NASA Astrophysics Data System (ADS)

    Gönül, B.; Özer, O.; Cançelik, Y.; Koçak, M.

    2000-10-01

    We deal with the Hamiltonian hierarchy problem of the Hulthén potential within the frame of the supersymmetric quantum mechanics and find that the associated supersymmetric partner potentials simulate the effect of the centrifugal barrier. Incorporating the supersymmetric solutions and using the first-order perturbation theory we obtain an expression for the energy levels of the Hulthén potential which gives satisfactory values for the non-zero angular momentum states.

  1. An application of Hamiltonian neurodynamics using Pontryagin's Maximum (Minimum) Principle.

    PubMed

    Koshizen, T; Fulcher, J

    1995-12-01

    Classical optimal control methods, notably Pontryagin's Maximum (Minimum) Principle (PMP) can be employed, together with Hamiltonians, to determine optimal system weights in Artificial Neural dynamical systems. A new learning rule based on weight equations derived using PMP is shown to be suitable for both discrete- and continuous-time systems, and moreover, can also be applied to feedback networks. Preliminary testing shows that this PMP learning rule compares favorably with Standard BackPropagations (SBP) on the XOR problem.

  2. Dynamical algebras for Poeschl-Teller Hamiltonian hierarchies

    SciTech Connect

    Kuru, S.; Negro, J.

    2009-12-15

    The dynamical algebras of the trigonometric and hyperbolic symmetric Poeschl-Teller Hamiltonian hierarchies are obtained. A kind of discrete-differential realizations of these algebras are found which are isomorphic to so(3, 2) Lie algebras. In order to get them, first the relation between ladder and factor operators is investigated. In particular, the action of the ladder operators on normalized eigenfunctions is found explicitly. Then, the whole dynamical algebras are generated in a straightforward way.

  3. Note on Subharmonic Solutions of a Hamiltonian Vector Field.

    DTIC Science & Technology

    1983-09-01

    34Quelques questions de geometrie symplectique" Seminaire BOURBAKI 1982/83, 610. (4) C.C. Conlex: "Isolated invariant sets and the Morse index" CBMS...approach. It is based on the Morse theory for periodic solutions developed in [5] which relates the winding number of a periodic solution to its Morse...Hamiltonian systems, periodic solutions, variational principles, Morse-type index theory , winding number of a periodic solution. Work Unit Number 1

  4. When a local Hamiltonian must be frustration-free

    PubMed Central

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

    2016-01-01

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

  5. Exact Solution of the Isovector Proton Neutron Pairing Hamiltonian

    SciTech Connect

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

    2005-12-02

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

  6. Superfield Hamiltonian quantization in terms of quantum antibrackets

    NASA Astrophysics Data System (ADS)

    Batalin, Igor A.; Lavrov, Peter M.

    2016-04-01

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

  7. Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

    NASA Astrophysics Data System (ADS)

    Tang, Wensheng; Sun, Yajuan; Cai, Wenjun

    2017-02-01

    In this article, we present a unified framework of discontinuous Galerkin (DG) discretizations for Hamiltonian ODEs and PDEs. We show that with appropriate numerical fluxes the numerical algorithms deduced from DG discretizations can be combined with the symplectic methods in time to derive the multi-symplectic PRK schemes. The resulting numerical discretizations are applied to the linear and nonlinear Schrödinger equations. Some conservative properties of the numerical schemes are investigated and confirmed in the numerical experiments.

  8. Unbounded Trace Orbits of Thue-Morse Hamiltonian

    NASA Astrophysics Data System (ADS)

    Liu, Qinghui; Qu, Yanhui; Yao, Xiao

    2017-03-01

    It is well known that, an energy is in the spectrum of Fibonacci Hamiltonian if and only if the corresponding trace orbit is bounded. However, it is not known whether the same result holds for the Thue-Morse Hamiltonian. In this paper, we give a negative answer to this question. More precisely, we construct two subsets Σ _{II} and Σ _{III} of the spectrum of the Thue-Morse Hamiltonian, both of which are dense and uncountable, such that each energy in Σ _{II}&ucedil;p Σ _{III} corresponds to an unbounded trace orbit. Exact estimates on the norm of the transfer matrices are also obtained for these energies: for Ein Σ _{II}&ucedil;p Σ _{III}, the norms of the transfer matrices behave like e^{c_1γ √{n}}≤Vert T_{ n}(E)Vert ≤e^{c_2γ √{n}}. However, two types of energies are quite different in the sense that each energy in Σ _{II} is associated with a two-sided pseudo-localized state, while each energy in Σ _{III} is associated with a one-sided pseudo-localized state. The difference is also reflected by the local dimensions of the spectral measure: the local dimension is 0 for energies in Σ _{II} and is larger than 1 for energies in Σ _{III}. As a comparison, we mention another known countable dense subset Σ _I. Each energy in Σ _I corresponds to an eventually constant trace map and the associated eigenvector is an extended state. In summary, the Thue-Morse Hamiltonian exhibits "mixed spectral nature".

  9. Quantum integrals of motion for variable quadratic Hamiltonians

    SciTech Connect

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

    2010-09-15

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  11. When a local Hamiltonian must be frustration-free

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  12. Ab initio theories for light nuclei and neutron stars

    NASA Astrophysics Data System (ADS)

    Gezerlis, Alexandros

    2016-09-01

    In this talk I will touch upon several features of modern ab initio low-energy nuclear theory. I will start by discussing what ``ab initio'' means in this context. Specifically, I will spend some time going over nucleon-nucleon and three-nucleon interactions and their connections with the underlying theory of Quantum Chromodynamics. I will then show how these interactions are used to describe light nuclei using essentially exact few-body methods. I will then discuss heavier systems, especially those of astrophysical relevance, as well as the methods used to tackle them. This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Canada Foundation for Innovation (CFI).

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

    PubMed Central

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

    2016-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Páez, Rocío Isabel; Locatelli, Ugo

    2015-10-01

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

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

    PubMed Central

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

    2014-01-01

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

  16. Runtime of unstructured search with a faulty Hamiltonian oracle

    NASA Astrophysics Data System (ADS)

    Temme, Kristan

    2014-08-01

    We show that it is impossible to obtain a quantum speedup for a faulty Hamiltonian oracle. The effect of dephasing noise to this continuous-time oracle model has first been investigated by Shenvi, Brown, and Whaley [Phys. Rev. A 68, 052313 (2003)., 10.1103/PhysRevA.68.052313]. The authors consider a faulty oracle described by a continuous-time master equation that acts as dephasing noise in the basis determined by the marked item. The analysis focuses on the implementation with a particular driving Hamiltonian. A universal lower bound for this oracle model, which rules out a better performance with a different driving Hamiltonian, has so far been lacking. Here, we derive an adversary-type lower bound which shows that the evolution time T has to be at least in the order of N, i.e., the size of the search space, when the error rate of the oracle is constant. This means that quadratic quantum speedup vanishes and the runtime assumes again the classical scaling. For the standard quantum oracle model this result was first proven by Regev and Schiff [in Automata, Languages and Programming, Lecture Notes in Computer Science Vol. 5125 (Springer, Berlin, 2008), pp. 773-781]. Here, we extend this result to the continuous-time setting.

  17. Production and transfer of energy and information in Hamiltonian systems.

    PubMed

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

    2014-01-01

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

  18. Finite-time thermodynamics of port-Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Delvenne, Jean-Charles; Sandberg, Henrik

    2014-01-01

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

  19. On the quantum mechanics of bicomplex Hamiltonian system

    NASA Astrophysics Data System (ADS)

    Banerjee, Abhijit

    2017-02-01

    We investigate the Schrödinger equation in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero-divisors. We propose an analytical method to solve bicomplex-version of Schrödinger equation corresponding to the systems of Hamiltonians of both hermitian (self-adjoint) and non-hermitian PT symmetric type. In our approach we extend the existing mathematical formulation of quantum system searching for the exact or quasi-exact solution for ground state energy eigenvalues and associated wave functions acting in bicomplex Hilbert space. The model concerning hermitian Hamiltonians is then applied to the problems of two bicomplex valued polynomial oscillators one involving x2 and another of isotonic type. The ground states and associated energy values for both the oscillators are found to be hyperbolic in nature. The model in connection to the unbroken PT symmetric Hamiltonians is then applied to illustrate the problems of complex and bicomplex valued shifted oscillators.

  20. Hamiltonian Dynamics of Several Rigid Bodies Interacting with Point Vortices

    NASA Astrophysics Data System (ADS)

    Weißmann, Steffen

    2014-04-01

    We derive the dynamics of several rigid bodies of arbitrary shape in a two-dimensional inviscid and incompressible fluid, whose vorticity is given by point vortices. We adopt the idea of Vankerschaver et al. (J. Geom. Mech. 1(2): 223-226, 2009) to derive the Hamiltonian formulation via symplectic reduction from a canonical Hamiltonian system. The reduced system is described by a noncanonical symplectic form, which has previously been derived for a single circular disk using heavy differential-geometric machinery in an infinite-dimensional setting. In contrast, our derivation makes use of the fact that the dynamics of the fluid, and thus the point vortex dynamics, is determined from first principles. Using this knowledge we can directly determine the dynamics on the reduced, finite-dimensional phase space, using only classical mechanics. Furthermore, our approach easily handles several bodies of arbitrary shape. From the Hamiltonian description we derive a Lagrangian formulation, which enables the system for variational time integrators. We briefly describe how to implement such a numerical scheme and simulate different configurations for validation.

  1. Hamiltonian of a homogeneous two-component plasma.

    PubMed

    Essén, Hanno; Nordmark, A

    2004-03-01

    The Hamiltonian of one- and two-component plasmas is calculated in the negligible radiation Darwin approximation. Since the Hamiltonian is the phase space energy of the system its form indicates, according to statistical mechanics, the nature of the thermal equilibrium that plasmas strive to attain. The main issue is the length scale of the magnetic interaction energy. In the past a screening length lambda=1/square root of r(e)n], with n number density and r(e) classical electron radius, has been derived. We address the question whether the corresponding longer screening range obtained from the classical proton radius is physically relevant and the answer is affirmative. Starting from the Darwin Lagrangian it is nontrivial to find the Darwin Hamiltonian of a macroscopic system. For a homogeneous system we resolve the difficulty by temporarily approximating the particle number density by a smooth constant density. This leads to Yukawa-type screened vector potential. The nontrivial problem of finding the corresponding, divergence free, Coulomb gauge version is solved.

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

    SciTech Connect

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

    2012-01-01

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

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

    SciTech Connect

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

    2012-01-01

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

  4. Experimental and Ab Initio Studies of the HDO Absorption Spectrum in the 13165-13500 1/cm Spectral Region

    NASA Technical Reports Server (NTRS)

    Schwenke, David; Naumenko, Olga; Bertseva, Elena; Campargue, Alain; Arnold, James O. (Technical Monitor)

    2000-01-01

    The HDO absorption spectrum has been recorded in the 13165 - 13500 cm(exp-1) spectral region by Intracavity Laser Absorption Spectroscopy. The spectrum (615 lines), dominated by the 2n2 + 3n3 and n1+3n3 bands was assigned and modeled leading to the derivation of 196 accurate energy levels of the (103) and (023) vibrational states. Finally, 150 of these levels have been reproduced by an effective Hamiltonian involving two vibrational dark states interacting with the (023) and ( 103) bright states. The rms deviation achieved by variation of 28 parameters is 0.05-1 cm, compared to an averaged experimental uncertainty of 0.007-1 cm, indicating the limit of validity of the effective Hamiltonian approach for HDO at high vibrational excitation. The predictions of previous ab initio calculations of the HDO spectrum were extensively used in the assignment process. The particular spectral region under consideration has been used to test and discuss the improvements of new ab initio calculations recently performed on the basis of the same potential energy surface but with an improved dipole moment surface. The improvements concern both the energy levels and the line intensities. In particular, the strong hybrid character of the n1+3n3 band is very well accounted for by the the new ab initio calculations.

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

    NASA Astrophysics Data System (ADS)

    Ogata, Yoshiko

    2016-12-01

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

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

    PubMed

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

    2016-08-25

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

  7. Generator coordinate method and nuclear collective motions (VII): the preservation of symmetry properties

    SciTech Connect

    XU Gong-ou

    1985-01-01

    In order to preserve all the symmetry properties for the effective collective Hamiltonian obtained with the generator coordinate method, it is necessary for the trial wave function to have proper transformation properties. The generator coordinates should then transform in the same way as the represented collective operators. Also, the center-of-mass motion should be independent of the internal motion in conformity with the invariance of the nuclear Hamiltonian with respect to space rotation and Galilean transformation.

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

    NASA Astrophysics Data System (ADS)

    Bianucci, Marco

    2016-08-01

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

  9. Lattice effects on Laughlin wave functions and parent Hamiltonians

    NASA Astrophysics Data System (ADS)

    Glasser, Ivan; Cirac, J. Ignacio; Sierra, Germán; Nielsen, Anne E. B.

    2016-12-01

    We investigate lattice effects on wave functions that are lattice analogs of bosonic and fermionic Laughlin wave functions with number of particles per flux ν =1 /q in the Landau levels. These wave functions are defined analytically on lattices with μ particles per lattice site, where μ may be different than ν . We give numerical evidence that these states have the same topological properties as the corresponding continuum Laughlin states for different values of q and for different fillings μ . These states define, in particular, particle-hole symmetric lattice fractional quantum Hall states when the lattice is half filled. On the square lattice it is observed that for q ≤4 this particle-hole symmetric state displays the topological properties of the continuum Laughlin state at filling fraction ν =1 /q , while for larger q there is a transition towards long-range ordered antiferromagnets. This effect does not persist if the lattice is deformed from a square to a triangular lattice, or on the kagome lattice, in which case the topological properties of the state are recovered. We then show that changing the number of particles while keeping the expression of these wave functions identical gives rise to edge states that have the same correlations in the bulk as the reference lattice Laughlin states but a different density at the edge. We derive an exact parent Hamiltonian for which all these edge states are ground states with different number of particles. In addition this Hamiltonian admits the reference lattice Laughlin state as its unique ground state of filling factor 1 /q . Parent Hamiltonians are also derived for the lattice Laughlin states at other fillings of the lattice, when μ ≤1 /q or μ ≥1 -1 /q and when q =4 also at half filling.

  10. Is the addition of an assisted driving Hamiltonian always useful for adiabatic evolution?

    NASA Astrophysics Data System (ADS)

    Sun, Jie; Lu, Songfeng; Li, Li

    2017-04-01

    It has been known that when an assisted driving item is added to the main system Hamiltonian, the efficiency of the resultant adiabatic evolution can be significantly improved. In some special cases, it can be seen that only through adding an assisted driving Hamiltonian can the resulting adiabatic evolution be made not to fail. Thus the additional driving Hamiltonian plays an important role in adiabatic computing. In this paper, we show that if the driving Hamiltonian is chosen inappropriately, the adiabatic computation may still fail. More importantly, we find that the adiabatic computation can only succeed if the assisted driving Hamiltonian has a relatively fixed form. This may help us understand why in the related literature all of the driving Hamiltonians used share the same form.

  11. The symmetry groups of bifurcations of integrable Hamiltonian systems

    SciTech Connect

    Orlova, E I

    2014-11-30

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

  12. Dynamics symmetries of Hamiltonian system on time scales

    SciTech Connect

    Peng, Keke Luo, Yiping

    2014-04-15

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

  13. Dynamics symmetries of Hamiltonian system on time scales

    NASA Astrophysics Data System (ADS)

    Peng, Keke; Luo, Yiping

    2014-04-01

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

  14. Nonholonomic Hamiltonian method for molecular dynamics simulations of reacting shocks

    NASA Astrophysics Data System (ADS)

    Bass, Joseph; Fahrenthold, Eric P.

    2017-01-01

    Conventional molecular dynamics simulations of reacting shocks employ a holonomic Hamiltonian formulation: the breaking and forming of covalent bonds is described by potential functions. In general the potential functions: (a) are algebraically complex, (b) must satisfy strict smoothness requirements, and (c) contain many fitted parameters. In recent research the authors have developed a new nonholonomic formulation of reacting molecular dynamics. In this formulation bond orders are determined by rate equations, and the bonding-debonding process need not be described by differentiable functions. This simplifies the representation of complex chemistry and reduces the number of fitted parameters.

  15. Quantization of non-Hamiltonian and dissipative systems

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2001-09-01

    A generalization of canonical quantization which maps a dynamical operator to a dynamical superoperator is suggested. Weyl quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables is a specific case of suggested quantization. This approach allows to define consistent quantization procedure for non-Hamiltonian and dissipative systems. Examples of the harmonic oscillator with friction (generalized Lorenz-Rossler-Leipnik-Newton equation), the Fokker-Planck-type system and Lorenz-type system are considered.

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

    PubMed

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

    2001-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2001-05-01

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

  18. Transient chaos in two coupled, dissipatively perturbed Hamiltonian Duffing oscillators

    NASA Astrophysics Data System (ADS)

    Sabarathinam, S.; Thamilmaran, K.; Borkowski, L.; Perlikowski, P.; Brzeski, P.; Stefanski, A.; Kapitaniak, T.

    2013-11-01

    The dynamics of two coupled, dissipatively perturbed, near-integrable Hamiltonian, double-well Duffing oscillators has been studied. We give numerical and experimental (circuit implementation) evidence that in the case of small positive or negative damping there exist two different types of transient chaos. After the decay of the transient chaos in the neighborhood of chaotic saddle we observe the transient chaos in the neighborhood of unstable tori. We argue that our results are robust and they exist in the wide range of system parameters.

  19. Polynomial approximation of Poincare maps for Hamiltonian system

    NASA Technical Reports Server (NTRS)

    Froeschle, Claude; Petit, Jean-Marc

    1992-01-01

    Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

  20. Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Kapela, Tomasz; Simó, Carles

    2017-03-01

    We set up a methodology for computer assisted proofs of the existence and the KAM stability of an arbitrary periodic orbit for Hamiltonian systems. We give two examples of application for systems with two and three degrees of freedom. The first example verifies the existence of tiny elliptic islands inside large chaotic domains for a quartic potential. In the 3-body problem we prove the KAM stability of the well-known figure eight orbit and two selected orbits of the so called family of rotating eights. Some additional theoretical and numerical information is also given for the dynamics of both examples.

  1. Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Chen, Zhaoxia; You, Xiong; Shi, Wei; Liu, Zhongli

    2012-01-01

    The ERKN methods proposed by H. Yang et al. [Comput. Phys. Comm. 180 (2009) 1777] are an important improvement of J.M. Franco's ARKN methods for perturbed oscillators [J.M. Franco, Comput. Phys. Comm. 147 (2002) 770]. This paper focuses on the symmetry and symplecticity conditions for ERKN methods solving oscillatory Hamiltonian systems. Two examples of symmetric and symplectic ERKN (SSERKN) methods of orders two and four respectively are constructed. The phase and stability properties of the new methods are analyzed. The results of numerical experiments show the robustness and competence of the SSERKN methods compared with some well-known methods in the literature.

  2. Non-Hermitian quantum Hamiltonians with PT symmetry

    SciTech Connect

    Jones-Smith, Katherine; Mathur, Harsh

    2010-10-15

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

  3. Scattering matrix of arbitrary tight-binding Hamiltonians

    NASA Astrophysics Data System (ADS)

    Ramírez, C.; Medina-Amayo, L. A.

    2017-03-01

    A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.

  4. Renormalization Group Reduction of Non Integrable Hamiltonian Systems

    SciTech Connect

    Stephan I. Tzenov

    2002-05-09

    Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail.

  5. AB INITIO AND CALPHAD THERMODYNAMICS OF MATERIALS

    SciTech Connect

    Turchi, P A

    2004-04-14

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

  6. Analysis of Nuclear Quantum Phase Transitions

    SciTech Connect

    Li, Z. P.; Meng, J.; Niksic, T.; Vretenar, D.; Lalazissis, G. A.; Ring, P.

    2009-08-26

    A microscopic analysis, based on nuclear energy density functionals, is presented for shape phase transitions in Nd isotopes. Low-lying excitation spectra and transition probabilities are calculated starting from a five-dimensional Hamiltonian, with parameters determined by constrained relativistic mean-field calculations for triaxial shapes. The results reproduce available data, and show that there is an abrupt change of structure at N = 90, that corresponds to a first-order quantum phase transition between spherical and axially deformed shapes.

  7. From light nuclei to nuclear matter the role of relativity?

    SciTech Connect

    Coester, F.; Physics

    2003-11-10

    The success of non-relativistic quantum dynamics in accounting for the binding energies and spectra of light nuclei with masses up to A=10 raises the question whether the same dynamics applied to infinite nuclear matter agrees with the empirical saturation properties of large nuclei. The simple unambiguous relation between few-nucleon and many-nucleon Hamiltonians is directly related to the Galilean covariance of nonrelativistic dynamics. Relations between the irreducible unitary representations of the Galilei and Poincare groups indicate that the 'nonrelativistic' nuclear Hamiltonians may provide sufficiently accurate approximations to Poincare invariant mass operators. In relativistic nuclear dynamics based on suitable Lagrangeans the intrinsic nucleon parity is an explicit, dynamically relevant, degree of freedom and the emphasis is on properties of nuclear matter. The success of this approach suggests the question how it might account for the spectral properties of light nuclei.

  8. Ab initio dynamical vertex approximation

    NASA Astrophysics Data System (ADS)

    Galler, Anna; Thunström, Patrik; Gunacker, Patrik; Tomczak, Jan M.; Held, Karsten

    2017-03-01

    Diagrammatic extensions of dynamical mean-field theory (DMFT) such as the dynamical vertex approximation (DΓ A) allow us to include nonlocal correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an Ab initio DΓ A approach (AbinitioDΓ A ) for electronic structure calculations of materials. The starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare nonlocal Coulomb interaction and all local vertex corrections. From this, we calculate the full nonlocal vertex and the nonlocal self-energy through the Bethe-Salpeter equation. The AbinitioDΓ A approach naturally generates all local DMFT correlations and all nonlocal G W contributions, but also further nonlocal correlations beyond: mixed terms of the former two and nonlocal spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO3.

  9. An ab initio calculation of the fundamental and overtone HCl stretching vibrations for the HCl dimer

    NASA Astrophysics Data System (ADS)

    Jensen, Per; Bunker, P. R.; Epa, V. C.; Karpfen, A.

    1992-02-01

    We have previously determined an analytical ab initio six-dimensional potential energy surface for the HCl dimer, and have used it to determine the minimum energy path for the trans-tunneling motion. In the present paper we refine this path by fitting to data. We calculate a further 178 ab initio points in order to determine the HCl stretching energies, and HCl stretching dipole moment functions, at eight positions along the minimum energy path. We use these ab initio results to compute the stretching wavenumbers and transition moments from the v1 = v2 = 0 state to all states of (HCl) 2 that have v1 + v2 ≤ 3, where v1 and v2 are the local mode quantum numbers for the HCl stretching vibrations. In doing this calculation we have assumed an adiabatic separation of the HCl stretching motion from the other vibrational motions in the dimer, and have used the semirigid bender Hamiltonian to average over the trans-tunneling motion. We obtain the fundamental "free-H" stretch v1 at 2877 cm -1 and the fundamental "bound-H" stretch v2 at 2861 cm -1; the experimental values are 2880 and 2854 cm -1, respectively.

  10. Lars Onsager Prize Talk: Flow Equations for Hamiltonians

    NASA Astrophysics Data System (ADS)

    Wegner, Franz

    2015-03-01

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

  11. Quantum spin Hamiltonians for the SU(2)k WZW model

    NASA Astrophysics Data System (ADS)

    Nielsen, Anne E. B.; Cirac, J. Ignacio; Sierra, Germán

    2011-11-01

    We propose to use null vectors in conformal field theories to derive model Hamiltonians of quantum spin chains and the corresponding ground state wavefunction(s). The approach is quite general, and we illustrate it by constructing a family of Hamiltonians whose ground states are the chiral correlators of the SU(2)k WZW model for integer values of the level k. The simplest example corresponds to k = 1 and is essentially a nonuniform generalization of the Haldane-Shastry model with long-range exchange couplings. At level k = 2, we analyse the model for N spin 1 fields. We find that the Renyi entropy and the two-point spin correlator show, respectively, logarithmic growth and algebraic decay. Furthermore, we use the null vectors to derive a set of algebraic, linear equations relating spin correlators within each model. At level k = 1, these equations allow us to compute the two-point spin correlators analytically for the finite chain uniform Haldane-Shastry model and to obtain numerical results for the nonuniform case and for higher-point spin correlators in a very simple way and without resorting to Monte Carlo techniques.

  12. The Hamiltonian Laceability of some Generalized Honeycomb Tori

    SciTech Connect

    Hsu Liyen; Lin Tungyi; Kao Shinshin

    2008-11-06

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

  13. The performance of the quantum adiabatic algorithm on spike Hamiltonians

    NASA Astrophysics Data System (ADS)

    Kong, Linghang; Crosson, Elizabeth

    Spike Hamiltonians arise from optimization instances for which the adiabatic algorithm provably out performs classical simulated annealing. In this work, we study the efficiency of the adiabatic algorithm for solving the “the Hamming weight with a spike” problem by analyzing the scaling of the spectral gap at the critical point for various sizes of the barrier. Our main result is a rigorous lower bound on the minimum spectral gap for the adiabatic evolution when the bit-symmetric cost function has a thin but polynomially high barrier, which is based on a comparison argument and an improved variational ansatz for the ground state. We also adapt the discrete WKB method for the case of abruptly changing potentials and compare it with the predictions of the spin coherent instanton method which was previously used by Farhi, Goldstone and Gutmann. Finally, our improved ansatz for the ground state leads to a method for predicting the location of avoided crossings in the excited energy states of the thin spike Hamiltonian, and we use a recursion relation to understand the ordering of some of these avoided crossings as a step towards analyzing the previously observed diabatic cascade phenomenon.

  14. Léon Rosenfeld's general theory of constrained Hamiltonian dynamics

    NASA Astrophysics Data System (ADS)

    Salisbury, Donald; Sundermeyer, Kurt

    2017-01-01

    This commentary reflects on the 1930 general theory of Léon Rosenfeld dealing with phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article in the context of ideas pursued by W. Pauli, F. Klein, E. Noether. We then comment on Rosenfeld's General Theory dealing with symmetries and constraints, symmetry generators, conservation laws and the construction of a Hamiltonian in the case of phase-space constraints. It is remarkable that he was able to derive expressions for all phase space symmetry generators without making explicit reference to the generator of time evolution. In his Applications, Rosenfeld treated the general relativistic example of Einstein-Maxwell-Dirac theory. We show, that although Rosenfeld refrained from fully applying his general findings to this example, he could have obtained the Hamiltonian. Many of Rosenfeld's discoveries were re-developed or re-discovered by others two decades later, yet as we show there remain additional firsts that are still not recognized in the community.

  15. Hamiltonian theory of the FQHE edge: Collective modes

    NASA Astrophysics Data System (ADS)

    Nguyen, Hoang; Joglekar, Yogesh; Murthy, Ganpathy

    2003-03-01

    We study the collective modes of the fractional quantum Hall edge states using the Hamiltonian formalism [1]. While most theoretical approaches start with an effective bosonic theory [2] in which all fermions are integrated out (an exception is the approach based on Chern-Simons theory [3]), the Hamiltonian theory treats the composite fermions as fully interacting. We obtain the gapless edge-modes using a conserving approximation which respects the constraints [4]. The implications of our study to the tunneling experiments into the edge of a fractional quantum Hall system [5] are discussed. [1] R.Shankar and G.Murthy, Phys.Rev.Lett. 79, 4437 (1997). [2] X.-G.Wen, Phys.Rev.Lett. 64, 2206 (1990); D.-H.Lee and X.-G.Wen, cond-mat/9809160; A.Lopez and E.Fradkin, Phys.Rev.B 59, 15323 (1999); U. Zulicke and A.H.MacDonald, Phys.Rev.B 60, 1837 (1999); V.J.Goldman and E.V.Tsiper, Phys.Rev.Lett. 86, 5841 (2001); S.S.Mandal and J.K.Jain, Phys.Rev.Lett. 89, 096801 (2002). [3] L.S.Levitov, A.V.Shytov, and B.I.Halperin, Phys. Rev. B 64, 075322 (2001). [4] N. Read, Phys.Rev.B 58, 16262 (1998); G. Murthy, Phys.Rev.B 64, 195310 (2001). [5] A.M.Chang et.al., Phys.Rev.Lett. 86, 143 (2000).

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

    NASA Astrophysics Data System (ADS)

    Ivancevic, Vladimir G.; Reid, Darryn J.

    2015-11-01

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

  17. Tight-binding Hamiltonian for LaFeAsO

    NASA Astrophysics Data System (ADS)

    Papaconstantopoulos, D. A.; Mehl, Michael; Johannes, Michelle; Parker, David

    2010-03-01

    We construct a realistic tight-binding Hamiltonian (TB) fitted to first-principles band structure calculations of the pnictide parent compound LaFeAsO. We have come to the conclusion that most previously derived (TB) Hamiltonians poorly reproduce the first-principles results. Here we use the NRL-TB method to fit our LAPW results as a function of volume and As displacement. The TB basis includes the Fe d, As p, and O p-orbitals. We omit the La d-orbitals, which only contribute to states well above the Fermi level. We find a TB band structure that fits an LAPW range of energies with a width of 3.5 eV. The bands near the Fermi level fit the LAPW results very well, reproducing the Fermi surface near γ and M. The TB densities of states agree with first-principles results. We also study the variation of the total energy with respect to the position of the As atoms. We find that the TB total energies fit the LAPW values very well even for structures not included in our fit. We use our accurate hopping parameters to uncover the origin of the so far unexplained pseudogap near the Fermi energy and explore the evolution of this gap with magnetism.

  18. Entanglement and corner Hamiltonian spectra of integrable open spin chains

    NASA Astrophysics Data System (ADS)

    Kim, Panjin; Katsura, Hosho; Trivedi, Nandini; Han, Jung Hoon

    2016-11-01

    We investigate the entanglement entropy (EE) and entanglement spectra (ES) of critical SU (N ) (2 ≤N ≤4 ) spin chains and other integrable models of finite length with the density matrix renormalization group method. For all models under investigation, we find a remarkable agreement of the level spacings and the degeneracy structure of the ES with the spectrum of the corner Hamiltonian (CS), defined as the generator of the associated corner transfer matrix. The correspondence holds between ES(n ) at the n th cut position from the edge of the spin model, and the spectrum CS(n ) of the corner Hamiltonian of length n , for all values of n that we have checked. The cut position dependence of the ES shows a period-N oscillatory behavior for a given SU (N ) chain, reminiscent of the oscillatory part of the entanglement entropy observed in the past for the same models. However, the oscillations of the ES do not die out in the bulk of the chain, in contrast to the asymptotically vanishing oscillation of the entanglement entropy. We present a heuristic argument based on Young tableaux construction that can explain the period-N structure of the ES qualitatively.

  19. Effective Hamiltonian for surface states of topological insulator nanotubes.

    PubMed

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

    2017-04-03

    In this work we derive an effective Hamiltonian for the surface states of a hollow topological insulator (TI) nanotube with finite width walls. Unlike a solid TI cylinder, a TI nanotube possesses both an inner as well as outer surface on which the states localized at each surface are coupled together. The curvature along the circumference of the nanotube leads to a spatial variation of the spin orbit interaction field experienced by the charge carriers as well as an asymmetry between the inner and outer surfaces of the nanotube. Both of these features result in terms in the effective Hamiltonian for a TI nanotube absent in that of a flat TI thin film of the same thickness. We calculate the numerical values of the parameters for a Bi2Se3 nanotube as a function of the inner and outer radius, and show that the differing relative magnitudes between the parameters result in qualitatively differing behaviour for the eigenstates of tubes of different dimensions.

  20. Effective Hamiltonian for surface states of topological insulator nanotubes

    PubMed Central

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

    2017-01-01

    In this work we derive an effective Hamiltonian for the surface states of a hollow topological insulator (TI) nanotube with finite width walls. Unlike a solid TI cylinder, a TI nanotube possesses both an inner as well as outer surface on which the states localized at each surface are coupled together. The curvature along the circumference of the nanotube leads to a spatial variation of the spin orbit interaction field experienced by the charge carriers as well as an asymmetry between the inner and outer surfaces of the nanotube. Both of these features result in terms in the effective Hamiltonian for a TI nanotube absent in that of a flat TI thin film of the same thickness. We calculate the numerical values of the parameters for a Bi2Se3 nanotube as a function of the inner and outer radius, and show that the differing relative magnitudes between the parameters result in qualitatively differing behaviour for the eigenstates of tubes of different dimensions. PMID:28367970

  1. The reachable set of single-mode quadratic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Shackerley-Bennett, Uther; Pitchford, Alexander; Genoni, Marco G.; Serafini, Alessio; Burgarth, Daniel K.

    2017-04-01

    Open-loop controllability in quantum mechanics refers to finding conditions on time-varying Hamiltonians such that a full group of unitary transformations can be enacted with them. For compact groups controllability is well understood and is dealt with using the Lie algebra rank criterion. Gaussian systems, however, evolve under Hamiltonians generating the non-compact symplectic group, rendering the rank criterion necessary but no longer sufficient. In this setting it is possible to satisfy the rank criterion without the ability to enact all symplectic transformations. We refer to such systems as ‘unstable’ and explore the set of symplectic transformations that remain reachable. We provide a partial analytical characterisation for the reachable set of a single-mode unstable system. From this it is proven that no orthogonal-symplectic operations (‘energy-preserving’ or ‘passive’ in the literature) may be reached with such controls. We then apply numerical optimal control algorithms to demonstrate a complete characterisation of the set in specific cases. These results suggest approaches to the long-standing open problem of controllability in n modes.

  2. Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states.

    PubMed

    Bonet-Luz, Esther; Tronci, Cesare

    2016-05-01

    The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest's theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie-Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature.

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

    SciTech Connect

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

    2013-10-15

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

  4. Local temperatures and local terms in modular Hamiltonians

    NASA Astrophysics Data System (ADS)

    Arias, Raúl E.; Blanco, David D.; Casini, Horacio; Huerta, Marina

    2017-03-01

    We show there are analogs to the Unruh temperature that can be defined for any quantum field theory and region of the space. These local temperatures are defined using relative entropy with localized excitations. We show that important restrictions arise from relative entropy inequalities and causal propagation between Cauchy surfaces. These suggest a large amount of universality for local temperatures, especially the ones affecting null directions. For regions with any number of intervals in two spacetime dimensions, the local temperatures might arise from a term in the modular Hamiltonian proportional to the stress tensor. We argue this term might be universal, with a coefficient that is the same for any theory, and check analytically and numerically that this is the case for free massive scalar and Dirac fields. In dimensions d ≥3 , the local terms in the modular Hamiltonian producing these local temperatures cannot be formed exclusively from the stress tensor. For a free scalar field, we classify the structure of the local terms.

  5. Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states

    NASA Astrophysics Data System (ADS)

    Bonet-Luz, Esther; Tronci, Cesare

    2016-05-01

    The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest's theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie-Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature.

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

    PubMed

    Baaquie, Belal E

    2009-10-01

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

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

    PubMed

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

    2016-01-01

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

  8. Nuclear rights - nuclear wrongs

    SciTech Connect

    Paul, E.F.; Miller, F.D.; Paul, J.; Ahrens, J.

    1986-01-01

    This book contains 11 selections. The titles are: Three Ways to Kill Innocent Bystanders: Some Conundrums Concerning the Morality of War; The International Defense of Liberty; Two Concepts of Deterrence; Nuclear Deterrence and Arms Control; Ethical Issues for the 1980s; The Moral Status of Nuclear Deterrent Threats; Optimal Deterrence; Morality and Paradoxical Deterrence; Immoral Risks: A Deontological Critique of Nuclear Deterrence; No War Without Dictatorship, No Peace Without Democracy: Foreign Policy as Domestic Politics; Marxism-Leninism and its Strategic Implications for the United States; Tocqueveille War.

  9. Erythema ab igne: Usual site, unusual cause.

    PubMed

    Manoharan, D

    2015-04-01

    Erythema ab igne is reticular erythematous pigmented dermatoses seen in patients exposed to prolonged or repeated sub-threshold Infrared radiation inadequate to cause burns. Here, we report a case of erythema ab igne in a 40-year-old male patient seen over the abdomen due to prolonged laptop use.

  10. Isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian with only 1-electron interactions

    NASA Astrophysics Data System (ADS)

    Liu, Jian

    2017-01-01

    We introduce the isomorphism between an multi-state Hamiltonian and the second-quantized many-electron Hamiltonian (with only 1-electron interactions). This suggests that all methods developed for the former can be employed for the latter, and vice versa. The resonant level (Landauer) model for nonequilibrium quantum transport is used as a proof-of-concept example. Such as the classical mapping models for the multi-state Hamiltonian proposed in our previous work [J. Liu, J. Chem. Phys. 145, 204105 (2016)] lead to exact results for this model problem. We further demonstrate how these methods can also be applied to the second-quantized many-electron Hamiltonian even when 2-electron interactions are included.

  11. Microhydration of caesium compounds: Cs, CsOH, CsI and Cs₂I₂ complexes with one to three H₂O molecules of nuclear safety interest.

    PubMed

    Sudolská, Mária; Cantrel, Laurent; Cernušák, Ivan

    2014-04-01

    Structure and thermodynamic properties (standard enthalpies of formation and Gibbs free energies) of hydrated caesium species of nuclear safety interest, Cs, CsOH, CsI and its dimer Cs₂I₂, with one up to three water molecules, are calculated to assess their possible existence in severe accident occurring to a pressurized water reactor. The calculations were performed using the coupled cluster theory including single, double and non-iterative triple substitutions (CCSD(T)) in conjunction with the basis sets (ANO-RCC) developed for scalar relativistic calculations. The second-order spin-free Douglas-Kroll-Hess Hamiltonian was used to account for the scalar relativistic effects. Thermodynamic properties obtained by these correlated ab initio calculations (entropies and thermal capacities at constant pressure as a function of temperature) are used in nuclear accident simulations using ASTEC/SOPHAEROS software. Interaction energies, standard enthalpies and Gibbs free energies of successive water molecules addition determine the ordering of the complexes. CsOH forms the most hydrated stable complexes followed by CsI, Cs₂I₂, and Cs. CsOH still exists in steam atmosphere even at quite high temperature, up to around 1100 K.

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

  13. QED theory of the nuclear magnetic shielding in hydrogenlike ions.

    PubMed

    Yerokhin, V A; Pachucki, K; Harman, Z; Keitel, C H

    2011-07-22

    The shielding of the nuclear magnetic moment by the bound electron in hydrogenlike ions is calculated ab initio with inclusion of relativistic, nuclear, and quantum electrodynamics (QED) effects. The QED correction is evaluated to all orders in the nuclear binding strength parameter and, independently, to the first order in the expansion in this parameter. The results obtained lay the basis for the high-precision determination of nuclear magnetic dipole moments from measurements of the g factor of hydrogenlike ions.

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

    SciTech Connect

    Bhattacharyya, Swarnendu Domcke, Wolfgang; Dai, Zuyang

    2015-11-21

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

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

    SciTech Connect

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

    2014-05-15

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

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

    PubMed

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

    2012-03-01

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

  17. Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

    NASA Astrophysics Data System (ADS)

    Pang, Shengshi; Jordan, Andrew N.

    2017-03-01

    Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

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

    NASA Astrophysics Data System (ADS)

    Ramezanpour, A.

    2016-06-01

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

  19. Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.

    PubMed

    Pang, Shengshi; Jordan, Andrew N

    2017-03-09

    Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T(2) time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T(4) in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

  20. Engineering photonic Floquet Hamiltonians through Fabry-Pérot resonators

    NASA Astrophysics Data System (ADS)

    Sommer, Ariel; Simon, Jonathan

    2016-03-01

    In this paper we analyze an optical Fabry-Pérot resonator as a time-periodic driving of the (2D) optical field repeatedly traversing the resonator, uncovering that resonator twist produces a synthetic magnetic field applied to the light within the resonator, while mirror aberrations produce relativistic dynamics, anharmonic trapping and spacetime curvature. We develop a Floquet formalism to compute the effective Hamiltonian for the 2D field, generalizing the idea that the intra-cavity optical field corresponds to an ensemble of non-interacting, massive, harmonically trapped particles. This work illuminates the extraordinary potential of optical resonators for exploring the physics of quantum fluids in gauge fields and exotic space-times.

  1. A Monte Carlo investigation of the Hamiltonian mean field model

    NASA Astrophysics Data System (ADS)

    Pluchino, Alessandro; Andronico, Giuseppe; Rapisarda, Andrea

    2005-04-01

    We present a Monte Carlo numerical investigation of the Hamiltonian mean field (HMF) model. We begin by discussing canonical Metropolis Monte Carlo calculations, in order to check the caloric curve of the HMF model and study finite size effects. In the second part of the paper, we present numerical simulations obtained by means of a modified Monte Carlo procedure with the aim to test the stability of those states at minimum temperature and zero magnetization (homogeneous Quasi stationary states), which exist in the condensed phase of the model just below the critical point. For energy densities smaller than the limiting value U∼0.68, we find that these states are unstable confirming a recent result on the Vlasov stability analysis applied to the HMF model.

  2. Quantum phase transitions in bosonic heteronuclear pairing Hamiltonians

    SciTech Connect

    Hohenadler, M.; Silver, A. O.; Bhaseen, M. J.; Simons, B. D.

    2010-07-15

    We explore the phase diagram of two-component bosons with Feshbach resonant pairing interactions in an optical lattice. It has been shown in previous work to exhibit a rich variety of phases and phase transitions, including a paradigmatic Ising quantum phase transition within the second Mott lobe. We discuss the evolution of the phase diagram with system parameters and relate this to the predictions of Landau theory. We extend our exact diagonalization studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising critical exponents for the longitudinal and transverse magnetic susceptibilities within the second Mott lobe. The numerical results for the ground-state energy and transverse magnetization are in good agreement with exact solutions of the Ising model in the thermodynamic limit. We also provide details of the low-energy spectrum, as well as density fluctuations and superfluid fractions in the grand canonical ensemble.

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

    SciTech Connect

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

    2014-08-15

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

  4. Hamiltonian of Tensionless Strings with Tensor Central Charge Coordinates

    NASA Astrophysics Data System (ADS)

    Zheltukhin, Aleksandr A.; Lindström, Ulf

    2002-01-01

    A new class of twistor-like string models in four-dimensional space-time extended by the addition of six tensorial central charge (TCC) coordinates zmn is studied. The hamiltonian of tensionless string in the extended space-time is derived and its symmetries are investigated. We establish that the string constraints reduce the number of independent TCC coordinates zmn to one real effective coordinate which composes an effective 5-dimensional target space together with the xm coordinates. We construct the P.B. algebra of the first class constraints and discover that it coincides with the P.B. algebra of tensionless strings. The Lorentz covariant antisymmetric Dirac hat C-matrix of the P.B. of the second class constraints is constructed and its algebraic structure is further presented.

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

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1989-01-01

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

  6. Forms of crystal field Hamiltonians - A critical review

    NASA Astrophysics Data System (ADS)

    Rudowicz, C.; Gnutek, P.; Karbowiak, M.

    2011-08-01

    Our survey reveals that various disparate forms, both compact and expanded ones, of crystal field (CF) Hamiltonians, HCF, expressed in the Wybourne notation have been used in the literature. It turns out that the disparities in the symbolic explicit forms of HCF are especially important for monoclinic and triclinic site symmetry. The extent of the inconsistencies identified in selected papers has prompted us to embark on a systematic critical review of the HCF forms employed in optical spectroscopy and related areas. Most crucial results of this survey are presented here. Comparative analysis has been carried out to establish the interrelations between CF parameters (CFPs) expressed in disparate forms. The usage of inconsistent or confusing HCF forms has implications also for CFP conversions between the Stevens and Wybourne notations as well as for theoretical modeling of CFPs. This review reveals that comparison of CFP data taken from various sources should be carried out with special care, especially for low symmetry cases.

  7. Error suppression for Hamiltonian quantum computing in Markovian environments

    NASA Astrophysics Data System (ADS)

    Marvian, Milad; Lidar, Daniel A.

    2017-03-01

    Hamiltonian quantum computing, such as the adiabatic and holonomic models, can be protected against decoherence using an encoding into stabilizer subspace codes for error detection and the addition of energy penalty terms. This method has been widely studied since it was first introduced by Jordan, Farhi, and Shor (JFS) in the context of adiabatic quantum computing. Here, we extend the original result to general Markovian environments, not necessarily in Lindblad form. We show that the main conclusion of the original JFS study holds under these general circumstances: Assuming a physically reasonable bath model, it is possible to suppress the initial decay out of the encoded ground state with an energy penalty strength that grows only logarithmically in the system size, at a fixed temperature.

  8. Gapless modes of fractional quantum Hall edges: a Hamiltonian study

    NASA Astrophysics Data System (ADS)

    Nguyen, Hoang; Joglekar, Yogesh; Murthy, Ganpathy

    2004-03-01

    We study the collective modes of the fractional quantum Hall edge states using the Hamiltonian formalism [1]. In this theory, the composite fermions are fully interacting; the collective modes are obtained within a conserving approximation which respects the constraints [2]. We present the gapless edge-mode dispersions at 1/3 and 2/5 filling fractions of unreconstructed and reconstructed edges. The dispersions are found to be nonlinear due to the variation of the effective magnetic field on the composite fermions. The implications of our study to the tunneling experiments into the edge of a fractional quantum Hall system [3] are discussed*. 1. R. Shankar and G. Murthy, Phys. Rev. Lett. 79, 4437 (1997). 2. G. Murthy, Phys. Rev. B 64, 195310 (2001). 3. A.M.Chang et. al., Phys. Rev. Lett. 86, 143 (2000). * Work supported by the NSF, Grant number DMR 031176.

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

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

  10. Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

    NASA Astrophysics Data System (ADS)

    Ndayiragije, F.; Van Assche, W.

    2013-12-01

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

  11. Exact solution of the two-axis countertwisting Hamiltonian

    NASA Astrophysics Data System (ADS)

    Pan, Feng; Zhang, Yao-Zhong; Draayer, Jerry P.

    2017-01-01

    It is shown that the two-axis countertwisting Hamiltonian is exactly solvable when the quantum number of the total angular momentum of the system is an integer after the Jordan-Schwinger (differential) boson realization of the SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz equations of the problem is derived. It is shown that solutions of the Bethe ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials. The total number of the four sets of the zeros equals exactly 2 J + 1 for a given integer angular momentum quantum number J, which proves the completeness of the solutions. It is also shown that double degeneracy in level energies may also occur in the J → ∞ limit for integer J case except a unique non-degenerate level with zero excitation energy.

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

    SciTech Connect

    Doroshin, Anton V.

    2010-03-01

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

  13. Long-range correlations in quantum systems with aperiodic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Lin, Zhifang; Goda, Masaki

    1997-03-01

    An efficient algorithm for the computation of correlation function (CF) at very long distances is presented for quantum systems whose Hamiltonian is formed by the substitution aperiodic sequence alternating over unit intervals in time or space. The algorithm reorganizes the expression of the CF in such a way that the evaluation of the CF at distances equal to some special numbers is related to a family of graphs generated recursively. As examples of applications, we evaluate the CF, over unprecedentedly long time intervals up to order of 1012, for aperiodic two-level systems subject to kicking perturbations that are in the Thue-Morse, the period-doubling, and the Rudin-Shapiro sequences, respectively. Our results show the presence of long-range correlations in all these aperiodic quantum systems.

  14. Common Hamiltonian and topological properties of extended MHD models

    NASA Astrophysics Data System (ADS)

    Miloshevich, George; Lingam, Manasvi; Morrison, Philip

    2016-10-01

    Extended MHD, a 1-fluid model endowed with 2-fluid effects (electron inertia and Hall drift) possesses a Hamiltonian structure. This formulation is described, as it unifies different classes of extended MHD models (including those that have mutually exclusive effects). The unification is further highlighted by showing that these models possess common topological invariants that are the generalizations of the fluid/magnetic helicity. They can be expressed naturally in a knot-theoretic framework via the Jones polynomial by exploiting techniques from Chern-Simons theory. It is also shown that extended MHD exhibits other commonalities such as: generalized Kelvin circulation theorems, and the existence of two Lie-dragged 2-forms closely connected with generalizations of the fluid vorticity. NSF Grant No. AGS-133894, DOE Grants No. DE-AC02-09CH-11466 and DE-FG02-04ER-54742.

  15. Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  16. Cluster Monte Carlo methods for the FePt Hamiltonian

    NASA Astrophysics Data System (ADS)

    Lyberatos, A.; Parker, G. J.

    2016-02-01

    Cluster Monte Carlo methods for the classical spin Hamiltonian of FePt with long range exchange interactions are presented. We use a combination of the Swendsen-Wang (or Wolff) and Metropolis algorithms that satisfies the detailed balance condition and ergodicity. The algorithms are tested by calculating the temperature dependence of the magnetization, susceptibility and heat capacity of L10-FePt nanoparticles in a range including the critical region. The cluster models yield numerical results in good agreement within statistical error with the standard single-spin flipping Monte Carlo method. The variation of the spin autocorrelation time with grain size is used to deduce the dynamic exponent of the algorithms. Our cluster models do not provide a more accurate estimate of the magnetic properties at equilibrium.

  17. Adiabatic theory, Liapunov exponents, and rotation number for quadratic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Delyon, François; Foulon, Patrick

    1987-11-01

    We consider the adiabatic problem for general time-dependent quadratic Hamiltonians and develop a method quite different from WKB. In particular, we apply our results to the Schrödinger equation in a strip. We show that there exists a first regular step (avoiding resonance problems) providing one adiabatic invariant, bounds on the Liapunov exponents, and estimates on the rotation number at any order of the perturbation theory. The further step is shown to be equivalent to a quantum adiabatic problem, which, by the usual adiabatic techniques, provides the other possible adiabatic invariants. In the special case of the Schrödinger equation our method is simpler and more powerful than the WKB techniques.

  18. The B AB AR detector

    NASA Astrophysics Data System (ADS)

    Aubert, B.; Bazan, A.; Boucham, A.; Boutigny, D.; De Bonis, I.; Favier, J.; Gaillard, J.-M.; Jeremie, A.; Karyotakis, Y.; Le Flour, T.; Lees, J. P.; Lieunard, S.; Petitpas, P.; Robbe, P.; Tisserand, V.; Zachariadou, K.; Palano, A.; Chen, G. P.; Chen, J. C.; Qi, N. D.; Rong, G.; Wang, P.; Zhu, Y. S.; Eigen, G.; Reinertsen, P. L.; Stugu, B.; Abbott, B.; Abrams, G. S.; Amerman, L.; Borgland, A. W.; Breon, A. B.; Brown, D. N.; Button-Shafer, J.; Clark, A. R.; Dardin, S.; Day, C.; Dow, S. F.; Fan, Q.; Gaponenko, I.; Gill, M. S.; Goozen, F. R.; Gowdy, S. J.; Gritsan, A.; Groysman, Y.; Hernikl, C.; Jacobsen, R. G.; Jared, R. C.; Kadel, R. W.; Kadyk, J.; Karcher, A.; Kerth, L. T.; Kipnis, I.; Kluth, S.; Kral, J. F.; Lafever, R.; LeClerc, C.; Levi, M. E.; Lewis, S. A.; Lionberger, C.; Liu, T.; Long, M.; Luo, L.; Lynch, G.; Luft, P.; Mandelli, E.; Marino, M.; Marks, K.; Matuk, C.; Meyer, A. B.; Minor, R.; Mokhtarani, A.; Momayezi, M.; Nyman, M.; Oddone, P. J.; Ohnemus, J.; Oshatz, D.; Patton, S.; Pedrali-Noy, M.; Perazzo, A.; Peters, C.; Pope, W.; Pripstein, M.; Quarrie, D. R.; Rasson, J. E.; Roe, N. A.; Romosan, A.; Ronan, M. T.; Shelkov, V. G.; Stone, R.; Strother, P. D.; Telnov, A. V.; von der Lippe, H.; Weber, T. F.; Wenzel, W. A.; Zizka, G.; Bright-Thomas, P. G.; Hawkes, C. M.; Kirk, A.; Knowles, D. J.; O'Neale, S. W.; Watson, A. T.; Watson, N. K.; Deppermann, T.; Koch, H.; Krug, J.; Kunze, M.; Lewandowski, B.; Peters, K.; Schmuecker, H.; Steinke, M.; Andress, J. C.; Barlow, N. R.; Bhimji, W.; Chevalier, N.; Clark, P. J.; Cottingham, W. N.; De Groot, N.; Dyce, N.; Foster, B.; Mass, A.; McFall, J. D.; Wallom, D.; Wilson, F. F.; Abe, K.; Hearty, C.; McKenna, J. A.; Thiessen, D.; Camanzi, B.; Harrison, T. J.; McKemey, A. K.; Tinslay, J.; Antohin, E. I.; Blinov, V. E.; Bukin, A. D.; Bukin, D. A.; Buzykaev, A. R.; Dubrovin, M. S.; Golubev, V. B.; Ivanchenko, V. N.; Kolachev, G. M.; Korol, A. A.; Kravchenko, E. A.; Mikhailov, S. F.; Onuchin, A. P.; Salnikov, A. A.; Serednyakov, S. I.; Skovpen, Yu. I.; Telnov, V. I.; Yushkov, A. N.; Booth, J.; Lankford, A. J.; Mandelkern, M.; Pier, S.; Stoker, D. P.; Zioulas, G.; Ahsan, A.; Arisaka, K.; Buchanan, C.; Chun, S.; Faccini, R.; MacFarlane, D. B.; Prell, S. A.; Rahatlou, Sh.; Raven, G.; Sharma, V.; Burke, S.; Callahan, D.; Campagnari, C.; Dahmes, B.; Hale, D.; Hart, P. A.; Kuznetsova, N.; Kyre, S.; Levy, S. L.; Long, O.; Lu, A.; May, J.; Richman, J. D.; Verkerke, W.; Witherell, M.; Yellin, S.; Beringer, J.; DeWitt, J.; Dorfan, D. E.; Eisner, A. M.; Frey, A.; Grillo, A. A.; Grothe, M.; Heusch, C. A.; Johnson, R. P.; Kroeger, W.; Lockman, W. S.; Pulliam, T.; Rowe, W.; Sadrozinski, H.; Schalk, T.; Schmitz, R. E.; Schumm, B. A.; Seiden, A.; Spencer, E. N.; Turri, M.; Walkowiak, W.; Wilder, M.; Williams, D. C.; Chen, E.; Dubois-Felsmann, G. P.; Dvoretskii, A.; Hanson, J. E.; Hitlin, D. G.; Kolomensky, Yu. G.; Metzler, S.; Oyang, J.; Porter, F. C.; Ryd, A.; Samuel, A.; Weaver, M.; Yang, S.; Zhu, R. Y.; Devmal, S.; Geld, T. L.; Jayatilleke, S.; Jayatilleke, S. M.; Mancinelli, G.; Meadows, B. T.; Sokoloff, M. D.; Bloom, P.; Broomer, B.; Erdos, E.; Fahey, S.; Ford, W. T.; Gaede, F.; van Hoek, W. C.; Johnson, D. R.; Michael, A. K.; Nauenberg, U.; Olivas, A.; Park, H.; Rankin, P.; Roy, J.; Sen, S.; Smith, J. G.; Wagner, D. L.; Blouw, J.; Harton, J. L.; Krishnamurthy, M.; Soffer, A.; Toki, W. H.; Warner, D. W.; Wilson, R. J.; Zhang, J.; Brandt, T.; Brose, J.; Dahlinger, G.; Dickopp, M.; Dubitzky, R. S.; Eckstein, P.; Futterschneider, H.; Kocian, M. L.; Krause, R.; Müller-Pfefferkorn, R.; Schubert, K. R.; Schwierz, R.; Spaan, B.; Wilden, L.; Behr, L.; Bernard, D.; Bonneaud, G. R.; Brochard, F.; Cohen-Tanugi, J.; Ferrag, S.; Fouque, G.; Gastaldi, F.; Matricon, P.; Mora de Freitas, P.; Renard, C.; Roussot, E.; T'Jampens, S.; Thiebaux, C.; Vasileiadis, G.; Verderi, M.; Anjomshoaa, A.; Bernet, R.; Di Lodovico, F.; Muheim, F.; Playfer, S.; Swain, J. E.; Falbo, M.; Bozzi, C.; Dittongo, S.; Folegani, M.; Piemontese, L.; Ramusino, A. C.; Treadwell, E.; Anulli, F.; Baldini-Ferroli, R.; Calcaterra, A.; de Sangro, R.; Falciai, D.; Finocchiaro, G.; Patteri, P.; Peruzzi, I. M.; Piccolo, M.; Xie, Y.; Zallo, A.; Bagnasco, S.; Buzzo, A.; Contri, R.; Crosetti, G.; Fabbricatore, P.; Farinon, S.; Lo Vetere, M.; Macri, M.; Minutoli, S.; Monge, M. R.; Musenich, R.; Pallavicini, M.; Parodi, R.; Passaggio, S.; Pastore, F. C.; Patrignani, C.; Pia, M. G.; Priano, C.; Robutti, E.; Santroni, A.; Bartoldus, R.; Dignan, T.; Hamilton, R.; Mallik, U.; Cochran, J.; Crawley, H. B.; Fischer, P. A.; Lamsa, J.; McKay, R.; Meyer, W. T.; Rosenberg, E. I.; Albert, J. N.; Beigbeder, C.; Benkebil, M.; Breton, D.; Cizeron, R.; Du, S.; Grosdidier, G.; Hast, C.; Höcker, A.; Lacker, H. M.; LePeltier, V.; Lutz, A. M.; Plaszczynski, S.; Schune, M. H.; Trincaz-Duvoid, S.; Truong, K.; Valassi, A.; Wormser, G.; Alford, O.; Behne, D.; Bionta, R. M.; Bowman, J.; Brigljević, V.; Brooks, A.; Dacosta, V. A.; Fackler, O.; Fujino, D.; Harper, M.; Lange, D. J.; Mugge, M.; O'Connor, T. G.; Olson, H.; Ott, L.; Parker, E.; Pedrotti, B.; Roeben, M.; Shi, X.; van Bibber, K.; Wenaus, T. J.; Wright, D. M.; Wuest, C. R.; Yamamoto, B.; Carroll, M.; Cooke, P.; Fry, J. R.; Gabathuler, E.; Gamet, R.; George, M.; Kay, M.; McMahon, S.; Muir, A.; Payne, D. J.; Sloane, R. J.; Sutcliffe, P.; Touramanis, C.; Aspinwall, M. L.; Bowerman, D. A.; Dauncey, P. D.; Eschrich, I.; Gunawardane, N. J. W.; Martin, R.; Nash, J. A.; Price, D. R.; Sanders, P.; Smith, D.; Azzopardi, D. E.; Back, J. J.; Dixon, P.; Harrison, P. F.; Newman-Coburn, D.; Potter, R. J. L.; Shorthouse, H. W.; Williams, M. I.; Vidal, P. B.; Cowan, G.; George, S.; Green, M. G.; Kurup, A.; Marker, C. E.; McGrath, P.; McMahon, T. R.; Salvatore, F.; Scott, I.; Vaitsas, G.; Brown, D.; Davis, C. L.; Li, Y.; Pavlovich, J.; Allison, J.; Barlow, R. J.; Boyd, J. T.; Fullwood, J.; Jackson, F.; Khan, A.; Lafferty, G. D.; Savvas, N.; Simopoulos, E. T.; Thompson, R. J.; Weatherall, J. H.; Bard, R.; Dallapiccola, C.; Farbin, A.; Jawahery, A.; Lillard, V.; Olsen, J.; Roberts, D. A.; Schieck, J. R.; Blaylock, G.; Flood, K. T.; Hertzbach, S. S.; Kofler, R.; Lin, C. S.; Willocq, S.; Wittlin, J.; Brau, B.; Cowan, R.; Taylor, F.; Yamamoto, R. K.; Britton, D. I.; Fernholz, R.; Houde, M.; Milek, M.; Patel, P. M.; Trischuk, J.; Lanni, F.; Palombo, F.; Bauer, J. M.; Booke, M.; Cremaldi, L.; Kroeger, R.; Reep, M.; Reidy, J.; Sanders, D. A.; Summers, D. J.; Arguin, J. F.; Beaulieu, M.; Martin, J. P.; Nief, J. Y.; Seitz, R.; Taras, P.; Woch, A.; Zacek, V.; Nicholson, H.; Sutton, C. S.; Cartaro, C.; Cavallo, N.; De Nardo, G.; Fabozzi, F.; Gatto, C.; Lista, L.; Piccolo, D.; Sciacca, C.; Cason, N. M.; LoSecco, J. M.; Alsmiller, J. R. G.; Gabriel, T. A.; Handler, T.; Heck, J.; Iwasaki, M.; Sinev, N. B.; Caracciolo, R.; Colecchia, F.; Dal Corso, F.; Galeazzi, F.; Marzolla, M.; Michelon, G.; Morandin, M.; Posocco, M.; Rotondo, M.; Santi, S.; Simonetto, F.; Stroili, R.; Torassa, E.; Voci, C.; Bailly, P.; Benayoun, M.; Briand, H.; Chauveau, J.; David, P.; De la Vaissière, C.; Del Buono, L.; Genat, J.-F.; Hamon, O.; Leruste, Ph.; Le Diberder, F.; Lebbolo, H.; Lory, J.; Martin, L.; Martinez-Vidal, F.; Roos, L.; Stark, J.; Versillé, S.; Zhang, B.; Manfredi, P. F.; Ratti, L.; Re, V.; Speziali, V.; Frank, E. D.; Gladney, L.; Guo, Q. H.; Panetta, J. H.; Angelini, C.; Batignani, G.; Bettarini, S.; Bondioli, M.; Bosi, F.; Carpinelli, M.; Forti, F.; Gaddi, A.; Gagliardi, D.; Giorgi, M. A.; Lusiani, A.; Mammini, P.; Morganti, M.; Morsani, F.; Neri, N.; Profeti, A.; Paoloni, E.; Raffaelli, F.; Rama, M.; Rizzo, G.; Sandrelli, F.; Simi, G.; Triggiani, G.; Haire, M.; Judd, D.; Paick, K.; Turnbull, L.; Wagoner, D. E.; Albert, J.; Bula, C.; Kelsey, M. H.; Lu, C.; McDonald, K. T.; Miftakov, V.; Sands, B.; Schaffner, S. F.; Smith, A. J. S.; Tumanov, A.; Varnes, E. W.; Bronzini, F.; Buccheri, A.; Bulfon, C.; Cavoto, G.; del Re, D.; Ferrarotto, F.; Ferroni, F.; Fratini, K.; Lamanna, E.; Leonardi, E.; Mazzoni, M. A.; Morganti, S.; Piredda, G.; Safai Tehrani, F.; Serra, M.; Voena, C.; Waldi, R.; Jacques, P. F.; Kalelkar, M.; Plano, R. J.; Adye, T.; Claxton, B.; Dowdell, J.; Egede, U.; Franek, B.; Galagedera, S.; Geddes, N. I.; Gopal, G. P.; Kay, J.; Lidbury, J.; Madani, S.; Metcalfe, S.; Metcalfe, S.; Markey, G.; Olley, P.; Watt, M.; Xella, S. M.; Aleksan, R.; Besson, P.; Bourgeois, P.; Convert, P.; De Domenico, G.; de Lesquen, A.; Emery, S.; Gaidot, A.; Ganzhur, S. F.; Georgette, Z.; Gosset, L.; Graffin, P.; Hamel de Monchenault, G.; Hervé, S.; Karolak, M.; Kozanecki, W.; Langer, M.; London, G. W.; Marques, V.; Mayer, B.; Micout, P.; Mols, J. P.; Mouly, J. P.; Penichot, Y.; Rolquin, J.; Serfass, B.; Toussaint, J. C.; Usseglio, M.; Vasseur, G.; Yeche, C.; Zito, M.; Copty, N.; Purohit, M. V.; Yumiceva, F. X.; Adam, I.; Adesanya, A.; Anthony, P. L.; Aston, D.; Bartelt, J.; Becla, J.; Bell, R.; Bloom, E.; Boeheim, C. T.; Boyarski, A. M.; Boyce, R. F.; Briggs, D.; Bulos, F.; Burgess, W.; Byers, B.; Calderini, G.; Chestnut, R.; Claus, R.; Convery, M. R.; Coombes, R.; Cottrell, L.; Coupal, D. P.; Coward, D. H.; Craddock, W. W.; DeBarger, S.; DeStaebler, H.; Dorfan, J.; Doser, M.; Dunwoodie, W.; Dusatko, J. E.; Ecklund, S.; Fieguth, T. H.; Freytag, D. R.; Glanzman, T.; Godfrey, G. L.; Haller, G.; Hanushevsky, A.; Harris, J.; Hasan, A.; Hee, C.; Himel, T.; Huffer, M. E.; Hung, T.; Innes, W. R.; Jessop, C. P.; Kawahara, H.; Keller, L.; King, M. E.; Klaisner, L.; Krebs, H. J.; Langenegger, U.; Langeveld, W.; Leith, D. W. G. S.; Louie, S. K.; Luitz, S.; Luth, V.; Lynch, H. L.; McDonald, J.; Manzin, G.; Marsiske, H.; Mattison, T.; McCulloch, M.; McDougald, M.; McShurley, D.; Menke, S.; Messner, R.; Metcalfe, S.; Morii, M.; Mount, R.; Muller, D. R.; Nelson, D.; Nordby, M.; O'Grady, C. P.; Olavson, L.; Olsen, J.; O'Neill, F. G.; Oxoby, G.; Paolucci, P.; Pavel, T.; Perl, J.; Pertsova, M.; Petrak, S.; Putallaz, G.; Raines, P. E.; Ratcliff, B. N.; Reif, R.; Robertson, S. H.; Rochester, L. S.; Roodman, A.; Russel, J. J.; Sapozhnikov, L.; Saxton, O. H.; Schietinger, T.; Schindler, R. H.; Schwiening, J.; Sciolla, G.; Seeman, J. T.; Serbo, V. V.; Shapiro, S.; Skarpass, K., Sr.; Snyder, A.; Soderstrom, E.; Soha, A.; Spanier, S. M.; Stahl, A.; Stiles, P.; Su, D.; Sullivan, M. K.; Talby, M.; Tanaka, H. A.; Va'vra, J.; Wagner, S. R.; Wang, R.; Weber, T.; Weinstein, A. J. R.; White, J. L.; Wienands, U.; Wisniewski, W. J.; Young, C. C.; Yu, N.; Burchat, P. R.; Cheng, C. H.; Kirkby, D.; Meyer, T. I.; Roat, C.; Henderson, R.; Khan, N.; Berridge, S.; Bugg, W.; Cohn, H.; Hart, E.; Weidemann, A. W.; Benninger, T.; Izen, J. M.; Kitayama, I.; Lou, X. C.; Turcotte, M.; Bianchi, F.; Bona, M.; Daudo, F.; Di Girolamo, B.; Gamba, D.; Grosso, P.; Smol, A.; Trapani, P. P.; Zanin, D.; Bosisio, L.; Della Ricca, G.; Lanceri, L.; Pompili, A.; Poropat, P.; Prest, M.; Rashevskaia, I.; Vallazza, E.; Vuagnin, G.; Panvini, R. S.; Brown, C.; De Silva, A.; Kowalewski, R.; Pitman, D.; Roney, J. M.; Band, H. R.; Charles, E.; Dasu, S.; Elmer, P.; Johnson, J. R.; Nielsen, J.; Orejudos, W.; Pan, Y.; Prepost, R.; Scott, I. J.; Walsh, J.; Wu, S. L.; Yu, Z.; Zobernig, H.; Moore, T. B.; Neal, H.

    2002-02-01

    B AB AR, the detector for the SLAC PEP-II asymmetric e +e - B Factory operating at the ϒ(4 S) resonance, was designed to allow comprehensive studies of CP-violation in B-meson decays. Charged particle tracks are measured in a multi-layer silicon vertex tracker surrounded by a cylindrical wire drift chamber. Electromagnetic showers from electrons and photons are detected in an array of CsI crystals located just inside the solenoidal coil of a superconducting magnet. Muons and neutral hadrons are identified by arrays of resistive plate chambers inserted into gaps in the steel flux return of the magnet. Charged hadrons are identified by d E/d x measurements in the tracking detectors and by a ring-imaging Cherenkov detector surrounding the drift chamber. The trigger, data acquisition and data-monitoring systems, VME- and network-based, are controlled by custom-designed online software. Details of the layout and performance of the detector components and their associated electronics and software are presented.

  19. Ab initio phonon limited transport

    NASA Astrophysics Data System (ADS)

    Verstraete, Matthieu

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

  20. Relativistic Hamiltonians and short-range structure of nuclei

    NASA Astrophysics Data System (ADS)

    Forest, Jun Lu

    1998-12-01

    This work is divided into two parts. In the first part, short-range structure of deuteron is studied using a nonrelativistic Hamiltonian. The equidensity surfaces for spin projection Ms = 0 distributions are found to be toroidal in shape, while those of Ms = ±1 have dumbbell shapes at large density. The toroidal shapes indicate that the tensor correlations have near maximal strength at the interparticle distance r < 2 fm. They provide new insights and simple explanations of the structure and electromagnetic form factors of the deuteron. In the second part, relativistic effects are studied using a relativistic Hamilionian defined as the sum of relativistic one-body kinetic energy, two- and three-body potentials and their boost corrections. Variational Monte Carlo method is used to study two kinds of relativistic effects in the binding energy of 3H and 4He. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP) and the second is from boost interaction. The OPEP contribution is reduced by ~15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of ~0.4 (1.9) MeV in 3H (4He) and account for ~1/3 of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians.

  1. Tight-binding Hamiltonian for LaOFeAs

    NASA Astrophysics Data System (ADS)

    Papaconstantopoulos, D. A.; Mehl, M. J.; Johannes, M. D.

    2010-08-01

    First-principles electronic-structure calculations have been very useful in understanding some of the properties of the new iron-based superconductors. Further explorations of the role of the individual atomic orbitals in explaining various aspects of research in these materials, including experimental work, would benefit from the availability of a tight-binding (TB) Hamiltonian that accurately reproduces the first-principles band-structure results. In this work we have used the Naval Research Laboratory-TB method to construct a TB Hamiltonian from linearized augmented plane wave (LAPW) results. Our TB model includes the Fed orbitals and the p orbitals from both As and O for the prototype material LaOFeAs. The resulting TB band structure agrees well with that of the LAPW calculations from 2.7 eV below to 0.8 eV above the Fermi level, ɛF , and the Fermi surface matches perfectly to that of the LAPW. The TB densities of states (DOSs) are also in very good agreement with those from the LAPW in the above energy range, including the per orbital decomposition. We use our results to provide insights on the existence of a pseudogap in the DOS just above the Fermi level. We have also performed a separate TB fit to a database of LAPW results as a function of volume and with variations in the As positions. This fit although less accurate regarding the band structure near ɛF , reproduces the LAPW total energies very well and has transferability to nonfitted energies.

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

    PubMed

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

    2010-07-07

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

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

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

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

  4. Four-band Hamiltonian for fast calculations in intermediate-band solar cells

    NASA Astrophysics Data System (ADS)

    Luque, Antonio; Panchak, Aleksandr; Vlasov, Alexey; Martí, Antonio; Andreev, Viacheslav

    2016-02-01

    The 8-dimensional Luttinger-Kohn-Pikus-Bir Hamiltonian matrix may be made up of four 4-dimensional blocks. A 4-band Hamiltonian is presented, obtained from making the non-diagonal blocks zero. The parameters of the new Hamiltonian are adjusted to fit the calculated effective masses and strained QD bandgap with the measured ones. The 4-dimensional Hamiltonian thus obtained agrees well with measured quantum efficiency of a quantum dot intermediate band solar cell and the full absorption spectrum can be calculated in about two hours using Mathematica© and a notebook. This is a hundred times faster than with the commonly-used 8-band Hamiltonian and is considered suitable for helping design engineers in the development of nanostructured solar cells.

  5. Hamiltonian-Driven Adaptive Dynamic Programming for Continuous Nonlinear Dynamical Systems.

    PubMed

    Yang, Yongliang; Wunsch, Donald; Yin, Yixin

    2017-02-01

    This paper presents a Hamiltonian-driven framework of adaptive dynamic programming (ADP) for continuous time nonlinear systems, which consists of evaluation of an admissible control, comparison between two different admissible policies with respect to the corresponding the performance function, and the performance improvement of an admissible control. It is showed that the Hamiltonian can serve as the temporal difference for continuous-time systems. In the Hamiltonian-driven ADP, the critic network is trained to output the value gradient. Then, the inner product between the critic and the system dynamics produces the value derivative. Under some conditions, the minimization of the Hamiltonian functional is equivalent to the value function approximation. An iterative algorithm starting from an arbitrary admissible control is presented for the optimal control approximation with its convergence proof. The implementation is accomplished by a neural network approximation. Two simulation studies demonstrate the effectiveness of Hamiltonian-driven ADP.

  6. Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian.

    PubMed

    Cheng, Lan; Gauss, Jürgen

    2011-08-28

    We report the implementation of analytic energy gradients for the evaluation of first-order electrical properties and nuclear forces within the framework of the spin-free (SF) exact two-component (X2c) theory. In the scheme presented here, referred to in the following as SFX2c-1e, the decoupling of electronic and positronic solutions is performed for the one-electron Dirac Hamiltonian in its matrix representation using a single unitary transformation. The resulting two-component one-electron matrix Hamiltonian is combined with untransformed two-electron interactions for subsequent self-consistent-field and electron-correlated calculations. The "picture-change" effect in the calculation of properties is taken into account by considering the full derivative of the two-component Hamiltonian matrix with respect to the external perturbation. The applicability of the analytic-gradient scheme presented here is demonstrated in benchmark calculations. SFX2c-1e results for the dipole moments and electric-field gradients of the hydrogen halides are compared with those obtained from nonrelativistic, SF high-order Douglas-Kroll-Hess, and SF Dirac-Coulomb calculations. It is shown that the use of untransformed two-electron interactions introduces rather small errors for these properties. As a first application of the analytic geometrical gradient, we report the equilibrium geometry of methylcopper (CuCH(3)) determined at various levels of theory.

  7. Ab initio derivation of multi-orbital extended Hubbard model for molecular crystals

    NASA Astrophysics Data System (ADS)

    Tsuchiizu, Masahisa; Omori, Yukiko; Suzumura, Yoshikazu; Bonnet, Marie-Laure; Robert, Vincent

    2012-01-01

    From configuration interaction (CI) ab initio calculations, we derive an effective two-orbital extended Hubbard model based on the gerade (g) and ungerade (u) molecular orbitals (MOs) of the charge-transfer molecular conductor (TTM-TTP)I3 and the single-component molecular conductor [Au(tmdt)2]. First, by focusing on the isolated molecule, we determine the parameters for the model Hamiltonian so as to reproduce the CI Hamiltonian matrix. Next, we extend the analysis to two neighboring molecule pairs in the crystal and we perform similar calculations to evaluate the inter-molecular interactions. From the resulting tight-binding parameters, we analyze the band structure to confirm that two bands overlap and mix in together, supporting the multi-band feature. Furthermore, using a fragment decomposition, we derive the effective model based on the fragment MOs and show that the staking TTM-TTP molecules can be described by the zig-zag two-leg ladder with the inter-molecular transfer integral being larger than the intra-fragment transfer integral within the molecule. The inter-site interactions between the fragments follow a Coulomb law, supporting the fragment decomposition strategy.

  8. Nuclear Medicine.

    ERIC Educational Resources Information Center

    Badawi, Ramsey D.

    2001-01-01

    Describes the use of nuclear medicine techniques in diagnosis and therapy. Describes instrumentation in diagnostic nuclear medicine and predicts future trends in nuclear medicine imaging technology. (Author/MM)

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

    NASA Astrophysics Data System (ADS)

    Nishioka, Hirotaka; Ando, Koji

    2011-05-01

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

  10. Effective representation of amide III, II, I, and A modes on local vibrational modes: Analysis of ab initio quantum calculation results

    NASA Astrophysics Data System (ADS)

    Hahn, Seungsoo

    2016-10-01

    The Hamiltonian matrix for the first excited vibrational states of a protein can be effectively represented by local vibrational modes constituting amide III, II, I, and A modes to simulate various vibrational spectra. Methods for obtaining the Hamiltonian matrix from ab initio quantum calculation results are discussed, where the methods consist of three steps: selection of local vibrational mode coordinates, calculation of a reduced Hessian matrix, and extraction of the Hamiltonian matrix from the Hessian matrix. We introduce several methods for each step. The methods were assessed based on the density functional theory calculation results of 24 oligopeptides with four different peptide lengths and six different secondary structures. The completeness of a Hamiltonian matrix represented in the reduced local mode space is improved by adopting a specific atom group for each amide mode and reducing the effect of ignored local modes. The calculation results are also compared to previous models using C=O stretching vibration and transition dipole couplings. We found that local electric transition dipole moments of the amide modes are mainly bound on the local peptide planes. Their direction and magnitude are well conserved except amide A modes, which show large variation. Contrary to amide I modes, the vibrational coupling constants of amide III, II, and A modes obtained by analysis of a dipeptide are not transferable to oligopeptides with the same secondary conformation because coupling constants are affected by the surrounding atomic environment.

  11. Effective representation of amide III, II, I, and A modes on local vibrational modes: Analysis of ab initio quantum calculation results.

    PubMed

    Hahn, Seungsoo

    2016-10-28

    The Hamiltonian matrix for the first excited vibrational states of a protein can be effectively represented by local vibrational modes constituting amide III, II, I, and A modes to simulate various vibrational spectra. Methods for obtaining the Hamiltonian matrix from ab initio quantum calculation results are discussed, where the methods consist of three steps: selection of local vibrational mode coordinates, calculation of a reduced Hessian matrix, and extraction of the Hamiltonian matrix from the Hessian matrix. We introduce several methods for each step. The methods were assessed based on the density functional theory calculation results of 24 oligopeptides with four different peptide lengths and six different secondary structures. The completeness of a Hamiltonian matrix represented in the reduced local mode space is improved by adopting a specific atom group for each amide mode and reducing the effect of ignored local modes. The calculation results are also compared to previous models using C=O stretching vibration and transition dipole couplings. We found that local electric transition dipole moments of the amide modes are mainly bound on the local peptide planes. Their direction and magnitude are well conserved except amide A modes, which show large variation. Contrary to amide I modes, the vibrational coupling constants of amide III, II, and A modes obtained by analysis of a dipeptide are not transferable to oligopeptides with the same secondary conformation because coupling constants are affected by the surrounding atomic environment.

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

    PubMed

    Nishioka, Hirotaka; Ando, Koji

    2011-05-28

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

  13. Erythema ab igne: evolving technology, evolving presentation.

    PubMed

    Kesty, Katarina; Feldman, Steven R

    2014-11-15

    We present a case of a 49-year-old woman with erythema ab igne on her posterior thighs owing to 2-4 hours per day of seat heater use in her car. Erythema ab igne is caused by prolonged exposure to a heat source. It used to be caused mainly by wood stoves used to heat homes. Erythema ab igne is now more often related to other heat sources, including heating pads, laptop computers, and car seat heaters, as in our case. As technology changes, so does the presentation of skin conditions that are related to technology.

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

    NASA Astrophysics Data System (ADS)

    Sobhani, Hadi; Hassanabadi, Hassan

    2016-08-01

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

  15. Particle-hole states in nuclear matter

    SciTech Connect

    Matyas, C.A.

    1985-01-01

    This work deals with the collective excitations in nuclear matter, from the point of view of the TDA approximation. Our calculations involved the construction of a Hamiltonian, expressed as a matrix in the space of particle-hole excitations with a given momentum transfer. We used in this Hamiltonian an average single nucleon potential, and (in some cases) an effective interaction obtained for the potential HEA in the relativistic Brueckner-Hartree Fock theory. The eigenvectors of the TDA-Hamiltonian were used to compute the strength of the collective response of nuclear matter to external probes. Our results, succinctly described in the last section, are summarized in a set of figures at the end of this monograph. The specific form of the TDA equations that we used, and the procedure to calculate the degree of collectivity of the solutions, is studied in detail in the fifth chapter. A derivation of the TDA equations, and a discussion of the solutions for a separable potential, is given in the fourth chapter. The structure of a non-relativistic potential for a system of two nucleons is examined in the third chapter, in several representations. On the other hand, the particle-hole states relevant to our discussions on the TDA equations are introduced in the first two chapters.

  16. Ab Initio Study of Polonium

    SciTech Connect

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

    2008-05-20

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

  17. Regularity of nuclear structure under random interactions

    SciTech Connect

    Zhao, Y. M.

    2011-05-06

    In this contribution I present a brief introduction to simplicity out of complexity in nuclear structure, specifically, the regularity of nuclear structure under random interactions. I exemplify such simplicity by two examples: spin-zero ground state dominance and positive parity ground state dominance in even-even nuclei. Then I discuss two recent results of nuclear structure in the presence of random interactions, in collaboration with Prof. Arima. Firstly I discuss sd bosons under random interactions, with the focus on excited states in the yrast band. We find a few regular patterns in these excited levels. Secondly I discuss our recent efforts towards obtaining eigenvalues without diagonalizing the full matrices of the nuclear shell model Hamiltonian.

  18. Resonance and aromaticity: an ab initio valence bond approach.

    PubMed

    Rashid, Zahid; van Lenthe, Joop H; Havenith, Remco W A

    2012-05-17

    Resonance energy is one of the criteria to measure aromaticity. The effect of the use of different orbital models is investigated in the calculated resonance energies of cyclic conjugated hydrocarbons within the framework of the ab initio Valence Bond Self-Consistent Field (VBSCF) method. The VB wave function for each system was constructed using a linear combination of the VB structures (spin functions), which closely resemble the Kekulé valence structures, and two types of orbitals, that is, strictly atomic (local) and delocalized atomic (delocal) p-orbitals, were used to describe the π-system. It is found that the Pauling-Wheland's resonance energy with nonorthogonal structures decreases, while the same with orthogonalized structures and the total mean resonance energy (the sum of the weighted off-diagonal contributions in the Hamiltonian matrix of orthogonalized structures) increase when delocal orbitals are used as compared to local p-orbitals. Analysis of the interactions between the different structures of a system shows that the resonance in the 6π electrons conjugated circuits have the largest contributions to the resonance energy. The VBSCF calculations also show that the extra stability of phenanthrene, a kinked benzenoid, as compared to its linear counterpart, anthracene, is a consequence of the resonance in the π-system rather than the H-H interaction in the bay region as suggested previously. Finally, the empirical parameters for the resonance interactions between different 4n+2 or 4n π electrons conjugated circuits, used in Randić's conjugated circuits theory or Herdon's semi-emprical VB approach, are quantified. These parameters have to be scaled by the structure coefficients (weights) of the contributing structures.

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

    SciTech Connect

    Roemelt, Michael

    2015-07-28

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

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

    NASA Astrophysics Data System (ADS)

    Roemelt, Michael

    2015-07-01

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