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Sample records for two-body hamiltonians bethe-salpeter

  1. The connection of two-particle relativistic quantum mechanics with the Bethe-Salpeter equation

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1986-02-01

    We show the formal equivalence between the wave equations of two-particle relativistic quantum mechanics, based on the manifestly covariant hamiltonian formalism with constraints, and the Bethe-Salpeter equation. This is achieved by algebraically transforming the latter so as to separate it into two independent equations which match the equations of hamiltonian relativistic quantum mechanics. The first equation determines the relative time evolution of the system, while the second one yields a three-dimensional eigenvalue equation. A connection is thus established between the Bethe-Salpeter wave function and its kernel on the one hand and the quantum mechanical wave function and interaction potential on the other. For the sector of solutions of the Bethe-Salpeter equation having non-relativistic limits, this relationship can be evaluated in perturbation theory. We also device a generalized form of the instantaneous approximation which simplifies the various expressions involved in the above relations. It also permits the evaluation of the normalization condition of the quantum mechanical wave function as a three-dimensional integral

  2. Numerical studies of the Bethe-Salpeter equation for a two-fermion bound state

    Science.gov (United States)

    de Paula, W.; Frederico, T.; Salmè, G.; Viviani, M.

    2018-03-01

    Some recent advances on the solution of the Bethe-Salpeter equation (BSE) for a two-fermion bound system directly in Minkowski space are presented. The calculations are based on the expression of the Bethe-Salpeter amplitude in terms of the so-called Nakanishi integral representation and on the light-front projection (i.e. the integration of the light-front variable k - = k 0 - k 3). The latter technique allows for the analytically exact treatment of the singularities plaguing the two-fermion BSE in Minkowski space. The good agreement observed between our results and those obtained using other existing numerical methods, based on both Minkowski and Euclidean space techniques, fully corroborate our analytical treatment.

  3. Stochastic integration of the Bethe-Salpeter equation for two bound fermions

    International Nuclear Information System (INIS)

    Salomon, M.

    1988-09-01

    A non-perturbative method using a Monte Carlo algorithm is used to integrate the Bethe-Salpeter equation in momentum space. Solutions for two scalars and two fermions with an arbitrary coupling constant are calculated for bound states in the ladder approximation. The results are compared with other numerical methods. (Author) (13 refs., 2 figs.)

  4. Bethe-Salpeter amplitudes and static properties of the deuteron

    International Nuclear Information System (INIS)

    Kaptari, L.P.; Bondarenko, S.G.; Khanna, F.C.; Kaempfer, B.; Technische Univ. Dresden

    1996-04-01

    Extended calculations of the deuteron's static properties, based on the numerical solution of the Bethe-Salpeter equation, are presented. A formalism is developed, which provides a comparative analysis of the covariant amplitudes in various representations and nonrelativistic wave functions. The magnetic and quadrupole moments of the deuteron are calculated in the Bethe-Salpeter formalism and the role of relativistic corrections is discussed. (orig.)

  5. GW and Bethe-Salpeter study of small water clusters

    Energy Technology Data Exchange (ETDEWEB)

    Blase, Xavier, E-mail: xavier.blase@neel.cnrs.fr; Boulanger, Paul [CNRS, Institut NEEL, F-38042 Grenoble (France); Bruneval, Fabien [CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif-sur-Yvette (France); Fernandez-Serra, Marivi [Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800 (United States); Institute for Advanced Computational Sciences, Stony Brook University, Stony Brook, New York 11794-3800 (United States); Duchemin, Ivan [INAC, SP2M/L-Sim, CEA/UJF Cedex 09, 38054 Grenoble (France)

    2016-01-21

    We study within the GW and Bethe-Salpeter many-body perturbation theories the electronic and optical properties of small (H{sub 2}O){sub n} water clusters (n = 1-6). Comparison with high-level CCSD(T) Coupled-Cluster at the Single Double (Triple) levels and ADC(3) Green’s function third order algebraic diagrammatic construction calculations indicates that the standard non-self-consistent G{sub 0}W{sub 0}@PBE or G{sub 0}W{sub 0}@PBE0 approaches significantly underestimate the ionization energy by about 1.1 eV and 0.5 eV, respectively. Consequently, the related Bethe-Salpeter lowest optical excitations are found to be located much too low in energy when building transitions from a non-self-consistent G{sub 0}W{sub 0} description of the quasiparticle spectrum. Simple self-consistent schemes, with update of the eigenvalues only, are shown to provide a weak dependence on the Kohn-Sham starting point and a much better agreement with reference calculations. The present findings rationalize the theory to experiment possible discrepancies observed in previous G{sub 0}W{sub 0} and Bethe-Salpeter studies of bulk water. The increase of the optical gap with increasing cluster size is consistent with the evolution from gas to dense ice or water phases and results from an enhanced screening of the electron-hole interaction.

  6. Glueball properties from the Bethe-Salpeter equation

    International Nuclear Information System (INIS)

    Kellermann, Christian

    2012-01-01

    For over thirty years bound states of gluons are an outstanding problem of both theoretical and experimental physics. Being predicted by Quantum-Chromodynamics their experimental confirmation is one of the foremost goals of large experimental facilities currently under construction like FAIR in Darmstadt. This thesis presents a novel approach to the theoretical determination of physical properties of bound states of two gluons, called glueballs. It uses the consistent combination of Schwinger-Dyson equations for gluons and ghosts and appropriate Bethe-Salpeter equations describing their corresponding bound-states. A rigorous derivation of both sets of equations, starting from an 2PI effective action is given as well as a general determination of appropriate decompositions of Bethe-Salpeter amplitudes to a given set of quantum numbers of a glueball. As an application example bound state masses of glueballs in a simple truncation scheme are calculated. (orig.)

  7. On the energy spectrum of the Bethe-Salpeter equation; Ob ehnergeticheskom spektre uravneniya Bete-Solpitera

    Energy Technology Data Exchange (ETDEWEB)

    Dorkin, S M [Dal` nevostochnyj Gosudarstvennyj Univ., Vladivostok (Russian Federation); Kaptar` , L P; Semikh, S S [Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Theoretical Physics

    1997-12-31

    The problem of calculating the energy spectrum of a two-fermion bound state within the Bethe-Salpeter formalism is discussed. An expansion of the kernel of the spinor-spinor Bethe-Salpeter equation in the ladder approximation is found in terms of a bi-orthogonal basis of the generalized Gilbert-Schmidt series for symmetric equations of the Fredholm type. According to this expansion, a new method of solving the Bethe-Salpeter equation and finding the mass spectrum is proposed. Methodological result of numerical solutions of equations with scalar interaction is presented. (author). 20 refs., 3 figs.

  8. Validity of various approximations for the Bethe-Salpeter equation and their WKB quantization

    International Nuclear Information System (INIS)

    Silvestre-Brac, B.; Bilal, A.; Gignoux, C.; Schuck, P.

    1984-01-01

    The validity of the instantaneous approximation for the Bethe-Salpeter equation is questioned within the framework of the simple scalar-scalar model of Cutkosky. Detailed numerous results for various approximations are compared to the exact ones. WKB quantization is applied to these relativistic approximations. An unexpected question arises: is the currently used Bethe-Salpeter equation (i.e., the ladder approximation) well suited to describe two interacting relativistic particles

  9. Single-time reduction of bethe-salpeter formalism for two-fermion system

    International Nuclear Information System (INIS)

    Arkhipov, A.A.

    1988-01-01

    The single-time reduction method proposed in other refs. for the system of two scalar particles is generalized for the case of two-fermion system. A self-consistent procedure of single-time reduction has been constructed both in terms of the Bethe-Salpeter wave function and in terms of the Green's function of two-fermion system. Three-dimensional dynamic equations have been obtained for single-time wave functions and two-time Green's functions of a two-fermion system and the Schroedinger structure of the equations obtained is shown to be a consequence of the causality structure of the local QFT. 32 refs

  10. Solution to Bethe-Salpeter equation via Mellin-Barnes transform

    International Nuclear Information System (INIS)

    Allendes, Pedro; Kniehl, Bernd; Kondrashuk, Igor; Rojas Medar, Marko; Notte Cuello, Eduardo A.

    2012-06-01

    We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in d=4 dimensions. It is shown how multi-fold MB transform of the momentum integral corresponding to any number of rungs is reduced to two-fold MB transform. For this purpose we use Belokurov-Usyukina reduction method for four-dimensional scalar integrals in the position space. The result is represented in terms of Euler ψ-function and its derivatives. We derive new formulas for MB two-fold integration in the complex planes of two complex variables. We demonstrate that these formulas solve Bethe-Salpeter equation. We comment on further applications of solution to Bethe-Salpeter equation for vertices in N=4 supersymmetric Yang-Mills theory. We show that the recursive property of MB transforms observed in the present work for that kind of diagrams has nothing to do with quantum field theory, theory of integral transforms, or with theory of polylogarithms in general, but has an origin in a simple recursive property for smooth functions which can be shown by using basic methods of mathematical analysis.

  11. Solution to Bethe-Salpeter equation via Mellin-Barnes transform

    Energy Technology Data Exchange (ETDEWEB)

    Allendes, Pedro [Concepcion Univ. (Chile). Dept. de Fisica; Kniehl, Bernd [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kondrashuk, Igor; Rojas Medar, Marko [Univ. del Bio-Bio, Chillan (Chile). Dept. de Ciencias Basicas; Notte Cuello, Eduardo A. [Univ. de La Serena (Chile). Facultad de Ciencias

    2012-06-15

    We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in d=4 dimensions. It is shown how multi-fold MB transform of the momentum integral corresponding to any number of rungs is reduced to two-fold MB transform. For this purpose we use Belokurov-Usyukina reduction method for four-dimensional scalar integrals in the position space. The result is represented in terms of Euler {psi}-function and its derivatives. We derive new formulas for MB two-fold integration in the complex planes of two complex variables. We demonstrate that these formulas solve Bethe-Salpeter equation. We comment on further applications of solution to Bethe-Salpeter equation for vertices in N=4 supersymmetric Yang-Mills theory. We show that the recursive property of MB transforms observed in the present work for that kind of diagrams has nothing to do with quantum field theory, theory of integral transforms, or with theory of polylogarithms in general, but has an origin in a simple recursive property for smooth functions which can be shown by using basic methods of mathematical analysis.

  12. Euclidean to Minkowski Bethe-Salpeter amplitude and observables

    International Nuclear Information System (INIS)

    Carbonell, J.; Frederico, T.; Karmanov, V.A.

    2017-01-01

    We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)

  13. Euclidean to Minkowski Bethe-Salpeter amplitude and observables

    Energy Technology Data Exchange (ETDEWEB)

    Carbonell, J. [Universite Paris-Sud, IN2P3-CNRS, Institut de Physique Nucleaire, Orsay Cedex (France); Frederico, T. [Instituto Tecnologico de Aeronautica, DCTA, Sao Jose dos Campos (Brazil); Karmanov, V.A. [Lebedev Physical Institute, Moscow (Russian Federation)

    2017-01-15

    We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)

  14. Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel

    Energy Technology Data Exchange (ETDEWEB)

    Rebolini, Elisa, E-mail: elisa.rebolini@kjemi.uio.no; Toulouse, Julien, E-mail: julien.toulouse@upmc.fr [Laboratoire de Chimie Théorique, Sorbonne Universités, UPMC Univ Paris 06, CNRS, 4 place Jussieu, F-75005 Paris (France)

    2016-03-07

    We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of the He and Be atoms and small molecules (H{sub 2}, N{sub 2}, CO{sub 2}, H{sub 2}CO, and C{sub 2}H{sub 4}). The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.

  15. Bethe-salpeter equation from many-body perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Sander, Tobias; Starke, Ronald; Kresse, Georg [Computational Materials Physics, University of Vienna, Sensengasse 8/12, 1090 Vienna (Austria)

    2013-07-01

    The Green function formalism is a powerful tool to calculate not only electronic structure within the quasi-particle (QP) picture, but it also gives access to optical absorption spectra. Starting from QP energies within the GW method, the polarizability, as central quantity, is calculated from the solution of a Bethe-Salpeter-like equation (BSE). It is usually solved within the Tamm-Dancoff Approximation (TDA) which neglects the coupling of resonant (positive frequency branch) and anti-resonant (negative frequency branch) excitations. In this work we solve the full BSE (beyond TDA) based on self-consistently calculated QP orbitals and energies for typical systems. The dielectric function is averaged over many low dimensional shifted k-meshes to obtain k-point converged results. We compare the results to recently introduced approximation to the BSE kernel. Additionally, the time-evolution ansatz is employed to calculate the polarizability, which avoids the direct solution of the BSE.

  16. Excited charmonium states from Bethe-Salpeter Equation

    Czech Academy of Sciences Publication Activity Database

    Šauli, Vladimír; Bicudo, P.

    2012-01-01

    Roč. 7, 043 (2012), s. 1-10 ISSN 1824-8039. [International Workshop on QCD Green’s Functions. Tranto, 05.09.2011-09.09.2011] R&D Projects: GA MŠk(CZ) LG11005 Institutional research plan: CEZ:AV0Z10480505 Keywords : charmonium * Bethe-Salpeter Equation Subject RIV: BE - Theoretical Physics http:// pos .sissa.it/archive/conferences/136/043/QCD-TNT-II_043.pdf

  17. Bayesian extraction of the parton distribution amplitude from the Bethe-Salpeter wave function

    Science.gov (United States)

    Gao, Fei; Chang, Lei; Liu, Yu-xin

    2017-07-01

    We propose a new numerical method to compute the parton distribution amplitude (PDA) from the Euclidean Bethe-Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe-Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method (MEM). The Nakanishi weight function as well as the corresponding light-front parton distribution amplitude (PDA) can be well determined. We confirm prior work on PDA computations, which was based on different methods.

  18. Construction of Bethe Salpeter wave functions and applications in QCD

    International Nuclear Information System (INIS)

    Gromes, D.

    1993-01-01

    We suggest an ansatz for the Bethe Salpeter wave function which is strictly covariant, obeys the spectrum conditions, and has the correct non relativistic limit. As a first simple application we present a wave function for the pion. It contains two parameters, one of them being the quark mass. The decay constant and the form factor derived from this are in excellent agreement with the data. (orig.)

  19. Bethe-Salpeter analysis of the radiative pion disintegration

    Energy Technology Data Exchange (ETDEWEB)

    Abad, J.; Pacheco, A.F. (Zaragoza Univ. (Spain). Dept. de Fisica Teorica); Rodriguez-Trias, R.; Esteve, J.G. (Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique et Hautes Energies)

    1990-04-01

    The structure-dependent amplitude of the decay {pi}{yields}e{nu}{gamma} is evaluated in the framework of a Bethe-Salpeter description for the pion. We assume a general B-S wave function in the S-wave. Within this hypothesis, we show that the gauge invariance constrains the different contributions of the wave functions to the amplitude, resulting in the vanishing of the axial form factor. (orig.).

  20. Covariant Bethe-Salpeter wave functions for heavy hadrons

    International Nuclear Information System (INIS)

    Hussain, F.

    1992-09-01

    In recent years the dynamics of heavy mesons and baryons has considerably simplified by the development of the so-called heavy quark effective theory (HQET). A covariant formulation of heavy meson and heavy baryon decays in the leading order of the HQET is presented. The method is based on a Bethe-Salpeter formulation in the limit of the heavy quark mass going to infinity. 15 refs, 4 figs

  1. The decay constants of heavy-light mesons in a two-tier Bethe-Salpeter model

    International Nuclear Information System (INIS)

    Pagnamenta, A.; Illinois Univ., Chicago, IL; Gupta, K.K.; Mitra, A.N.; Singh, N.N.; Ramanathan, R.

    1990-01-01

    Leptonic decay widths for pseudoscalar mesons are calculated in a QCD-motivated Bethe-Salpeter formalism on a two-tier basis. This model, which is characterised by a Lorentz-invariant confining kernel that depends on the relativistic reduced mass defined in accordance with the Wightman-Garding definition of the internal 4-momenta q μ , has already shown precision fits to the spectra of qq-bar, qQ-bar and qqq hadrons apart from exhibiting an eplicit Regge-asymptotic behaviour (M 2 ∼N). The leptonic decay constants thus obtained with no free parameters, are (in MeV units), f P =134(π), 166(K); 158(D); 94.9(B), 114(B S ). (author)

  2. Heavy quark effective theory, interpolating fields and Bethe-Salpeter amplitudes

    International Nuclear Information System (INIS)

    Hussain, F.; Thomspon, G.

    1994-07-01

    We use the LSZ reduction theorem and interpolating fields, along with the heavy quark effective theory, to investigate the structure of the Bethe-Salpeter amplitude for heavy hadrons. We show how a simple form of this amplitude, used extensively in heavy hadron decay calculations, follows naturally up to O(1/M) from these field theoretic considerations. (author). 13 refs, 1 tab

  3. Covariant solutions of the Bethe-Salpeter equation

    International Nuclear Information System (INIS)

    Williams, A.G.; Kusaka, K.; Simpson, K.M.

    1997-01-01

    There is a need for covariant solutions of bound state equations in order to construct realistic QCD based models of mesons and baryons. Furthermore, we ideally need to know the structure of these bound states in all kinematical regimes, which makes a direct solution in Minkowski space (without any 3-dimensional reductions) desirable. The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved for arbitrary scattering kernels in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional Euclidean approach, where the BSE can only be solved in ladder approximation after a Wick rotation. (author)

  4. A separable approximation of the NN-Paris-potential in the framework of the Bethe-Salpeter equation

    International Nuclear Information System (INIS)

    Schwarz, K.; Haidenbauer, J.; Froehlich, J.

    1985-09-01

    The Bethe-Salpeter equation is solved with a separable kernel for the most important nucleon-nucleon partial wave states. We employ the Ernst Shakin-Thaler method in the framework of minimal relativity (Blankenbeckler-Sugar equation) to generate a separable representation of the meson-theoretical Paris potential. These separable interactions, which closely approximate the on-shell- and half-off-shell behaviour of the Paris potential, are then cast into a covariant form for application in the Bethe-Salpeter equation. The role of relativistic effects is discussed with respect to on-shell and off-shell properties of the NN-system. (Author)

  5. Projecting the Bethe-Salpeter Equation onto the Light-Front and Back: A Short Review

    International Nuclear Information System (INIS)

    Frederico, T.; Salme, G.

    2011-01-01

    The technique of projecting the four-dimensional two-body Bethe-Salpeter equation onto the three-dimensional Light-Front hypersurface, combined with the quasi-potential approach, is briefly illustrated, by placing a particular emphasis on the relation between the projection method and the effective dynamics of the valence component of the Light-Front wave function. Some details on how to construct the Fock expansion of both (a) the Light-Front effective interaction and (b) the electromagnetic current operator, satisfying the proper Ward-Takahashi identity, will be presented, addressing the relevance of the Fock content in the operators living onto the Light-Front hypersurface. Finally, the generalization of the formalism to the three-particle case will be outlined. (author)

  6. Deep inelastic scattering on the deuteron in the Bethe-Salpeter formalism

    International Nuclear Information System (INIS)

    Kaptari, L.P.; Kazakov, K.Yu.; Umnikov, A.Yu.; Khanna, F.C.

    1996-01-01

    The nuclear effects in the spin structure functions of the deuteron g 1 and b 2 are estimated in a fully covariant approach of the Bethe-Salpeter formalism. The construction of the relativistic wave function of the deuteron is discussed in detail. Numerical results for g 1 and b 2 are compared with nonrelativistic results and relativistic corrections are discussed [ru

  7. Solution of the Bethe-Salpeter equation in the field of a plane electromagnetic wave

    International Nuclear Information System (INIS)

    Starostin, V.S.

    1988-01-01

    A solution is obtained of the Bethe--Salpeter equation for positronium in the field of linearly and circularly polarized plane electromagnetic waves at frequencies much higher than atomic. It is not assumed that the field is weak

  8. Covariant solutions of the Bethe-Salpeter equation and an application to the nucleon structure function

    International Nuclear Information System (INIS)

    Williams, A.G.

    1998-01-01

    There is a need for covariant solutions of bound state equations in order to construct realistic QCD based models of mesons and baryons. Furthermore, we ideally need to know the structure of these bound states in all kinematical regimes, which makes a direct solution in Minkowski space (without any 3-dimensional reductions) desirable. The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved for arbitrary scattering kernels in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional Euclidean approach, where the BSE can only be solved in ladder approximation after a Wick rotation. An application of covariant Bethe-Salpeter solutions to a quark-diquark model of the nucleon is also briefly discussed. (orig.)

  9. Efficient implementation of core-excitation Bethe-Salpeter equation calculations

    Science.gov (United States)

    Gilmore, K.; Vinson, John; Shirley, E. L.; Prendergast, D.; Pemmaraju, C. D.; Kas, J. J.; Vila, F. D.; Rehr, J. J.

    2015-12-01

    We present an efficient implementation of the Bethe-Salpeter equation (BSE) method for obtaining core-level spectra including X-ray absorption (XAS), X-ray emission (XES), and both resonant and non-resonant inelastic X-ray scattering spectra (N/RIXS). Calculations are based on density functional theory (DFT) electronic structures generated either by ABINIT or QuantumESPRESSO, both plane-wave basis, pseudopotential codes. This electronic structure is improved through the inclusion of a GW self energy. The projector augmented wave technique is used to evaluate transition matrix elements between core-level and band states. Final two-particle scattering states are obtained with the NIST core-level BSE solver (NBSE). We have previously reported this implementation, which we refer to as OCEAN (Obtaining Core Excitations from Ab initio electronic structure and NBSE) (Vinson et al., 2011). Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previously possible; containing up to a few thousand electrons. These improvements include the implementation of optimal basis functions that reduce the cost of the initial DFT calculations, more complete parallelization of the screening calculation and of the action of the BSE Hamiltonian, and various memory reductions. Scaling is demonstrated on supercells of SrTiO3 and example spectra for the organic light emitting molecule Tris-(8-hydroxyquinoline)aluminum (Alq3) are presented. The ability to perform large-scale spectral calculations is particularly advantageous for investigating dilute or non-periodic systems such as doped materials, amorphous systems, or complex nano-structures.

  10. Comment on the analysis of Bethe-Salpeter scattering states by Hormozdiari and Huang

    International Nuclear Information System (INIS)

    Tryon, E.P.

    1978-01-01

    The analysis of Bethe-Salpeter scattering states by Hormozdiari and Huang appears to contain invalid mathematical arguments. When these arguments are rectified, one arrives at substantially different conclusions. In particular, the prescription of Hormozdiari and Huang for constructing such states does not seem applicable to any process occurring in nature

  11. Anomalous magnetic nucleon moments in a Bethe-Salpeter model

    International Nuclear Information System (INIS)

    Chak Wing Chan.

    1978-01-01

    We investigate the anomalous magnetic moment of the nucleon in a field theoretic many-channel model for the electromagnetic form factors of the N anti N, the ππ, the K anti K, the πω and the πrho systems. Propagator self-energy corrections from the Ward idendity and phenomenological strong vertex corrections are both included. The photon is coupled minimally to pions, kaons and nucleons with power multiplicative renormalization. With solutions in the framework of the Bethe-Salpeter equation we obtain a value 1.84 for the isovector moment and a value -0.02 for the isoscalar moment. (orig.)

  12. Bethe-Salpeter kernels and particle structure in the Yukawa2 quantum field theory

    International Nuclear Information System (INIS)

    Cooper, A.S.

    1981-01-01

    The author discusses the extension to the (weakly coupled) Yukawa quantum field theory in two space-time dimensions (Y 2 ), with equal bare masses, of some techniques used in the analysis of particle structure for weakly coupled even P(PHI) 2 . In particular he considers existence, regularity, and decay properties for the inverse two point functions and various Bethe-Salpeter kernels of the theory. These properties suffice to ensure that in the +-2 fermion sectors the mass spectrum is discrete below 2m 0 and the S-matrix is unitary up to 2m 0 + epsilon. (Auth.)

  13. The Bethe-Salpeter equation with fermions

    International Nuclear Information System (INIS)

    Efimov, G.V.

    2007-01-01

    The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents) with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation in the configuration Euclidean x-space with the symmetric kernel K for which Tr K 2 = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K 0 + K I . The operator K 0 with Tr K 0 2 ∞ is of the 'fall at the center' potential type and describes a continuous spectrum only. Besides the presence of this operator leads to a restriction on the value of the coupling constant. The kernel K I with Tr K I 2 2 c 2 and the variational procedure of calculations of eigenvalues and eigenfunctions can be applied. The quantum pseudoscalar and scalar mesodynamics is considered. The binding energy of the state 1 + (deuteron) as a function of the coupling constant is calculated in the framework of the procedure formulated above. It is shown that this bound state is absent in the pseudoscalar mesodynamics and does exist in the scalar mesodynamics. A comparison with the non-relativistic Schroedinger picture is made. (author)

  14. Low-lying qq(qq)-bar states in a relativistic model based on the Bethe-Salpeter equation

    International Nuclear Information System (INIS)

    Ram, B.; Kriss, V.

    1985-01-01

    Low-lying qq(qq)-bar states are analysed in a previously given relativistic model based on the Bethe-Salpeter equation. It is not got M-diquonia, P-mesonia, or meson molecules, but it is got T-diquonia

  15. Numerical Solutions of One Reduced Bethe-Salpeter Equation for the Coulombic Bound States Composed of Virtual Constituents

    Science.gov (United States)

    Chen, Jiao-Kai

    2018-04-01

    We present one reduction of the Bethe-Salpeter equation for the bound states composed of two off-mass-shell constituents. Both the relativistic effects and the virtuality effects can be considered in the obtained spinless virtuality distribution equation. The eigenvalues of the spinless virtuality distribution equation are perturbatively calculated and the bound states e+e-, μ+μ-, τ+τ-, μ+e-, and τ+e- are discussed.

  16. Approach to calculation of mass spectra and two-photon decays of c c¯ mesons in the framework of Bethe-Salpeter equation

    Science.gov (United States)

    Bhatnagar, Shashank; Alemu, Lmenew

    2018-02-01

    In this work we calculate the mass spectra of charmonium for 1 P ,…,4 P states of 0++ and 1++, for 1 S ,…,5 S states of 0-+, and for 1 S ,…,4 D states of 1- along with the two-photon decay widths of the ground and first excited states of 0++ quarkonia for the process O++→γ γ in the framework of a QCD-motivated Bethe-Salpeter equation (BSE). In this 4 ×4 BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of χc 0. Our results are in reasonable agreement with data (where available) and other models.

  17. A separable approach to the Bethe-Salpeter equation and its application to nucleon-nucleon scattering

    International Nuclear Information System (INIS)

    Schwarz, K.; Froehlich, J.; Zingl, H.F.K.

    1980-01-01

    The Bethe-Salpeter equation is solved in closed form with the help of a four dimensional separable 'potential'. For possible applications to three-nucleon investigations the authors have fitted all nucleon-nucleon S-wave phase shifts in a sufficient way by this method; in addition they also present an example for a P-wave. (Auth.)

  18. Bound states of quarks calculated with stochastic integration of the Bethe-Salpeter equation

    International Nuclear Information System (INIS)

    Salomon, M.

    1992-07-01

    We have computed the masses, wave functions and sea quark content of mesons in their ground state by integrating the Bethe-Salpeter equation with a stochastic algorithm. This method allows the inclusion of a large set of diagrams. Inspection of the kernel of the equation shows that q-q-bar pairs with similar constituent masses in a singlet spin state exhibit a high bound state which is not present in other pairs. The pion, kaon and eta belongs to this category. 19 refs., 2 figs., 2 tabs

  19. Perturbation theory for the Bethe-Salpeter equation in the field of a plane electromagnetic wave

    International Nuclear Information System (INIS)

    Starostin, V.S.; Litskevich, I.K.

    1990-01-01

    The completeness and orthogonality of the solutions of the Bethe-Salpeter equation is proven. A correct derivation of perturbation-theory equations is given. A generalization that includes the field of a plane electromagnetic wave is proposed. The rate of one-photon annihilation of positronium in this field is calculated. If the one-photon decay is allowed, the stationary states of the system are found (states of light-positronium)

  20. Spinless Salpeter equation: Laguerre bounds on energy levels

    International Nuclear Information System (INIS)

    Lucha, W.; Schoeberl, F.F.

    1996-08-01

    The spinless Salpeter equation may be considered either as a standard approximation to the Bethe-Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a certain extent relativistic generalization of the customary non relativistic Schroedinger formalism. Because of the presence of the rather difficult-to-handle square-root operator of the relativistic kinetic energy in the corresponding Hamiltonian, very frequently the corresponding (discrete) spectrum of energy eigenvalues cannot be determined analytically. Therefore, we show how to calculate, by some clever choice of basis vectors in the Hilbert space of solutions, for the rather large class of power-law potentials, at least (sometimes excellent) upper bounds on these energy eigenvalues, for the lowest-lying levels this even analytically. (author)

  1. Bethe-Salpeter equation for fermion-antifermion system in the ladder approximation

    International Nuclear Information System (INIS)

    Fukui, Ichio; Seto, Noriaki; Yoshida, Toshihiro.

    1977-01-01

    The Bethe-Salpeter (B-S) equation is important for studying hadron physics. Especially intensive investigation on the fermion-antifermion B-S equation is indispensable for the phenomenological studies of hardrons. However, many components of the B-S amplitude and the Wick-rotated integral kernel of non-Fredholm type have prevented from knowing details the solutions even in the ladder approximation. Some particular solutions are known in case of the vanishing four-momenta of bound states. The B-S equation for the bound state of fermion-anti-fermion system interacting through vector (axial-vector) particle exchange was studied in the ladder approximation with Feynman gauge. The reduced equations were obtained for suitably decomposed amplitude, and it is shown that, in the S-wave case, the coupled equations separate into two parts. In the nonrelativistic limit, large components of the amplitude satisfy the Wick-Cutkosky equation, and small components are expressed in terms of the large ones. Equations are derived for the equal-time amplitudes. (Kobatake, H.)

  2. Optical properties of bulk semiconductors and graphene/boron nitride: the Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies

    DEFF Research Database (Denmark)

    Yan, Jun; Jacobsen, Karsten W.; Thygesen, Kristian S.

    2012-01-01

    -dimensional systems of graphene and hexagonal boron-nitride (h-BN) we find good agreement with previous many-body calculations. For the graphene/h-BN interface we find that the fundamental and optical gaps of the h-BN layer are reduced by 2.0 and 0.7 eV, respectively, compared to freestanding h-BN. This reduction......We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method Grid-based projector-augmented wave method (GPAW). Single-particle energies and wave functions are obtained from the Gritsenko, Leeuwen, Lenthe...

  3. Delta and Omega electromagnetic form factors in a Dyson-Schwinger/Bethe-Salpeter approach

    Energy Technology Data Exchange (ETDEWEB)

    Diana Nicmorus, Gernot Eichmann, Reinhard Alkofer

    2010-12-01

    We investigate the electromagnetic form factors of the Delta and the Omega baryons within the Poincare-covariant framework of Dyson-Schwinger and Bethe-Salpeter equations. The three-quark core contributions of the form factors are evaluated by employing a quark-diquark approximation. We use a consistent setup for the quark-gluon dressing, the quark-quark bound-state kernel and the quark-photon interaction. Our predictions for the multipole form factors are compatible with available experimental data and quark-model estimates. The current-quark mass evolution of the static electromagnetic properties agrees with results provided by lattice calculations.

  4. Bethe-Salpeter equation for non-self conjugate mesons in a power-law potential

    International Nuclear Information System (INIS)

    Ikhdair, S.M.

    1992-07-01

    We develop an approach to the solution of the spinless Bethe-Salpeter equation for the different-mass case. Although the calculations are developed for spin-zero particles in any arbitrary spherically symmetric potential, the non-Coulombic effective power-law potential is used as a kernel to produce the spin-averaged bound states of the non-self-conjugate mesons. The analytical formulae are also applicable to the self-conjugate mesons in the equal-mass case. The flavor-independent case is investigated in this work. The calculations are carried out to the third-order correction of the energy series. Results are consistent with those obtained before. (author). 14 refs, 1 tab

  5. Quarkonia in the Bethe--Salpeter formalism with background fields

    International Nuclear Information System (INIS)

    Mathur, Y.K.; Mitra, A.N.

    1989-01-01

    A QCD-oriented Bethe--Salpeter (BS) equation for a q bar q system is formulated in which the quark 4-momenta p μ are modified as p μ →p μ -gA μ (x) in the inverse propagators therein, and a Fock--Schwinger (FS) gauge expansion is employed for the gluon fields A μ (x). The first term (∼x μ ) of the FS representation yields a harmonic kernel when the BS equation is reduced to a 3-dimensional level via the null-plane ansatz (NPA). It also generates a spin-dependent interaction proportional to (j 1 +s 1 )·(j 2 +s 2 ), in close parallel to a J·S term generated by a vector-like (γ (1) gamma(2)) harmonic model for the q bar q interaction proposed earlier by the Delhi Group. A possible mechanism for confinement in an asymptotically linear scene is proposed within the BS framework, taking cue partly from the suggestions of multiple correlation effects (Shifman), and partly from the postulation of stochastic fields (Simonov)

  6. A systematic approach to sketch Bethe-Salpeter equation

    Directory of Open Access Journals (Sweden)

    Qin Si-xue

    2016-01-01

    Full Text Available To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark–anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD’s gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symmetry breaking (DCSB. The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.

  7. QCD-oriented Bethe-Salpeter dynamics for all flavours, light and heavy

    International Nuclear Information System (INIS)

    Mitra, A.N.

    1987-01-01

    A QCD oriented Bethe-Salpeter approach with a vector-like confinement which looks harmonic in the instantaneous approximation (IA), was found to describe several features of qanti q and qqq systems (mass spectra and structural properties) adequately, with little extra assumptions. The model had the following drawbacks: (a) The IA, being non-covariant, had restricted the application of the model to slow hadrons; (b) The zero-point energies were poorly described without additional assumptions; (c) The predicted Qanti Q spacings were too large for the data. These limitations have recently been overcome and the model now has a wide sweep of successful predictions, not only on the mass spectra for both light and heavy sectors, but also for transition amplitudes involving fast moving hadrons. A sketchy but consolidated account is given of the main features of the model (as modified through the new assumptions) and the nature of its successes on the experimental front (mostly mass spectra) are indicated. 20 refs

  8. Short-distance behavior of the Bethe--Salpeter wave function in the ladder approximation

    International Nuclear Information System (INIS)

    Guth, A.H.; Soper, D.E.

    1975-01-01

    We investigate the short-distance behavior of the (Wick-rotated) Bethe--Salpeter wave function for the two spin-1/2 quarks bound by the exchange of a massive vector meson. We use the ladder-model kernel, which has the same p -4 scaling behavior as the true kernel in a theory with a fixed point of the renormalization group at g not equal to 0. For a bound state with the quantum numbers of the pion, the leading asymptotic behavior is chi (q/sup μ/) approx. cq/sup -4 + epsilon(g)/γ 5 , where epsilon (g) =1- (1-g 2 /π 2 ) 1 / 2 . Our method also provides the full asymptotic series, although it should be noted that the nonleading terms will depend on the nonleading behavior of the ladder-model kernel. A general term has the form cq - /sup a/(lnq)/sup n/phi (q/sup μ/), where c is an unknown constant, a may be integral or nonintegral, n is an integer, and phi (q/sup μ/) is a representation function of the rotation group in four dimensions

  9. Elastic eD scattering in the Bethe-Salpeter approach for the deuteron with the positive- and negative-energy states

    International Nuclear Information System (INIS)

    Bondarenko, S.G.; Burov, V.V.; Hamamoto, N.; Manabe, Y.; Hosaka, A.; Toki, H.

    2005-01-01

    Recent results obtained by the application of the Bethe-Salpeter approach to the analysis of elastic electron-deuteron scattering with the separable NN kernel are presented. We analyze the impact of the P waves (negative-energy components) on the electromagnetic properties of the deuteron and compare it with experimental data. It was shown that the contribution of the P waves must be taken into account to explain tensor polarization and charge form factor of the deuteron

  10. Generalized structure of hadron-quark vertex function in Bethe-Salpeter framework: applications to leptonic decays of V-mesons

    Energy Technology Data Exchange (ETDEWEB)

    Bhatnagar, Shashank [Department of Physics, Addis Ababa University, PO Box 101739, Addis Ababa (Ethiopia); Li Shiyuan [Department of Physics, Shandong University, Jinan, 250100 (China)

    2006-07-15

    We employ the framework of the Bethe-Salpeter equation under a covariant instantaneous ansatz to study the leptonic decays of vector mesons. The structure of the hadron-quark vertex function {gamma} is generalized to include various Dirac covariants (other than i{gamma} . {epsilon}) from their complete set. They are incorporated in accordance with a naive power counting rule order-by-order in powers of the inverse of the meson mass. The decay constants for {rho}, {omega} and {phi} mesons are calculated with the incorporation of leading-order covariants.

  11. Generalized structure of hadron-quark vertex function in Bethe-Salpeter framework: applications to leptonic decays of V-mesons

    International Nuclear Information System (INIS)

    Bhatnagar, Shashank; Li Shiyuan

    2006-01-01

    We employ the framework of the Bethe-Salpeter equation under a covariant instantaneous ansatz to study the leptonic decays of vector mesons. The structure of the hadron-quark vertex function Γ is generalized to include various Dirac covariants (other than iγ . ε) from their complete set. They are incorporated in accordance with a naive power counting rule order-by-order in powers of the inverse of the meson mass. The decay constants for ρ, ω and φ mesons are calculated with the incorporation of leading-order covariants

  12. Null-plane formulation of Bethe-Salpeter qqq dynamics: Baryon mass spectra

    International Nuclear Information System (INIS)

    Kulshreshtha, D.S.; Mitra, A.N.

    1988-01-01

    The Bethe-Salpeter (BS) equation for a qqq system is formulated in the null-plane approximation (NPA) for the BS wave function, as a direct generalization of a corresponding QCD-motivated formalism developed earlier for qq-bar systems. The confinement kernel is assumed vector type (γ/sub μ//sup (1)/γ/sub μ//sup (2)/) for both qq-bar and qq pairs, with identical harmonic structures, and with the spring constant proportional, among other things, to the running coupling constant α/sub s/ (for an explicit QCD motivation). The harmonic kernel is given a suitable Lorentz-invariant definition [not D'Alembertian 2 δ 4 (q)], which is amenable to NPA reduction in a covariant form. The reduced qqq equation in NPA is solved algebraically in a six-dimensional harmonic-oscillator (HO) basis, using the techniques of SO(2,1) algebra interlinked with S 3 symmetry. The results on the nonstrange baryon mass spectra agree well with the data all the way up to N = 6, thus confirming the asymptotic prediction M∼N/sup 2/3/ characteristic of vector confinement in HO form. There are no extra parameters beyond the three basic constants (ω 0 ,C 0 ,m/sub u//sub d/) which were earlier found to provide excellent fits to meson spectra (qq-bar)

  13. Topological color codes and two-body quantum lattice Hamiltonians

    Science.gov (United States)

    Kargarian, M.; Bombin, H.; Martin-Delgado, M. A.

    2010-02-01

    Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2×Z2 of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings. We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model. The emerging fermions are coupled to nontrivial gauge fields. We show that for particular 2-colexes, the fermions can see the background fluxes in the ground state. Also, we use the Jordan-Wigner transformation in order to test the integrability of the model via introducing Majorana fermions. The four-valent structure of the lattice prevents the

  14. Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach

    Energy Technology Data Exchange (ETDEWEB)

    Hilger, T.; Krassnigg, A. [University of Graz, NAWI Graz, Institute of Physics, Graz (Austria); Gomez-Rocha, M. [ECT*, Villazzano, Trento (Italy)

    2017-09-15

    We investigate the light-quarkonium spectrum using a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach to QCD. We discuss splittings among as well as orbital angular momentum properties of various states in detail and analyze common features of mass splittings with regard to properties of the effective interaction. In particular, we predict the mass of anti ss exotic 1{sup -+} states, and identify orbital angular momentum content in the excitations of the ρ meson. Comparing our covariant model results, the ρ and its second excitation being predominantly S-wave, the first excitation being predominantly D-wave, to corresponding conflicting lattice-QCD studies, we investigate the pion-mass dependence of the orbital-angular-momentum assignment and find a crossing at a scale of m{sub π} ∝ 1.4 GeV. If this crossing turns out to be a feature of the spectrum generated by lattice-QCD studies as well, it may reconcile the different results, since they have been obtained at different values of m{sub π}. (orig.)

  15. Toric codes and quantum doubles from two-body Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Brell, Courtney G; Bartlett, Stephen D; Doherty, Andrew C [Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney (Australia); Flammia, Steven T, E-mail: cbrell@physics.usyd.edu.au [Perimeter Institute for Theoretical Physics, Waterloo (Canada)

    2011-05-15

    We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.

  16. Excitonic effects in solids : time-dependent density functional theory versus the Bethe-Salpeter equation

    International Nuclear Information System (INIS)

    Sagmeister, S.

    2009-01-01

    The aim of this work is to compare two state-of-the-art methods for the investigation of excitonic effects in solids, namely Time-Dependent Density Functional Theory (TDDFT) and Many-Body Perturbation Theory (MBPT), for selected simple gap systems as well as semiconducting polymers. Within TDDFT, the linear response framework is used and the Dyson equation for the density-density response function is solved, whereas within MBPT, the Bethe-Salpeter equation (BSE) for the electron-hole correlation function is solved. The dielectric function is obtained as a last step. Both techniques take into account the excitonic effects caused by the interaction of electron-hole pairs. In the former these effects are included in the exchange-correlation (xc) kernel, whereas in the latter they are located in the interaction kernel of the BSE. Kohn-Sham single-particle wave functions obtained from Density Functional Theory within the linearized augmented planewave (LAPW) method are used to calculate all relevant quantities of the formalism. For the simple systems GaAs, Si and LiF are chosen. The role of several approximations to the xc kernel is studied and it is found that for GaAs and Si simple semi-empirical models provide a dielectric function in accordance with the BSE. For the case of LiF, being a system with a weak screening and a strongly bound exciton, only an xc kernel derived from MBPT yields reasonable results but still a slight discrepancy to the BSE is observed. Finally, the semiconducting polymers poly-acetylene and poly(phenylene-vinylene) (PPV) are studied. For both materials the concept of semi-empirical approximations to the xc kernel turns out to be ambiguous due to their low-dimensional character. In the case of poly-acetylene, the xc kernel derived from MBPT yields a dielectric function which is in close but not exact agreement with the one obtained from the BSE. (author) [de

  17. Topics in Bethe Ansatz

    Science.gov (United States)

    Wang, Chunguang

    Integrable quantum spin chains have close connections to integrable quantum field. theories, modern condensed matter physics, string and Yang-Mills theories. Bethe. ansatz is one of the most important approaches for solving quantum integrable spin. chains. At the heart of the algebraic structure of integrable quantum spin chains is. the quantum Yang-Baxter equation and the boundary Yang-Baxter equation. This. thesis focuses on four topics in Bethe ansatz. The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N. sites have solutions containing ±i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be. determined using a generalization of the Bethe equations. These generalized Bethe. equations provide a practical way of determining which singular solutions correspond. to eigenvectors of the model. The Bethe equations for the periodic XXX and XXZ spin chains admit singular. solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to bephysical, in which case they correspond to genuine eigenvalues and eigenvectors of. the Hamiltonian. We analyze the ground state of the open spin-1/2 isotropic quantum spin chain. with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots. split evenly into two sets: those that remain finite, and those that become infinite. We. argue that the former satisfy conventional Bethe equations, while the latter satisfy a. generalization of the Richardson-Gaudin equations. We derive an expression for the. leading correction to the boundary energy in terms of the boundary parameters. We argue that the Hamiltonians for A(2) 2n open quantum spin chains

  18. Modification of the quantum-mechanical equations for the system of charged Dirac particles by including additional tensor terms of the Pauli type. Pt. 1. [Amplified Bethe-Salpeter, radiative corrections, fine structure

    Energy Technology Data Exchange (ETDEWEB)

    Janyszek, H [Uniwersytet Mikolaja Kopernika, Torun (Poland). Instytut Fizyki

    1974-01-01

    A new modified quasirelativistic equation (different from that of Breit) for N charged Dirac particles in the external stationary electromagnetic field is proposed. This equation is an amplified quantum-mechanical Bethe-Salpeter equation obtained by adding (in a semi-phenomenological manner) terms which take into account radiative corrections. The application of this approximate equations is limited to third order terms in the fine structure constant ..cap alpha...

  19. Null-plane Bethe-Salpeter dynamics: Mass spectra, decay constants of pseudoscalar mesons, and the pion form factor

    International Nuclear Information System (INIS)

    Gupta, K.K.; Mitra, A.N.; Singh, N.N.

    1990-01-01

    A new relativistic definition of the reduced mass (μ 12 ) of a q bar q pair, so as to be in conformity with the standard Wightman-Garding definition of its relative four-momenta q μ , is introduced into the kernel of an ongoing Bethe-Salpeter (BS) program on a two-tier basis. The new definition of μ 12 (involving the hadron mass M) is found to produce a natural Regge asymptotic behavior (M 2 ∼N) in the hadron mass spectra, while retaining the property of an asymptotically linear (∼r) confinement in the three-dimensional structure of the BS kernel. The relativistic structure of μ 12 is responsible for a significant improvement in the fits to the ground-state masses of q bar q and Q bar q mesons as compared to its nonrelativistic definition m 1 m 2 /(m 1 +m 2 ). The leptonic decay constants f p and the charge radii thus calculated are also in excellent agreement with data (π,k) where available, while f p predictions for Q bar q mesons have good overlap with recent lattice predictions. Further, the scaling property (∼k μ -2 ) of the hadron's electromagnetic form factor at large k 2 is a consequence of the ''on-shell'' form of its null-plane wave function. All these results (which are indicated in the barest outline) are preceded by a perspective summary of the theoretical premises and practical working of the BS equation with a four-fermion interaction kernel as a necessary background on a two-tier basis

  20. Three-body unitarity with isobars revisited

    Energy Technology Data Exchange (ETDEWEB)

    Mai, M.; Hu, B. [The George Washington University, Washington, DC (United States); Doering, M. [The George Washington University, Washington, DC (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Pilloni, A. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Szczepaniak, A. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Indiana University, Center for Exploration of Energy and Matter, Bloomington, IN (United States); Indiana University, Physics Department, Bloomington, IN (United States)

    2017-09-15

    The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. In this study we start from the 3 → 3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. This property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes. (orig.)

  1. Complete characterization of the ground-space structure of two-body frustration-free Hamiltonians for qubits

    International Nuclear Information System (INIS)

    Ji Zhengfeng; Wei Zhaohui; Zeng Bei

    2011-01-01

    The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is always a ground state that is a product of single- or two-qubit states. However, it remains unclear whether the whole ground space is of any succinct structure. Here, we give a complete characterization of the ground space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a span of tree tensor network states of the same tree structure. This characterization allows us to show that the problem of determining the ground-state degeneracy is as hard as, but no harder than, its classical analog.

  2. A structure preserving Lanczos algorithm for computing the optical absorption spectrum

    Energy Technology Data Exchange (ETDEWEB)

    Shao, Meiyue [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.; Jornada, Felipe H. da [Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Science Div.; Lin, Lin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.; Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.; Deslippe, Jack [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Louie, Steven G. [Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Science Div.

    2016-11-16

    We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe-Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

  3. Optical properties of body-centered tetragonal C4: Insights from many-body perturbation and time-dependent density functional theories

    Science.gov (United States)

    Tarighi Ahmadpour, Mahdi; Rostamnejadi, Ali; Hashemifar, S. Javad

    2018-04-01

    We study the electronic structure and optical properties of a body-centered tetragonal phase of carbon (bct-C4) within the framework of time-dependent density functional theory and Bethe-Salpeter equation. The results indicate that the optical properties of bct-C4 are strongly affected by the electron-hole interaction. It is demonstrated that the long-range corrected exchange-correlation kernels could fairly reproduce the Bethe-Salpeter equation results. The effective carrier number reveals that at energies above 30 eV, the excitonic effects are not dominant any more and that the optical transitions originate mainly from electronic excitations. The emerged peaks in the calculated electron energy loss spectra are discussed in terms of plasmon excitations and interband transitions. The results of the research indicate that bct-C4 is an indirect wide-band-gap semiconductor, which is transparent in the visible region and opaque in the ultraviolet spectral range.

  4. Obituary: Edwin E. Salpeter (1924-2008)

    Science.gov (United States)

    Trimble, Virginia; Terzian, Yervant

    2009-12-01

    Edwin E. Salpeter, who died 26 November 2008 at his home in Ithaca, NY, belonged to the "second wave" of Jewish scientific refugees from Nazi-dominated Europe, those who left as children just before the onset of WWII and so completed their educations elsewhere. Salpeter was born in Vienna on 3 December 1924, and arrived with his family in Australia in 1939, his father was a physicist and a close friend of Erwin Schrodinger. In Australia, he finished high school, and he entered the University of Sydney at the early age of 16. He received his BS and MSc degrees in physics and mathematics from the University of Sydney, before moving on to a PhD from the University of Birmingham in 1948, for work with Rudolf Peierls on the electrodynamic self-energy of the electron, the first of more than 380 inventoried publications. He had chosen Birmingham over Cambridge or Oxford because of Peierls, and then chose Cornell over Princeton because of Hans Bethe's presence there. His autobiography describes those as two of his very best decisions ever. Marrying psychobiology student Miriam (Mika) Mark less than a year after arriving at Cornell was surely the third, and they remained in Ithaca the rest of their lives, eventually collaborating on some projects in neurobiology before her death in 2000. Their household was a secular one, but (Ed told a colleague) their two daughters received a basic Jewish education "just in case." Daughter Shelley Salpeter and her son Nicholas Buckley were also collaborators with Salpeter on 21st century projects in meta-analysis, epidemiology, and other statistics-heavy problems in biomedicine. Ed Salpeter is survived by his second wife, Antonia (Lhamo) Shouse. Astronomers may be interested to learn that the Cornell press release announcing his death was prepared by Lauren Gold, daughter of Thomas Gold (and Carrie Gold) the co-author of the steady state theory. Apparently, Ed's father Jakob Salpeter late in life considered the anisotropy reported in the

  5. On the effects of the two-body non-fine-structure operators of the Breit-Pauli Hamiltonian

    International Nuclear Information System (INIS)

    Badnell, N.R.

    1997-01-01

    We have incorporated the two-body non-fine-structure operators of the Breit-Pauli Hamiltonian, namely contact spin-spin, two-body Darwin and orbit-orbit, into the program AUTOSTRUCTURE. Illustrative results are presented, including some for reactions involving the process of autoionization. (author)

  6. The average kinetic energy of the heavy quark in Λb in the Bethe-Salpeter equation approach

    International Nuclear Information System (INIS)

    Guo, X.-H.; Wu, H.-K.

    2007-01-01

    In the previous paper, based on the SU(2) f xSU(2) s heavy quark symmetries of the QCD Lagrangian in the heavy quark limit, the Bethe-Salpeter equation for the heavy baryon Λ b was established with the picture that Λ b is composed of a heavy quark and a scalar light diquark. In the present work, we apply this model to calculate μ π 2 for Λ b , the average kinetic energy of the heavy quark inside Λ b . This quantity is particularly interesting since it can be measured in experiments and since it contributes to the inclusive semileptonic decays of Λ b when contributions from higher order terms in 1/M b expansions are taken into account and consequently influences the determination of the Cabibbo-Kobayashi-Maskawa matrix elements V ub and V cb . We find that μ π 2 for Λ b is 0.25GeV 2 ∼0.95GeV 2 , depending on the parameters in the model including the light diquark mass and the interaction strength between the heavy quark and the light diquark in the kernel of the BS equation. We also find that this result is consistent with the value of μ π 2 for Λ b which is derived from the experimental value of μ π 2 for the B meson with the aid of the heavy quark effective theory

  7. Norm of Bethe vectors in models with gl(m|n symmetry

    Directory of Open Access Journals (Sweden)

    A. Hutsalyuk

    2018-01-01

    Full Text Available We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(m|n-invariant R-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show that the square of the norm obeys a number of properties that uniquely fix it. We also show that a Jacobian of the system of Bethe equations obeys the same properties. In this way we prove a generalized Gaudin hypothesis for the norm of the Hamiltonian eigenstates.

  8. Light-front Ward-Takahashi identity for two-fermion systems

    International Nuclear Information System (INIS)

    Marinho, J. A. O.; Frederico, T.; Pace, E.; Salme, G.; Sauer, P. U.

    2008-01-01

    We propose a three-dimensional electromagnetic current operator within light-front dynamics that satisfies a light-front Ward-Takahashi identity for two-fermion systems. The light-front current operator is obtained by a quasipotential reduction of the four-dimensional current operator and acts on the light-front valence component of bound or scattering states. A relation between the light-front valence wave function and the four-dimensional Bethe-Salpeter amplitude both for bound or scattering states is also derived, such that the matrix elements of the four-dimensional current operator can be fully recovered from the corresponding light-front ones. The light-front current operator can be perturbatively calculated through a quasipotential expansion, and the divergence of the proposed current satisfies a Ward-Takahashi identity at any given order of the expansion. In the quasipotential expansion the instantaneous terms of the fermion propagator are accounted for by the effective interaction and two-body currents. We exemplify our theoretical construction in the Yukawa model in the ladder approximation, investigating in detail the current operator at the lowest nontrivial order of the quasipotential expansion of the Bethe-Salpeter equation. The explicit realization of the light-front form of the Ward-Takahashi identity is verified. We also show the relevance of instantaneous terms and of the pair contribution to the two-body current and the Ward-Takahashi identity

  9. Meson spectra from two-body dirac equations with minimal interactions

    International Nuclear Information System (INIS)

    Crater, H.W.; Becker, R.L.; Wong, C.Y.

    1991-01-01

    Many authors have used two-body relativistic wave equations with spin in nonperturbative numerical quark model calculations of the meson spectrum. Usually, they adopt a truncation of the Bethe-Salpeter equation of QED and/or scalar. QED and replace the static Coulomb interactions of those field theories with a semiphenomenological Q bar Q potential whose insertion in the Breit terms give the corresponding spin corrections. However, the successes of these wave equations in QED have invariably depended on perturbative treatment of the terms in each beyond the Coulomb terms. There have been no successful nonperturbative numerical test of two-body quantum wave equations in QED, because in most equations the effective potentials beyond the Coulomb are singular and can only be treated perturbatively. This is a glaring omission that we rectify here for the case of the two-body Dirac equations of constraint dynamics. We show in this paper that a nonperturbative numerical treatment of these equations for QED yields the same spectral results as a perturbative treatment of them which in turn agrees with the standard spectral results for positronium and muonium. This establishes that the vector and scalar interaction structures of our equations accurately incorporate field theoretic interactions in a bone fide relativistic wave equation. The last portion of this work will report recent quark model calculations using these equations with the Adler-Piran static Q bar Q potential

  10. Relativistic treatment of fermion-antifermion bound states

    International Nuclear Information System (INIS)

    Lucha, W.; Rupprecht, H.; Schoeberl, F.F.

    1990-01-01

    We discuss the relativistic treatment of fermion-antifermion bound states by an effective-Hamiltonian method which imitates their description in terms of nonrelativistic potential models: the effective interaction potential, to be used in a Schroedinger equation which incorporates relativistic kinematics, is derived from the underlying quantum field theory. This approach is equivalent to the instantaneous approximation to the Bethe-Salpeter equation called Salpeter equation but comes closer to physical intuition than the latter one. (Author) 14 refs

  11. Bethe-Salpeter wave functions of ηc(1S, 2S) and ψ(1S, 2S) states: local-potential description of the charmonium system revisited

    Science.gov (United States)

    Nochi, Kazuki; Kawanai, Taichi; Sasaki, Shoichi

    2018-03-01

    The quark potential models with an energy-independent central potential have been successful for understanding the conventional charmonium states especially below the open charm threshold. As one might consider, however, the interquark potential is in general energy-dependent, and its tendency gets stronger in higher lying states. Confirmation of whether the interquark potential is energy-independent is also important to verify the validity of the quark potential models. In this talk, we examine the energy dependence of the charmonium potential, which can be determined from the Bethe-Salpeter (BS) amplitudes of cc̅ mesons in lattice QCD.We first calculate the BS amplitudes of radially excited charmonium states, the ηc(2S) and ψ(2S) states, using the variational method and then determine both the quark kinetic mass and the charmonium potential within the HAL QCD method. Through a direct comparison of charmonium potentials determined from both the 1S and 2S states, we confirm that neither the central nor spin-spin potential shows visible energy dependence at least up to 2S state.

  12. Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

    Energy Technology Data Exchange (ETDEWEB)

    Cirilo António, N., E-mail: nantonio@math.ist.utl.pt [Centro de Análise Funcional e Aplicações, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Manojlović, N., E-mail: nmanoj@ualg.pt [Grupo de Física Matemática da Universidade de Lisboa, Av. Prof. Gama Pinto 2, PT-1649-003 Lisboa (Portugal); Departamento de Matemática, F.C.T., Universidade do Algarve, Campus de Gambelas, PT-8005-139 Faro (Portugal); Salom, I., E-mail: isalom@ipb.ac.rs [Institute of Physics, University of Belgrade, P.O. Box 57, 11080 Belgrade (Serbia)

    2014-12-15

    We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

  13. Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

    Science.gov (United States)

    Cirilo António, N.; Manojlović, N.; Salom, I.

    2014-12-01

    We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

  14. Covariant equations for the three-body bound state

    International Nuclear Information System (INIS)

    Stadler, A.; Gross, F.; Frank, M.

    1997-01-01

    The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical solution. The equations are first written in operator form and compared to the Bethe-Salpeter equation, then expanded into plane wave momentum states, and finally expanded into partial waves using the three-body helicity formalism first introduced by Wick. In order to solve the equations, the two-body scattering amplitudes must be boosted from the overall three-body rest frame to their individual two-body rest frames, and all effects which arise from these boosts, including Wigner rotations and p-spin decomposition of the shell-particle, are treated exactly. In their final form, the equations reduce to a coupled set of Faddeev-like double integral equations with additional channels arising from the negative p-spin states of the off-shell particle

  15. Relativistic three-body approach to NN scattering at intermediate energies

    International Nuclear Information System (INIS)

    van Faassen, E.; Tjon, J.A.

    1986-01-01

    The Bethe-Salpeter equation for coupled-channel N-Δ scattering is extended to satisfy unitarity in the NN and NNπ sectors. The procedure eliminates the unitarity violations characteristic of the standard ladder Bethe-Salpeter equation in the inelastic region, and improves the description of pion production near threshold. Results are presented for the NN phase shift and a number of observables up to 1 GeV. In particular, the 1D 2 inelasticity is found to be considerably smaller than found from phase shift analysis. In this context, the importance of the pion deuteron channel for the inelasticity parameter of is pointed out. 33 refs., 16 figs., 4 tabs

  16. Excitation spectrum and staggering transformations in lattice quantum models.

    Science.gov (United States)

    Faria da Veiga, Paulo A; O'Carroll, Michael; Schor, Ricardo

    2002-08-01

    We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semigroup of Ginzburg-Landau models with Langevin stochastic dynamics, the Hamiltonian of a scalar quantum field theory, and the Hamiltonian associated with the transfer matrix of a classical ferromagnetic spin system at high temperature. The low-lying spectrum consists of a one-particle state and a two-particle band. The two-particle spectrum is determined using a lattice version of the Bethe-Salpeter equation. In addition to the two-particle band, depending on the lattice dimension and on the attractive or repulsive character of the interaction between the particles of the system, there is, respectively, a bound state below or above the two-particle band. We show how the existence or nonexistence of these bound states can be understood in terms of a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential. A staggering transformation relates the spectra of the attractive and the repulsive cases.

  17. Relativistic Many-Body Theory A New Field-Theoretical Approach

    CERN Document Server

    Lindgren, Ingvar

    2011-01-01

    Relativistic Many-Body Theory treats — for the first time — the combination of relativistic atomic many-body theory with quantum-electrodynamics (QED) in a unified manner. This book can be regarded as a continuation of the book by Lindgren and Morrison, Atomic Many-Body Theory (Springer 1986), which deals with the non-relativistic theory of many-electron systems, describing several means of treating the electron correlation to essentially all orders of perturbation theory. The treatment of the present book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insuffici...

  18. An integral transform of the Salpeter equation

    International Nuclear Information System (INIS)

    Krolikowski, W.

    1980-03-01

    We find a new form of relativistic wave equation for two spin-1/2 particles, which arises by an integral transformation (in the position space) of the wave function in the Salpeter equation. The non-locality involved in this transformation is extended practically over the Compton wavelength of the lighter of two particles. In the case of equal masses the new equation assumes the form of the Breit equation with an effective integral interaction. In the one-body limit it reduces to the Dirac equation also with an effective integral interaction. (author)

  19. A comprehensive treatment of electromagnetic interactions and the three-body spectator equations

    Energy Technology Data Exchange (ETDEWEB)

    Jiri Adam; Jay Van Orden

    2004-10-01

    We present a general derivation the three-body spectator (Gross) equations and the corresponding electromagnetic currents. As in previous paper on two-body systems, the wave equations and currents are derived from those for Bethe-Salpeter equation with the help of algebraic method using a concise matrix notation. The three-body interactions and currents introduced by the transition to the spectator approach are isolated and the matrix elements of the e.m. current are presented in detail for system of three indistinguishable particles, namely for elastic scattering and for two and three body break-up. The general expressions are reduced to the one-boson-exchange approximation to make contact with previous work. The method is general in that it does not rely on introduction of the electromagnetic interaction with the help of the minimal replacement. It would therefore work also for other external fields.

  20. Two site spin correlation function in Bethe-Peierls approximation for Ising model

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, D [Roorkee Univ. (India). Dept. of Physics

    1976-07-01

    Two site spin correlation function for an Ising model above Curie temperature has been calculated by generalising Bethe-Peierls approximation. The results derived by a graphical method due to Englert are essentially the same as those obtained earlier by Elliott and Marshall, and Oguchi and Ono. The earlier results were obtained by a direct generalisation of the cluster method of Bethe, while these results are derived by retaining that class of diagrams , which is exact on Bethe lattice.

  1. Accurate X-Ray Spectral Predictions: An Advanced Self-Consistent-Field Approach Inspired by Many-Body Perturbation Theory.

    Science.gov (United States)

    Liang, Yufeng; Vinson, John; Pemmaraju, Sri; Drisdell, Walter S; Shirley, Eric L; Prendergast, David

    2017-03-03

    Constrained-occupancy delta-self-consistent-field (ΔSCF) methods and many-body perturbation theories (MBPT) are two strategies for obtaining electronic excitations from first principles. Using the two distinct approaches, we study the O 1s core excitations that have become increasingly important for characterizing transition-metal oxides and understanding strong electronic correlation. The ΔSCF approach, in its current single-particle form, systematically underestimates the pre-edge intensity for chosen oxides, despite its success in weakly correlated systems. By contrast, the Bethe-Salpeter equation within MBPT predicts much better line shapes. This motivates one to reexamine the many-electron dynamics of x-ray excitations. We find that the single-particle ΔSCF approach can be rectified by explicitly calculating many-electron transition amplitudes, producing x-ray spectra in excellent agreement with experiments. This study paves the way to accurately predict x-ray near-edge spectral fingerprints for physics and materials science beyond the Bethe-Salpether equation.

  2. Cluster-Bethe-Lattice study of a planar antiferromagnet: Rb2NiF4

    International Nuclear Information System (INIS)

    Cruz, G.A.C. de la; Silva, C.E.T.G. da

    1979-01-01

    A discussion of the Cluster-Bethe-Lattice method is presented for a planar antiferromagnet for which the hamiltonian parameters are known and the one-magnon density of states may be computed exactly. All the square clusters of 1 to 121 atoms are studied both connected to and isolated from the Bethe lattices. It is shown that, even for the largest cluster treated, the approximation is still far from the exact result. It is discussed the limitations of the method [pt

  3. Two-body and three-body correlations in Os-shell nuclei

    International Nuclear Information System (INIS)

    Halderson, D.W.

    1974-01-01

    It is well known that conventional Brueckner calculations with modern nucleon-nucleon potentials have failed to reproduce experimental saturation properties of finite nuclei. The intent was to determine whether the discrepancies are due to the methods of calculation or the nucleon-nucleon potentials. Brueckner procedures which include only two-body correlations were applied to Os-shell nuclei. Calculations were performed with and without the Hartree-Fock condition, with and without partial occupation probabilities, and with various propagators and Pauli correction techniques. Then the entire class of three-body correlations was calculated by matrix solution of the Bethe-Faddeev equations. The convergence necessary to validate this technique was achieved by constructing a set of basic functions which contain no center of mass excitations and yet are still properly antisymmetrized. The two-body calculations yielded typical Brueckner results. The nuclei were underbound or the radii were too small. However, the three-body calculations yielded reasonable radii and moderate overbinding for the Reid soft core and Hamada-Johnston potentials. Therefore, the Bethe-Faddeev formalism has been shown to be a reasonable approach to calculation of the three-body correlations in finite nuclei; and the results of []these calculations demonstrate that the underbinding and collapsed radii of two-body calculations were largely due to the uncalculated correlations. (auth)

  4. On the discrete spectrum of the N-body quantum mechanical Hamiltonian. Pt. 2

    International Nuclear Information System (INIS)

    Iorio, R.J. Jr.

    1981-01-01

    Using the Weinberg-van Winter equations we prove finiteness of the discrete spectrum of the N-body quantum mechanical Hamiltonian with pair potentials satisfying vertical stroke V(x) vertical stroke 2 ) - sup(rho), rho > 1 increase the threshold of the continuous spectrum is negative and determined exclusively by eigenvalues of two-cluster Hamiltonians. (orig.)

  5. Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

    Science.gov (United States)

    Manojlović, N.; Salom, I.

    2017-10-01

    The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.

  6. Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

    International Nuclear Information System (INIS)

    Manojlović, N.; Salom, I.

    2017-01-01

    The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.

  7. Supersymmetric two-particle equations

    International Nuclear Information System (INIS)

    Sissakyan, A.N.; Skachkov, N.B.; Shevchenko, O.Yu.

    1986-01-01

    In the framework of the scalar superfield model, a particular case of which is the well-known Wess-Zumino model, the supersymmetric Schwinger equations are found. On their basis with the use of the second Legendre transformation the two-particle supersymmetric Edwards and Bethe-Salpeter equations are derived. A connection of the kernels and inhomogeneous terms of these equations with generating functional of the second Legendre transformation is found

  8. Medium modifications of mesons. Chiral symmetry restoration, in-medium QCD sum rules for D and ρ mesons, and Bethe-Salpeter equations

    Energy Technology Data Exchange (ETDEWEB)

    Hilger, Thomas Uwe

    2012-04-11

    The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D- anti D and B- anti B mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D{sub s} and D{sup *}{sub 0} mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the ρ meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpeter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.

  9. Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

    Directory of Open Access Journals (Sweden)

    N. Manojlović

    2017-10-01

    Full Text Available The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.

  10. Relativistic many-body theory a new field-theoretical approach

    CERN Document Server

    Lindgren, Ingvar

    2016-01-01

    This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title.  In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into...

  11. Low-temperature excitations within the Bethe approximation

    International Nuclear Information System (INIS)

    Biazzo, I; Ramezanpour, A

    2013-01-01

    We propose the variational quantum cavity method to construct a minimal energy subspace of wavevectors that are used to obtain some upper bounds for the energy cost of the low-temperature excitations. Given a trial wavefunction we use the cavity method of statistical physics to estimate the Hamiltonian expectation and to find the optimal variational parameters in the subspace of wavevectors orthogonal to the lower-energy wavefunctions. To this end, we write the overlap between two wavefunctions within the Bethe approximation, which allows us to replace the global orthogonality constraint with some local constraints on the variational parameters. The method is applied to the transverse Ising model and different levels of approximations are compared with the exact numerical solutions for small systems. (paper)

  12. Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions

    International Nuclear Information System (INIS)

    Wu Junfang; Zhang Chunmin; Yue Ruihong; Li Runling

    2005-01-01

    The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the general boundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K ± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.

  13. A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

    International Nuclear Information System (INIS)

    Hibberd, K.E.; Dunning, C.; Links, J.

    2006-01-01

    We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PT-symmetric wavefunctions defined on a contour in the complex plane

  14. Non-skew-symmetric classical r-matrices, algebraic Bethe ansatz, and Bardeen-Cooper-Schrieffer-type integrable systems

    International Nuclear Information System (INIS)

    Skrypnyk, T.

    2009-01-01

    We construct quantum integrable systems associated with non-skew-symmetric gl(2)-valued classical r-matrices. We find a new explicit multiparametric family of such the non-skew-symmetric classical r-matrices. We consider two classes of examples of the corresponding integrable systems, namely generalized Gaudin systems with and without an external magnetic field. In the case of arbitrary r-matrices diagonal in a standard gl(2)-basis, we calculate the spectrum of the corresponding quantum integrable systems using the algebraic Bethe ansatz. We apply these results to a construction of integrable fermionic models and obtain a wide class of integrable Bardeen-Cooper-Schrieffer (BCS)-type fermionic Hamiltonians containing the pairing and electrostatic interaction terms. We also consider special cases when the corresponding integrable Hamiltonians contain only pairing interaction term and are exact analogs of the 'reduced BCS Hamiltonian' of Richardson

  15. Study of Y and Lu iron garnets using Bethe-Peierls-Weiss method

    Science.gov (United States)

    Goveas, Neena; Mukhopadhyay, G.; Mukhopadhyay, P.

    1994-11-01

    We study here the magnetic properties of Y- and Lu- Iron Garnets using the Bethe- Peierls-Weiss method modified to suit complex systems like these Garnets. We consider these Garnets as described by Heisenberg Hamiltonian with two sublattices (a,d) and determine the exchange interaction parameters Jad, Jaa and Jdd by matching the exerimental susceptibility curves. We find Jaa and Jdd to be much smaller than those determined by Néel theory, and consistent with those obtained by the study of spin wave spectra; the spin wave dispersion relation constant obtained using these parameters gives good agreement with the experimental values.

  16. Bethe Ansatz and supersymmetric vacua

    International Nuclear Information System (INIS)

    Nekrasov, Nikita; Shatashvili, Samson

    2009-01-01

    Supersymmetric vacua of two dimensional N = 4 gauge theories with matter, softly broken by the twisted masses down to N = 2, are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. Examples include: the Heisenberg SU(2)XXX spin chain which is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain which is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T 2 . A consequence of our correspondence is the isomorphism of the quantum cohomology ring of various quiver varieties, such as cotangent bundles to (partial) flag varieties and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. Compactifications of four dimensional N = 2 theories on a two-sphere lead to the instanton-corrected Bethe equations.

  17. Effects of molecular packing in organic crystals on singlet fission with ab initio many body perturbation theory

    Science.gov (United States)

    Haber, Jonah; Refaely-Abramson, Sivan; da Jornada, Felipe H.; Louie, Steven G.; Neaton, Jeffrey B.

    Multi-exciton generation processes, in which multiple charge carriers are generated from a single photon, are mechanisms of significant interest for achieving efficiencies beyond the Shockley-Queisser limit of conventional p-n junction solar cells. One well-studied multiexciton process is singlet fission, whereby a singlet decays into two spin-correlated triplet excitons. Here, we use a newly developed computational approach to calculate singlet-fission coupling terms and rates with an ab initio Green's function formalism based on many-body perturbation theory (MBPT) within the GW approximation and the Bethe-Salpeter equation approach. We compare results for crystalline pentacene and TIPS-pentacene and explore the effect of molecular packing on the singlet fission mechanism. This work is supported by the Department of Energy.

  18. Bethe ansatz for two-magnon scattering states in 2D and 3D Heisenberg–Ising ferromagnets

    Science.gov (United States)

    Bibikov, P. N.

    2018-04-01

    Two different versions of Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg–Ising ferromagnets on square and simple cubic lattices. It is shown that the two-magnon sector is subdivided on two subsectors related to non-interacting and scattering magnons. The former subsector possess an integrable regular dynamics and may be described by a natural modification of the usual Bethe Ansatz. The latter one is characterized by a non-integrable chaotic dynamics and may be treated only within discrete degenerative version of Bethe Ansatz previously suggested by the author. Some of these results are generalized for multi-magnon states of the Heisenberg–Ising ferromagnet on a D dimensional hyper cubic lattice. Dedicated to the memory of L D Faddeev.

  19. On the absence of pentaquark states from dynamics in strongly coupled lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Anjos, Petrus Henrique Ribeiro dos [Universidade Federal de Goias (UFG), Goiania, GO (Brazil); Veiga, Paulo Afonso Faria da; O' Carroll, Michael [Universidade de Sao Paulo (USP), SP (Brazil); Francisco Neto, Antonio [Universidade Federal de Ouro Preto (UFOP), MG (Brazil)

    2011-07-01

    Full text: We consider an imaginary time functional integral formulation of a two-flavor, 3 + 1 lattice QCD model with Wilson's action and in the strong coupling regime (with a small hopping parameter, {kappa}0, and a much smaller plaquette coupling, {beta} = 1/g{sub 0}{sup 2}, so that the quarks and glueballs are heavy). The model has local SU(3){sub c} gauge and global SU(2){sub f} flavor symmetries, and incorporates the corresponding part of the eightfold way particles: baryons (mesons) of asymptotic mass -3ln{kappa}(-2 ln {kappa}). We search for pentaquark states as meson-baryon bound states in the energy-momentum spectrum of the model, using a lattice Bethe-Salpeter equation. This equation is solved within a ladder approximation, given by the lowest nonvanishing order in {kappa} and {beta} of the Bethe-Salpeter kernel. It includes order 2 contributions with a q-barq exchange potential together with a contribution that is a local-in-space, energy-dependent potential. The attractive or repulsive nature of the exchange interaction depends on the spin of the meson-baryon states. The Bethe-Salpeter equation presents integrable singularities, forcing the couplings to be above a threshold value for the meson and the baryon to bind in a pentaquark. We analyzed all the total isospin sectors, I = 1/2/3/2/ 5/2, for the system. For all I, the net attraction resulting from the two sources of interaction is not strong enough for the meson and the baryon to bind. Thus, within our approximation, these pentaquark states are not present up to near the free meson-baryon energy threshold of - 5 ln{kappa}. This result is to be contrasted with the spinless case for which our method detects meson-baryon bound states, as well as for Yukawa effective baryon and meson field models. A physical interpretation of our results emerges from an approximate correspondence between meson-baryon bound states and negative energy states of a one-particle lattice Schroedinger Hamiltonian

  20. Eikonal multiple scattering model within the framework of Feynman's positron theory

    International Nuclear Information System (INIS)

    Tekou, A.

    1986-07-01

    The Bethe Salpeter equation for nucleon-nucleon, nucleon-nucleus and nucleus-nucleus scattering is eikonalized. Multiple scattering series is obtained. Contributions of three body interations are included. The model presented below may be used to investigate atomic collisions. (author)

  1. Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

    Science.gov (United States)

    Minesaki, Yukitaka

    2018-04-01

    We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

  2. Comparison of the Schrodinger and Salpeter equations

    International Nuclear Information System (INIS)

    Jacobs, S.; Olsson, M.G.

    1985-01-01

    A unified approach to the solution of the Schrodinger and spinless Salpeter equations is presented. Fits to heavy quark bound state energies using various potential models are employed to determine whether the Salpeter equation provides a better description of heavy quark systems than the Schrodinger equation

  3. Sequential Bethe vectors and the quantum Ernst system

    International Nuclear Information System (INIS)

    Niedermaier, M.; Samtleben, H.

    2000-01-01

    We give a brief review on the use of Bethe Ansatz techniques to construct solutions of recursive functional equations which emerged in a bootstrap approach to the quantum Ernst system. The construction involves two particular limits of a rational Bethe Ansatz system with complex inhomogeneities. First, we pinch two insertions to the critical value. This links Bethe systems with different number of insertions and leads to the concept of sequential Bethe vectors. Second, we study the semiclassical limit of the system in which the scale parameter of the insertions tends to infinity. (author)

  4. Calculation of scalar products of wave functions and form factors in the framework of the algebraic Bethe ansatz

    International Nuclear Information System (INIS)

    Slavnov, N.A.

    1989-01-01

    The Bethe ansatz method is widely used to investigate two-dimensional completely integrable models. In the framework of the quantum inverse scattering method it has proved to be possible to construct an algebraic scheme of the Bethe ansatz, and this has been successfully applied to calculation of correlation functions. One of the important questions of the method is that of the scalar products of the wave functions. In particular, knowledge of the properties of the scalar products is necessary for investigating the form factors and correlation function. In the present paper the author considers a generalized model with R matrix of the model of the nonlinear Schroedinger equation. The main formulas and notation are given in Sec. 2. In Sec. 3 he calculates the scalar product of an arbitrary function and an eigenfunction of the Hamiltonian. The generalized two-site model is introduced in Sec. 4. In Sec. 5 he calculates the form factor of the particle number operator

  5. Recent advances in bound state quantum electrodynamics

    International Nuclear Information System (INIS)

    Brodsky, S.J.; Lepage, G.P.

    1977-06-01

    Recent developments are reviewed in four areas of computational quantum electrodynamics: a new relativistic two-body formalism equal in rigor to the Bethe-Salpeter formalism but with strong calculational advantages is discussed; recent work on the computation of the decay rate of bound systems (positronium in particular) is presented; limits on possible composite structure of leptons are discussed; a new multidimensional integration program ('VEGAS') suitable for higher order calculations is presented

  6. Two-photon processes of π0, η, η', ηc and ηb

    International Nuclear Information System (INIS)

    Klabucar, D.

    1997-01-01

    Two-photon processes of π 0 , η, η', η c and η b are studied in the consistently coupled Schwinger-Dyson (SD) and Bethe-Salpeter (BS) approach, where dynamical chiral symmetry breaking (DχSB) is obtained through the SD equation for the quark propagator which is then used in the BS equation. It is shown that the coupled SD-BS approach is similarly successful in the description of two-photon processes of pseudoscalar mesons over a wide range of masses. (K.A.)

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

    Science.gov (United States)

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

    2009-09-01

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

  8. Intertwined Hamiltonians in two-dimensional curved spaces

    International Nuclear Information System (INIS)

    Aghababaei Samani, Keivan; Zarei, Mina

    2005-01-01

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

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

    Science.gov (United States)

    Pavlov, Maxim V

    2014-12-08

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

  10. Some issues linked to the description of systems in strong interaction

    International Nuclear Information System (INIS)

    Theussl, L.

    2001-06-01

    In the first part of this work we have dealt with some issues that are relevant in the area of nucleonic resonances within different constituent quark models. In this context we have concentrated on the theoretical description of Pi and Nu decays for N and Delta resonances. The results obtained point to the necessity of a more microscopic description of the dynamics which is at the same time responsible for the binding of quarks inside baryons and the decay of the latter ones. In the second part we have contributed to the study of crossed two-boson exchanges in the Bethe-Salpeter equation as well as to the investigation of different three-dimensional approaches that follow from the Bethe-Salpeter equation in a certain non-relativistic reduction scheme. These one include in particular an equation whose interaction depends on the total energy of the system. It was shown that such an equation is able to account for a certain number of properties of Bethe-Salpeter equation, in particular, that there also arise abnormal solutions in such an approach. (author)

  11. Spectrum of quantum transfer matrices via classical many-body systems

    Energy Technology Data Exchange (ETDEWEB)

    Gorsky, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Zabrodin, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Institute of Biochemical Physics,Kosygina str. 4, 119991, Moscow (Russian Federation); National Research University Higher School of Economics,Myasnitskaya str. 20, 101000, Moscow (Russian Federation); Zotov, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Steklov Mathematical Institute, RAS,Gubkina str. 8, 119991, Moscow (Russian Federation)

    2014-01-15

    In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous gl{sub n}-invariant XXX spin chain on N sites with twisted boundary conditions can be found in terms of velocities of particles in the rational N-body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all N particles and the other one is an N-dimensional Lagrangian submanifold obtained by fixing levels of N classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the gl{sub n} Gaudin model with N marked points (on the quantum side) and the Calogero-Moser system with N particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed.

  12. Separation of different wave components in the Bethe–Salpeter ...

    Indian Academy of Sciences (India)

    the obtained formulae, different wave components in the Salpeter wave ... the results are consistent with the results obtained by L–S coupling analysis. ..... from the main terms f5,6 in eqs (4) and (6), the Salpeter wave function (4) for the bound.

  13. Fermionic bound states in Minkowski space. Light-cone singularities and structure

    Energy Technology Data Exchange (ETDEWEB)

    Paula, Wayne de; Frederico, Tobias; Pimentel, Rafael [Instituto Tecnologico de Aeronautica, DCTA, Dept. de Fisica, Sao Jose dos Campos, Sao Paulo (Brazil); Salme, Giovanni [Istituto Nazionale di Fisica Nucleare, Rome (Italy); Viviani, Michele [Istituto Nazionale di Fisica Nucleare, Pisa (Italy)

    2017-11-15

    The Bethe-Salpeter equation for two-body bound system with spin 1/2 constituent is addressed directly in the Minkowski space. In order to accomplish this aim we use the Nakanishi integral representation of the Bethe-Salpeter amplitude and exploit the formal tool represented by the exact projection onto the null-plane. This formal step allows one (i) to deal with end-point singularities one meets and (ii) to find stable results, up to strongly relativistic regimes, which settle in strongly bound systems. We apply this technique to obtain the numerical dependence of the binding energies upon the coupling constants and the light-front amplitudes for a fermion-fermion 0{sup +} state with interaction kernels, in ladder approximation, corresponding to scalar-, pseudoscalar- and vector-boson exchanges, respectively. After completing the numerical survey of the previous cases, we extend our approach to a quark-antiquark system in 0{sup -} state, taking both constituent-fermion and exchanged-boson masses, from lattice calculations. Interestingly, the calculated light-front amplitudes for such a mock pion show peculiar signatures of the spin degrees of freedom. (orig.)

  14. High-energy gravitational scattering and the general relativistic two-body problem

    Science.gov (United States)

    Damour, Thibault

    2018-02-01

    A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys. Rev. D 94, 104015 (2016), 10.1103/PhysRevD.94.104015]. Using this technique, we derive, for the first time, to second-order in Newton's constant (i.e. one classical loop) the Hamiltonian of two point masses having an arbitrary (possibly relativistic) relative velocity. The resulting (second post-Minkowskian) Hamiltonian is found to have a tame high-energy structure which we relate both to gravitational self-force studies of large mass-ratio binary systems, and to the ultra high-energy quantum scattering results of Amati, Ciafaloni and Veneziano. We derive several consequences of our second post-Minkowskian Hamiltonian: (i) the need to use special phase-space gauges to get a tame high-energy limit; and (ii) predictions about a (rest-mass independent) linear Regge trajectory behavior of high-angular-momenta, high-energy circular orbits. Ways of testing these predictions by dedicated numerical simulations are indicated. We finally indicate a way to connect our classical results to the quantum gravitational scattering amplitude of two particles, and we urge amplitude experts to use their novel techniques to compute the two-loop scattering amplitude of scalar masses, from which one could deduce the third post-Minkowskian effective one-body Hamiltonian.

  15. Effect of three-body transformed Hamiltonian (H3) using full ...

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 90; Issue 3 ... Research Article Volume 90 Issue 3 March 2018 Article ID 36 ... Valence universal multireference coupled cluster (VUMRCC) method via eigenvalue independent partitioning has been applied to estimate the effect of three-body transformed Hamiltonian ...

  16. Introduction to Hamiltonian dynamical systems and the N-body problem

    CERN Document Server

    Meyer, Kenneth R

    2017-01-01

    This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary exa...

  17. Lagrangian-Hamiltonian formalism for the gravitational two-body problem with spin and parametrized post-Newtonian parameters γ and β

    International Nuclear Information System (INIS)

    Barker, B.M.; O'Connell, R.F.

    1976-01-01

    We generalize the Lagrangian and Hamiltonian of our previous work on the gravitational two-body problem with spin by including the parametrized-post-Newtonian parameters γ and β. By this procedure we are able to obtain the precession of the orbit as well as the precession of the spin. Equations of motion corresponding to an arbitrary-spin supplementary condition are also given. Finally we show how the masses of the binary pulsar PSR 1913 + 16 and its companion are related to the orbit and spin precessions. Combining this with a result derivable from the second-order Doppler effect and the gravitational red-shift, we obtain a relation constraining the values that γ and β can take

  18. Collective Hamiltonians for dipole giant resonances

    International Nuclear Information System (INIS)

    Weiss, L.I.

    1991-07-01

    The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)

  19. Where are the roots of the Bethe Ansatz equations?

    Energy Technology Data Exchange (ETDEWEB)

    Vieira, R.S., E-mail: rsvieira@df.ufscar.br; Lima-Santos, A., E-mail: dals@df.ufscar.br

    2015-10-02

    Changing the variables in the Bethe Ansatz Equations (BAE) for the XXZ six-vertex model we had obtained a coupled system of polynomial equations. This provided a direct link between the BAE deduced from the Algebraic Bethe Ansatz (ABA) and the BAE arising from the Coordinate Bethe Ansatz (CBA). For two magnon states this polynomial system could be decoupled and the solutions given in terms of the roots of some self-inversive polynomials. From theorems concerning the distribution of the roots of self-inversive polynomials we made a thorough analysis of the two magnon states, which allowed us to find the location and multiplicity of the Bethe roots in the complex plane, to discuss the completeness and singularities of Bethe's equations, the ill-founded string-hypothesis concerning the location of their roots, as well as to find an interesting connection between the BAE with Salem’s polynomials.

  20. Gauge-invariant, nonperturbative approach to the infrared-finite bound-state problem in QCD

    International Nuclear Information System (INIS)

    Gogokhia, V.Sh.

    1989-09-01

    Gauge invariant, nonperturbative approach to the bound state problem within the infrared finite Bethe-Salpeter equation is presented. Condition of cancellation of the nonperturbative infrared divergences is derived. Solutions for the quark propagator and corresponding quark gluon vertex function are written down which can be directly applied to the Bethe-Salpeter equation, in particular to the 'generalized ladder' approximation of this equation. (author) 18 refs.; 3 figs

  1. Hamiltonian quantum simulation with bounded-strength controls

    International Nuclear Information System (INIS)

    Bookatz, Adam D; Wocjan, Pawel; Viola, Lorenza

    2014-01-01

    We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed. (papers)

  2. Optical absorption in disordered monolayer molybdenum disulfide

    Science.gov (United States)

    Ekuma, C. E.; Gunlycke, D.

    2018-05-01

    We explore the combined impact of sulfur vacancies and electronic interactions on the optical properties of monolayer MoS2. First, we present a generalized Anderson-Hubbard Hamiltonian that accounts for both randomly distributed sulfur vacancies and the presence of dielectric screening within the material. Second, we parametrize this energy-dependent Hamiltonian from first-principles calculations based on density functional theory and the Green's function and screened Coulomb (GW) method. Third, we apply a first-principles-based many-body typical medium method to determine the single-particle electronic structure. Fourth, we solve the Bethe-Salpeter equation to obtain the charge susceptibility χ with its imaginary part being related to the absorbance A . Our results show that an increased vacancy concentration leads to decreased absorption both in the band continuum and from exciton states within the band gap. We also observe increased absorption below the band-gap threshold and present an expression, which describes Lifshitz tails, in excellent qualitative agreement with our numerical calculations. This latter increased absorption in the 1.0 -2.5 eV range makes defect engineering of potential interest for solar cell applications.

  3. Combinatorics of Generalized Bethe Equations

    Science.gov (United States)

    Kozlowski, Karol K.; Sklyanin, Evgeny K.

    2013-10-01

    A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over {{Z}^M}, and on the other hand, they count integer points in certain M-dimensional polytopes.

  4. QCD bound states at finite temperature and baryon number

    International Nuclear Information System (INIS)

    Kalinovsky, Yu.L.; Muenchow, L.

    1991-04-01

    Quark-antiquark bound states are described within the Bethe-Salpeter equation for a class of quark models with instantaneous 4-quark interaction at finite temperature. Thereby decompositions of the Bethe-Salpeter vertex and wave functions according to their Lorentz structures and the particles content are used. As an application of general scheme, we determine the mass spectrum of low-lying mesons for a special Nambu-Jona-Lasinio model inspired by QCD for hadrons. (orig.)

  5. Expanding the Bethe/Gauge dictionary

    Science.gov (United States)

    Bullimore, Mathew; Kim, Hee-Cheol; Lukowski, Tomasz

    2017-11-01

    We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2, 2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe states as orbifold defects in the A-twisted supersymmetric gauge theory and study their correlation functions. We also present an alternative description of off-shell Bethe states as boundary conditions in an effective N = 4 supersymmetric quantum mechanics. Finally, we interpret spin chain R-matrices as correlation functions of Janus interfaces for mass parameters in the supersymmetric quantum mechanics.

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

    Science.gov (United States)

    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.

  7. Helicity eigenstates of a relativistic spin-0 and spin-1/2 constituent bound by minimal electrodynamics: Zero orbital angular momentum, zero four-momentum solutions

    International Nuclear Information System (INIS)

    Mainland, G.B.

    1988-01-01

    Zero four-momentum, helicity eigenstates of the Bethe--Salpeter equation are found for a composite system consisting of a charged, spin-0 constituent and a charged, spin- 1/2 constituent bound by minimal electrodynamics. The form of the Bethe--Salpeter equation used to describe the bound state includes the contributions from both single photon exchange (ladder approximation) and the ''seagull'' diagram. Attention is restricted to zero orbital angular momentum states since these appear to be the most interesting physically

  8. Relativistic three-particle dynamical equations: I. Theoretical development

    International Nuclear Information System (INIS)

    Adhikari, S.K.; Tomio, L.; Frederico, T.

    1993-11-01

    Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, three dimensional scattering integral equations satisfying constrains of relativistic unitarity and covariance are rederived. These equations were first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence it is shown to perform and relate dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, several three dimensional three-particle scattering equations satisfying constraints of relativistic unitary and covariance are derived. Two of these three-particle equations are related by a transformation of variables as in the two-particle case. The three-particle equations obtained are very practical and suitable for performing relativistic scattering calculations. (author)

  9. Distinct solutions of infinite U Hubbard model through nested Bethe ansatz and Gutzwiller projection operator approach

    International Nuclear Information System (INIS)

    Mishra, A.K.; Kishore, R.

    2009-01-01

    The exact nested Bethe ansatz solution for the one dimensional (1-D) U infinity Hubbard model show that the state vectors are a product of spin-less fermion and spin wavefunctions, or an appropriate superposition of such factorized wavefunctions. The spin-less fermion component of the wavefunctions ensures no double occupancy at any site. It had been demonstrated that the nested Bethe ansatz wavefunctions in the U infinity limit obey orthofermi statistics. Gutzwiller projection operator formalism is the another well known technique employed to handle U infinity Hubbard model. In general, this approach does not lead to spin-less fermion wavefunctions. Therefore, the nested Bethe ansatz and Gutzwiller projection operator approach give rise to different kinds of the wavefunctions for the U infinity limit of 1-D Hubbard Hamiltonian. To compare the consequences of this dissimilarity in the wavefunctions, we have obtained the ground state energy of a finite system consisting of three particles on a four site closed chain. It is shown that in the nested Bethe ansatz implemented through orthofermion algebra, all the permissible 2 3 spin configurations are degenerate in the ground state. This eight fold degeneracy of the ground state is absent in the Gutzwiller projection operator approach. This finding becomes relevant in the context of known exact U infinity results, which require that all the energy levels are 2 N -fold degenerate for an N particle system.

  10. Gauge transformations in relativistic two-particle constraint theory

    International Nuclear Information System (INIS)

    Jallouli, H.; Sazdjian, H.

    1996-01-01

    The forms of the local potentials in linear covariant gauges are investigated and relationships are found between them. The gauge transformation properties of the Green's function and of the Bethe-Salpeter wave function are reviewed. The infinitesimal gauge transformation laws of the constraint theory wave functions and potentials are determined. The case of the local approximation of potentials is considered. The general properties of the gauge transformations in the local approximation are studied. (K.A.)

  11. A universality test of the quantum string Bethe ansatz

    DEFF Research Database (Denmark)

    Freyhult, L.; Kristjansen, C.

    2006-01-01

    We show that the quantum corrected string Bethe ansatz passes an important universality test by demonstrating that it correctly incorporates the non-analytical terms in the string sigma model one-loop correction for rational three-spin strings with two out of the three spins identical. Subsequent......, we use the quantum corrected string Bethe ansatz to predict the exact form of the non-analytic terms for the generic rational three-spin string.......We show that the quantum corrected string Bethe ansatz passes an important universality test by demonstrating that it correctly incorporates the non-analytical terms in the string sigma model one-loop correction for rational three-spin strings with two out of the three spins identical. Subsequently...

  12. Exact solution of the p + ip pairing Hamiltonian and a hierarchy of integrable models

    International Nuclear Information System (INIS)

    Dunning, Clare; Ibañez, Miguel; Sierra, Germán; Links, Jon; Zhao, Shao-You

    2010-01-01

    Using the well-known trigonometric six-vertex solution of the Yang–Baxter equation we derive an integrable pairing Hamiltonian with anyonic degrees of freedom. The exact algebraic Bethe ansatz solution is obtained using standard techniques. From this model we obtain several limiting models, including the pairing Hamiltonian with p + ip-wave symmetry. An in-depth study of the p + ip model is then undertaken, including a mean-field analysis, analytical and numerical solutions of the Bethe ansatz equations and an investigation of the topological properties of the ground-state wavefunction. Our main result is that the ground-state phase diagram of the p + ip model consists of three phases. There is the known boundary line with gapless excitations that occurs for vanishing chemical potential, separating the topologically trivial strong pairing phase and the topologically non-trivial weak pairing phase. We argue that a second boundary line exists separating the weak pairing phase from a topologically trivial weak coupling BCS phase, which includes the Fermi sea in the limit of zero coupling. The ground state on this second boundary line is the Moore–Read state

  13. Nonperturbative calculation of the shear viscosity in hot $\\phi^{4}$ theory in real time

    CERN Document Server

    Wang, E; Wang, Enke; Heinz, Ulrich

    1999-01-01

    Starting from the Kubo formula we calculate the shear viscosity in hot phi**4 theory nonperturbatively by resumming ladders with a real-time version of the Bethe-Salpeter equation at finite temperature. In the weak coupling limit, the generalized Fluctuation-Dissipation Theorem is shown to decouple the Bethe-Salpeter equations for the different real-time components of the 4-point function. The resulting scalar integral equation is identical with the one obtained by Jeon using diagrammatic ``cutting rules'' in the Imaginary Time Formalism.

  14. Power counting of various Dirac covariants in hadronic Bethe–Salpeter wave functions for pseudoscalar meson decays

    International Nuclear Information System (INIS)

    Bhatnagar, S.; Li, Shiyuan; Mahecha, J.

    2011-01-01

    We have employed the framework of Bethe–Salpeter equation under covariant instantaneous ansatz to calculate leptonic decay constants of unequal mass pseudoscalar mesons like π ± , K, D, D S and B, and radiative decay constants of neutral pseudoscalar mesons like π 0 and η c into two photons. In the Dirac structure of hadronic Bethe–Salpeter wave function, the covariants are incorporated from their complete set in accordance with a recently proposed power counting rule. The contribution of both leading order and next-to-leading order Dirac covariants to decay constants are studied. The results are found to improve and hence validating the power counting rule which provides a practical means of incorporating Dirac covariants in the Bethe–Salpeter wave function for a hadron. (author)

  15. The two-body problem of a pseudo-rigid body and a rigid sphere

    DEFF Research Database (Denmark)

    Kristiansen, Kristian Uldall; Vereshchagin, M.; Gózdziewski, K.

    2012-01-01

    n this paper we consider the two-body problem of a spherical pseudo-rigid body and a rigid sphere. Due to the rotational and "re-labelling" symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow a reduction procedure similar to that undertaken...... in the study of the two-body problem of a rigid body and a sphere so that the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the notions of locally central and planar equilibria coincide. Finally, we show that Riemann's theorem on pseudo......-rigid bodies has an extension to this system for planar relative equilibria....

  16. Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians

    Science.gov (United States)

    Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.

    2011-12-01

    The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

  17. Greenberger-Horne-Zeilinger states and few-body Hamiltonians.

    Science.gov (United States)

    Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V

    2011-12-23

    The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

  18. Obituary: Hans Albrecht Bethe, 1906-2005

    Science.gov (United States)

    Wijers, Ralph

    2007-12-01

    head-on and not allowing himself to be side-tracked by those who would deem the problem be much more complex and difficult, moving straight forward like an intellectual battleship ("The H.A. Bethe Way," as his collaborator Gerald E. Brown would dub the style). Bethe's involvement in the Project brought to light his abilities in the managerial and political arena, which he used later to much effect to influence the wider world; he was among those who fought hard during the Cold War to contain the impact of the terrible weapons he had helped invent. As his two children, Henry and Monica, were born, the war years also made him a family man. As his father did with him, he often took them on long walks, in the hills around Ithaca or further afield; he much enjoyed walking, and mountains. Just after the war, during and following the June 1947 Shelter Island Conference, Bethe made another of his great contributions to physics—some might say his greatest. The experiments by Willis Lamb and Robert Retherford, on what came to be known as the "Lamb shift," were discussed, and during the meeting the assembled crowd (Richard Feynman, Julian Schwinger, and Hendrick Kramers among them) got stuck on the infinities of QED. During the train ride home, Bethe managed to compute the correct answer by realizing that the complex QED machinery could be bypassed, the H.A. Bethe Way. His 1967 Nobel Prize spurred a brief revival of Bethe's interest in astrophysics, but his work in the following years continued to focus on nuclear physics and dense matter (and disarmament and nuclear power, of course). In 1978 he re-entered astrophysics with a bang: Bethe was losing interest in nuclear physics and, after a few years of trying, Gerry Brown lured him back to astrophysics during a stay at the Nordic Institute for Theoretical Physics (NORDITA). The refugee from Hitler and the refugee from McCarthy jointly attacked the problem of supernova collapse. Bethe had the crucial insight that the low entropy

  19. Charm-conserving strangeness-changing two body hadronic decays of charmed baryons

    International Nuclear Information System (INIS)

    Khanna, M.P.

    1993-10-01

    The charm-conserving strangeness-changing two body hadronic decays of charmed baryons are examined in the SU(4) symmetry scheme. In addition to the 20''-Hamiltonian, we consider a 15-piece of the weak Hamiltonian which may arise due to SU(4) breaking or due to some non-conventional dynamics. The numerical estimates for decay widths of some of the modes are presented. (author). 15 refs, 3 tabs

  20. Meson-meson bound state in a 2+1 lattice QCD model with two flavors and strong coupling

    International Nuclear Information System (INIS)

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

    2005-01-01

    We consider the existence of bound states of two mesons in an imaginary-time formulation of lattice QCD. We analyze an SU(3) theory with two flavors in 2+1 dimensions and two-dimensional spin matrices. For a small hopping parameter and a sufficiently large glueball mass, as a preliminary, we show the existence of isoscalar and isovector mesonlike particles that have isolated dispersion curves (upper gap up to near the two-particle threshold ∼-4lnκ). The corresponding meson masses are equal up to and including O(κ 3 ) and are asymptotically of order -2lnκ-κ 2 . Considering the zero total isospin sector, we show that there is a meson-meson bound state solution to the Bethe-Salpeter equation in a ladder approximation, below the two-meson threshold, and with binding energy of order bκ 2 ≅0.02359κ 2 . In the context of the strong coupling expansion in κ, we show that there are two sources of meson-meson attraction. One comes from a quark-antiquark exchange. This is not a meson exchange, as the spin indices are not those of the meson particle, and we refer to this as a quasimeson exchange. The other arises from gauge field correlations of four overlapping bonds, two positively oriented and two of opposite orientation. Although the exchange part gives rise to a space range-one attractive potential, the main mechanism for the formation of the bound state comes from the gauge contribution. In our lattice Bethe-Salpeter equation approach, this mechanism is manifested by an attractive distance-zero energy-dependent potential. We recall that no bound state appeared in the one-flavor case, where the repulsive effect of Pauli exclusion is stronger

  1. Light tetraquarks and mesons in a DSE/BSE approach

    Energy Technology Data Exchange (ETDEWEB)

    Heupel, Walter

    2015-07-01

    Bound states and their properties are an inherent non-perturbative feature of QCD. Moreover, QCD is a confining theory so that instead of the elementary quarks and gluons themselves, only colourless bound states formed of these elementary particles are directly measurable. One non-perturbative framework to describe QCD are the Dyson-Schwinger equations, which interrelate all Green functions of the theory by an infinite tower of integral equations, and the corresponding Bethe-Salpeter equations that define the bound states of the theory. To reduce the infinite tower to a tractable form, the equations have to be truncated. In this thesis the so-called rainbow ladder' truncation was used that reduces the quark-gluon vertex to the bare vertex and replaces the gluon by an effective modeled one so that the only Green function that has to be solved, is the quark propagator. This truncation preserves the important axial Ward-Takahashi-identity and the Gell-Mann-Oakes-Renner relation. For the effective gluon the Maris-Tandy interaction was used, modeled to reproduce the pion mass and decay constant. Starting from this well-established truncation, the four-body tetraquark Bethe-Salpeter equation was constructed. To solve the tetraquark Bethe-Salpeter equation, a fully covariant basis for the tetraquark amplitude is necessary. Additionally, the basis has to reflect the quantum numbers of the tetraquark and has to fulfill the Pauli principle. The construction of such a basis was performed for all parts of the amplitude: The Dirac-tensor structure, the phase space, the colour and the flavour tensor structure. Upon solving the tetraquark bound state equation, dynamical pion poles in the tetraquark amplitude phase space appeared, reflecting the actual physics that determines the tetraquark: The tetraquark is dominated by two-body correlations which manifest themselves as poles in the phase space. It is especially noteworthy that these two-body correlations in form of poles

  2. Magnetic properties of the mixed ferrimagnetic ternary system with a single-ion anisotropy on the Bethe lattice

    Energy Technology Data Exchange (ETDEWEB)

    Deviren, Bayram [Institute of Science, Erciyes University, 38039 Kayseri (Turkey); Canko, Osman [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); School of Computational Science, Florida State University, Tallahassee, FL 32306-4120 (United States); Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)], E-mail: keskin@erciyes.edu.tr

    2009-05-15

    The magnetic properties of the ternary system ABC consisting of spins {sigma}=1/2 , S=1, and m=3/2 are investigated on the Bethe lattice by using the exact recursion relations. We consider both ferromagnetic and antiferromagnetic exchange interactions. The exact expressions for magnetizations and magnetic susceptibilities are found, and thermal behaviors of magnetizations and susceptibilities are studied. We construct the phase diagrams and find that the system exhibits one, two or even three compensation temperatures depending on the values of the interaction parameters in the Hamiltonian. Moreover, the system undergoes a second-order phase transition for the coordination number q{<=}3 and a second- and first-order phase transitions for q>3; hence the system gives a tricritical point. The system also exhibits the reentrant behaviors.

  3. Magnetic properties of the mixed ferrimagnetic ternary system with a single-ion anisotropy on the Bethe lattice

    International Nuclear Information System (INIS)

    Deviren, Bayram; Canko, Osman; Keskin, Mustafa

    2009-01-01

    The magnetic properties of the ternary system ABC consisting of spins σ=1/2 , S=1, and m=3/2 are investigated on the Bethe lattice by using the exact recursion relations. We consider both ferromagnetic and antiferromagnetic exchange interactions. The exact expressions for magnetizations and magnetic susceptibilities are found, and thermal behaviors of magnetizations and susceptibilities are studied. We construct the phase diagrams and find that the system exhibits one, two or even three compensation temperatures depending on the values of the interaction parameters in the Hamiltonian. Moreover, the system undergoes a second-order phase transition for the coordination number q≤3 and a second- and first-order phase transitions for q>3; hence the system gives a tricritical point. The system also exhibits the reentrant behaviors

  4. An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.

    Science.gov (United States)

    Ilias, Miroslav; Saue, Trond

    2007-02-14

    The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.

  5. Experimental Hamiltonian identification for controlled two-level systems

    International Nuclear Information System (INIS)

    Schirmer, S.G.; Kolli, A.; Oi, D.K.L.

    2004-01-01

    We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable

  6. Superconductivity in a Repulsive Model

    DEFF Research Database (Denmark)

    Feldman, Joel; Knoerrer, Horst; Sinclair, Robert

    1997-01-01

    A two-dimensional system of Fermions with classical dispersion relationand a purely repulsive delta function pair potential generates the dominant attractive coupling in the third order Bethe-Salpeter approximation for the Cooper channel. This suggests that the ground state is an l=1 superconductor....

  7. Derivation of a configuration space Hamiltonian for heavy atoms: three body potentials

    International Nuclear Information System (INIS)

    Mittleman, M.H.

    1981-01-01

    A brief history of the difficulties associated with the derivation of a configuration space Hamiltonian is presented. One of the problems encountered is the definition of the projection operators which must occur. A variational definition is obtained and, with simplifying assumptions, the optimum projection operators are those which project onto Hartree-Fock orbitals. This puts many previously performed numerical calculations on a firm footing. The form of the two body interactions is discussed in the context of the gauge freedom. The Coulomb gauge is the favored one but it is pointed out that it has never been proven to be the best one. Finally a form for the relativistic three election potential is given and the possibility of its observation is discussed

  8. Effective Hamiltonians, two level systems, and generalized Maxwell-Bloch equations

    International Nuclear Information System (INIS)

    Sczaniecki, L.

    1981-02-01

    A new method is proposed involving a canonical transformation leading to the non-secular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating wave approximation is written anew within the framework of our formalism. (author)

  9. Comparison of different boost transformations for the calculation of form factors in relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Theussl, L.; Noguera, S.; Amghar, A.; Desplanques, B.

    2003-01-01

    The effect of different boost expressions, pertinent to the instant, front and point forms of relativistic quantum mechanics, is considered for the calculation of the ground-state form factor of a two-body system in simple scalar models. Results with a Galilean boost as well as an explicitly covariant calculation based on the Bethe-Salpeter approach are given for comparison. It is found that the present so-called point-form calculations of form factors strongly deviate from all the other ones. This suggests that the formalism which underlies them requires further elaboration. A proposition in this sense is made. (author)

  10. Hans Bethe, Powering the Stars, and Nuclear Physics

    Science.gov (United States)

    dropdown arrow Site Map A-Z Index Menu Synopsis Hans Bethe, Energy Production in Stars, and Nuclear Physics physics, built atomic weapons, and called for a halt to their proliferation. Bethe's dual legacy is one of Laboratory] from 1943 to 1946. Prior to joining the Manhattan Project, Bethe taught physics at Cornell

  11. Absence of level-repulsion in a two-state Hamiltonian

    International Nuclear Information System (INIS)

    Ahmed, Zafar

    2007-01-01

    But for the inclusion of scattering states, we point out that the two-state method (the so called perturbation method of nearly degenerate levels) for a perturbed two-state Hamiltonian is exact , yet the prediction of the level-repulsion by this method could be contradicted by the exact quantal eigenvalues. (author)

  12. Three-body unitary transformations, three-body forces, and trinucleon bound state properties

    International Nuclear Information System (INIS)

    Haftel, M.I.

    1976-01-01

    A three-body unitary transformation method for the study of three-body forces is presented. Starting with a three-body Hamiltonian with two-body forces, unitary transformations are introduced to generate Hamiltonians that have both two- and three-body forces. For cases of physical interest, the two-body forces of the altered Hamiltonians are phase equivalent (for two-body scattering) to the original and the three-body force vanishes when any interparticle distance is large. Specific examples are presented. Applications for studying the possible role of three-body forces in accounting for trinucleon bound state properties are examined. Calculations of the 3 He and 3 H charge form factors and Coulomb energy difference with hyperspherical radial transformations and with conventional N-N potentials are performed. The form factor calculations demonstrate how the proposed method can help obtain improved agreement with experiment by the introduction of appropriate three-body forces. Calculations of the Coulomb energy difference confirm previous estimates concerning charge symmetry breaking in the N-N interaction

  13. Quark-gluon vertex dressing and meson masses beyond ladder-rainbow truncation

    International Nuclear Information System (INIS)

    Matevosyan, Hrayr H.; Thomas, Anthony W.; Tandy, Peter C.

    2007-01-01

    We include a generalized infinite class of quark-gluon vertex dressing diagrams in a study of how dynamics beyond the ladder-rainbow truncation influences the Bethe-Salpeter description of light-quark pseudoscalar and vector mesons. The diagrammatic specification of the vertex is mapped into a corresponding specification of the Bethe-Salpeter kernel, which preserves chiral symmetry. This study adopts the algebraic format afforded by the simple interaction kernel used in previous work on this topic. The new feature of the present work is that in every diagram summed for the vertex and the corresponding Bethe-Salpeter kernel, each quark-gluon vertex is required to be the self-consistent vertex solution. We also adopt from previous work the effective accounting for the role of the explicitly non-Abelian three-gluon coupling in a global manner through one parameter determined from recent lattice-QCD data for the vertex. Within the current model, the more consistent dressed vertex limits the ladder-rainbow truncation error for vector mesons to be never more than 10% as the current quark mass is varied from the u/d region to the b region

  14. In Memoriam: Hans Bethe

    Science.gov (United States)

    Garwin, Richard L.; Von Hippel, Frank

    Hans Bethe, who died on March 6 at the age of 98, was exemplary as a scientist; a citizen-advocate seeking to stem the arms race; and an individual of warmth, generosity, tenacity, and modest habits. Bethe made major contributions to several areas of physics during his academic career. He earned a Nobel Prize in 1967 for his research into how the sun generates its energy by converting hydrogen to helium using carbon as a nuclear catalyst. A few years later, he made central contributions to the secret US World War II nuclear-weapon development programs (the "Manhattan Project").

  15. Covariant meson-baryon scattering with chiral and large Nc constraints

    International Nuclear Information System (INIS)

    Lutz, M.F.M.; Kolomeitsev, E.E.

    2001-05-01

    We give a review of recent progress on the application of the relativistic chiral SU(3) Lagrangian to meson-baryon scattering. It is shown that a combined chiral and 1/N c expansion of the Bethe-Salpeter interaction kernel leads to a good description of the kaon-nucleon, antikaon-nucleon and pion-nucleon scattering data typically up to laboratory momenta of p lab ≅ 500 MeV. We solve the covariant coupled channel Bethe-Salpeter equation with the interaction kernel truncated to chiral order Q 3 where we include only those terms which are leading in the large N c limit of QCD. (orig.)

  16. Hyperon interaction in free space and nuclear matter

    Energy Technology Data Exchange (ETDEWEB)

    Dhar, Madhumita [Justus-Liebig University Giessen (Germany); Lenske, Horst [Justus-Liebig University Giessen (Germany); GSI, Darmstadt (Germany)

    2016-07-01

    A new approach to the SU(3) flavour symmetric meson-exchange model is introduced to describe free space baryon-baryon interaction. The Bethe-Salpeter equations are solved in a 3-D reduction scheme. The coupling of the various channels of total strangeness S and conserved total charge Q is studied in detail. Special attention is paid to the physical thresholds. The derived vacuum interaction has then been used to derive nuclear medium effect by employing the Pauli projector operator in 3-D reduced Bethe-Salpeter equation. The in-medium properties of the interaction are clearly seen in the variation of the in-medium low-energy parameters as a function of density.

  17. A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity

    Energy Technology Data Exchange (ETDEWEB)

    Correggi, M., E-mail: michele.correggi@gmail.com [Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, Dipartimento di Matematica e Fisica (Italy); Dell’Antonio, G. [“Sapienza” Università di Roma, P.le A. Moro 5, Dipartimento di Matematica (Italy); Finco, D. [Università Telematica Internazionale Uninettuno, Corso V. Emanuele II 39, Facoltà di Ingegneria (Italy); Michelangeli, A. [Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265 (Italy); Teta, A. [“Sapienza” Università di Roma, P.le A. Moro 5, Dipartimento di Matematica (Italy)

    2015-12-15

    We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass m, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for m larger than a critical value m{sup ∗} ≃ (13.607){sup −1} a self-adjoint and lower bounded Hamiltonian H{sub 0} can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for m ∈ (m{sup ∗},m{sup ∗∗}), where m{sup ∗∗} ≃ (8.62){sup −1}, there is a further family of self-adjoint and lower bounded Hamiltonians H{sub 0,β}, β ∈ ℝ, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.

  18. A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity

    International Nuclear Information System (INIS)

    Correggi, M.; Dell’Antonio, G.; Finco, D.; Michelangeli, A.; Teta, A.

    2015-01-01

    We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass m, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for m larger than a critical value m ∗ ≃ (13.607) −1 a self-adjoint and lower bounded Hamiltonian H 0 can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for m ∈ (m ∗ ,m ∗∗ ), where m ∗∗ ≃ (8.62) −1 , there is a further family of self-adjoint and lower bounded Hamiltonians H 0,β , β ∈ ℝ, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide

  19. Nuclear forces the making of the physicist Hans Bethe

    CERN Document Server

    Schweber, Silvan S

    2012-01-01

    On the fiftieth anniversary of Hiroshima, Nobel-winning physicist Hans Bethe called on his fellow scientists to stop working on weapons of mass destruction. What drove Bethe, the head of Theoretical Physics at Los Alamos during the Manhattan Project, to renounce the weaponry he had once worked so tirelessly to create? That is one of the questions answered by "Nuclear Forces", a riveting biography of Bethe's early life and development as both a scientist and a man of principle. As Silvan Schweber follows Bethe from his childhood in Germany, to laboratories in Italy and England, and on to Cornell University, he shows how these differing environments were reflected in the kind of physics Bethe produced. Many of the young quantum physicists in the 1930s, including Bethe, had Jewish roots, and Schweber considers how Liberal Judaism in Germany helps explain their remarkable contributions. A portrait emerges of a man whose strategy for staying on top of a deeply hierarchical field was to tackle only those problems h...

  20. Bethe vectors for XXX-spin chain

    Science.gov (United States)

    Burdík, Čestmír; Fuksa, Jan; Isaev, Alexei

    2014-11-01

    The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra are expressed in basis of free fermions and used to calculate explicit form of Bethe vectors. Their relation to N-component models is used to prove conjecture about their form in general. Some remarks on inhomogeneous XXX-spin chain are included.

  1. Bethe vectors for XXX-spin chain

    International Nuclear Information System (INIS)

    Burdík, Čestmír; Fuksa, Jan; Isaev, Alexei

    2014-01-01

    The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra are expressed in basis of free fermions and used to calculate explicit form of Bethe vectors. Their relation to N-component models is used to prove conjecture about their form in general. Some remarks on inhomogeneous XXX-spin chain are included

  2. Large N and Bethe ansatz

    OpenAIRE

    Jurco, B.

    2003-01-01

    We describe an integrable model, related to the Gaudin magnet, and its relation to the matrix model of Brezin, Itzykson, Parisi and Zuber. Relation is based on Bethe ansatz for the integrable model and its interpretation using orthogonal polynomials and saddle point approximation. Lagre $N$ limit of the matrix model corresponds to the thermodynamic limit of the integrable system. In this limit (functional) Bethe ansatz is the same as the generating function for correlators of the matrix models.

  3. Spin-1 and -2 bilayer Bethe lattice: A Monte Carlo study

    International Nuclear Information System (INIS)

    Masrour, R.; Jabar, A.; Benyoussef, A.; Hamedoun, M.

    2016-01-01

    The magnetic behaviors of bilayer with spin-1 and 2 Ising model on the Bethe lattice are investigated using the Monte Carlo simulations. The thermal magnetizations, the magnetic susceptibilities and the transition temperature of the bilayer spin-1 and 2 on the Bethe lattice are studied for different values of crystal field and intralayer coupling constants of the two layers and interlayer coupling constant between the layers. The thermal and magnetic hysteresis cycles are given for different values of the crystal field, for different temperatures and for different exchange interactions. - Highlights: • The magnetic properties of bilayer on the Bethe lattice have been investigated. • The transition temperature has been deduced. • The magnetic coercive filed has been established.

  4. Spin-1 and -2 bilayer Bethe lattice: A Monte Carlo study

    Energy Technology Data Exchange (ETDEWEB)

    Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000 Safi (Morocco); Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Jabar, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Benyoussef, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)

    2016-03-01

    The magnetic behaviors of bilayer with spin-1 and 2 Ising model on the Bethe lattice are investigated using the Monte Carlo simulations. The thermal magnetizations, the magnetic susceptibilities and the transition temperature of the bilayer spin-1 and 2 on the Bethe lattice are studied for different values of crystal field and intralayer coupling constants of the two layers and interlayer coupling constant between the layers. The thermal and magnetic hysteresis cycles are given for different values of the crystal field, for different temperatures and for different exchange interactions. - Highlights: • The magnetic properties of bilayer on the Bethe lattice have been investigated. • The transition temperature has been deduced. • The magnetic coercive filed has been established.

  5. Analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation

    International Nuclear Information System (INIS)

    Durand, B.; Durand, L.

    1983-01-01

    We construct an analytic solution to the spinless S-wave Salpeter equation for two quarks interacting via a Coulomb potential, [2(-del 2 +m 2 )/sup 1/2/-M-α/r] psi(r) = 0, by transforming the momentum-space form of the equation into a mapping or boundary-value problem for analytic functions. The principal part of the three-dimensional wave function is identical to the solution of a one-dimensional Salpeter equation found by one of us and discussed here. The remainder of the wave function can be constructed by the iterative solution of an inhomogeneous singular integral equation. We show that the exact bound-state eigenvalues for the Coulomb problem are M/sub n/ = 2m/(1+α 2 /4n 2 )/sup 1/2/, n = 1,2,..., and that the wave function for the static interaction diverges for r→0 as C(mr)/sup -nu/, where #betta# = (α/π)(1+α/π+...) is known exactly

  6. Coulomb two-body problem with internal structure

    International Nuclear Information System (INIS)

    Kuperin, Yu.A.; Makarov, K.A.; Mel'nikov, Yu.B.

    1988-01-01

    The methods of the theory of extensions to an enlarged Hilbert space are used to construct a model of the interaction of the external (Coulomb) and internal (quark) channels in the two-body problem. The mutual influence of the spectra of the corresponding channel Hamiltonians is studied: it leads, in particular, to a rearrangement of the spectra of hadronic atoms. An explicit representation is obtained for the S matrix, and its singularities on the energy shell are studied

  7. Exotic states in the S=1 N-pi-K system and low-lying 1/2+ S=-1 resonances

    Directory of Open Access Journals (Sweden)

    Oset E.

    2010-04-01

    Full Text Available In this manuscript we discuss about our study of the $N pi ar{K}$ and the NπK systems made by solving the Faddeev equations with the two-body t-matrices obtained by solving the Bethe-Salpeter equations with the potentials obtained from chiral dynamics. In the strangeness = -1 case, we found that all the Λ and Σ resonances listed by the particle data group, with spin-parity 1/2+ , in the 1550-1800 MeV region get generated due to the involved three-body dynamics. This motivated us to study the strangeness =1 three-body system, i.e., NπK , where we did not find any evidence for the Θ+ (1542 but found a broad bump around 1700 MeV which has a κ(800N structure.

  8. Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle

    Science.gov (United States)

    Wang, Hong

    2017-09-01

    In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.

  9. Symmetry-adaptation and selection rules for effective crystal field Hamiltonians

    International Nuclear Information System (INIS)

    Tuszynski, J.A.

    1986-01-01

    The intention of this paper is to systematically derive an effective Hamiltonian in the presence of crystal fields in such a way as to incorporate relativistic effects and higher order perturbation corrections including configuration mixing. This Hamiltonian will then be conveniently represented as a symmetry-adapted series of one- and two-body double tensor operators whose matrix elements will be analyzed for selection rules. 16 references, 4 tables

  10. On the proton exchange contribution to electron-hydrogen atom elastic scattering

    International Nuclear Information System (INIS)

    Mignaco, J.A.; Tort, A.C.

    1979-05-01

    It is shown that the exchange contribution to the electron-proton potential Born term in elastic electron-hydrogen atom scattering arises as the non relativistic limit from the exchange of a proton between the two participant electrons - calculated from quantum electrodynamics including properly bound states (as solution of Bethe - Salpeter equation). (Author) [pt

  11. Practitioner Profile: An Interview with Beth Crittenden

    Directory of Open Access Journals (Sweden)

    Martie Gillen

    2016-12-01

    Full Text Available Beth Crittenden offers financial wellness coaching to people who want growth both professionally and personally. Beth has been working with finances as a focus since 2009, after training in somatic psychology, healthy communication in relationship, and mindful meditation practices and theory.

  12. Quasi-superconformal algebras in two dimensions and hamiltonian reduction

    International Nuclear Information System (INIS)

    Romans, L.J.

    1991-01-01

    In the standard quantum hamiltonian reduction, constraining the SL(3, R) WZNW model leads to a model of Zamolodchikov's W 3 -symmetry. In recent work, Polyakov and Bershadsky have considered an alternative reduction which leads to a new algebra, W 3 2 , a nonlinear extension of the Virasoro algebra by a spin-1 current and two bosonic spin-3/2 currents. Motivated by this result, we display two new infinite series of nonlinear extended conformal algebras, containing 2N bosonic spin-3/2 currents and spin-1 Kac-Moody currents for either U(N) or Sp(2 N); the W 3 2 algebra appears as the N = 1 member of the U(N) series. We discuss the relationship between these algebras and the Knizhnik-Bershadsky superconformal algebras, and provide realisations in terms of free fields coupled to Kac-Moody currents. We propose a specific procedure for obtaining the algebras for general N through hamiltonian reduction. (orig.)

  13. High energy asymptotics of perturbative multi-color QCD

    International Nuclear Information System (INIS)

    Lipatov, L.N.

    1993-01-01

    The structure functions of deep-inelastic scattering at small-x satisfy two different equations in the leading logarithmic approximation (LLA). The first one -- the GLAP equation, describes the Q 2 -evolution of partonic distributions h i (x). The second one -- the BFKL, equation determines the x-dependence of parton densities H i (x, k perpendicular ). Analogous equations for matrix elements of higher twist operators were constructed in Refs. 3 and 4. Here the author discusses the possibility of finding an exact solution for multi-gluon compound states in LLA for the color group SU(N), in the limit N → ∞. The contributions of diagrams with many reggeized gluons are important for the unitarization of the perturbative Pomeron in QCD. It is shown that the Bethe-Salpeter equations for compound states of many reggeized gluons are conformally invariant in the two-dimensional impact parameter space. Their solutions can be written in holomorphically factorized form and there is a differential operator commuting with the holomorphic part of the corresponding Hamiltonian

  14. Heavy-to-light correlators beyond the light cone

    International Nuclear Information System (INIS)

    Lucha, W.; Melikhov, D. I.; Simula, S.

    2008-01-01

    We present the first systematic analysis of the off-light-cone effects in correlators relevant for the extraction of the heavy-to-light form factors within the method of light-cone sum rules. In a model with scalar constituents, the correlator is calculated in two different ways: (i) by performing the expansion of the Bethe-Salpeter amplitude of the light meson near the light cone x 2 = 0 and (ii) by adopting the known solution for the Bethe-Salpeter amplitude which allows one to calculate the correlator without invoking any expansion. We demonstrate that the contributions to the correlator from the off-light-cone terms x 2 ≠ 0 are not suppressed by any large parameter compared to the contribution of the light-cone term x 2 0. For decays of heavy particles of mass in the range 1.5-5 GeV, the light-cone correlator is shown to systematically overestimate the full correlator, numerically the difference being 10-20%

  15. Heavy-to-light correlators beyond the light cone

    International Nuclear Information System (INIS)

    Lucha, W.; Melikhov, D. I.; Simula, S.

    2008-01-01

    We present the first systematic analysis of the off-light-cone effects in correlators relevant for the extraction of the heavy-to-light form factors within the method of light-cone sum rules. In a model with scalar constituents, the correlator is calculated in two different ways: (i) by performing the expansion of the Bethe-Salpeter amplitude of the light meson near the light cone x 2 = 0 and (ii) by adopting the known solution for the Bethe-Salpeter amplitude which allows one to calculate the correlator without invoking any expansion. We demonstrate that the contributions to the correlator from the off-light-cone terms x 2 ≠ 0 are not suppressed by any large parameter compared to the contribution of the light-cone term x 2 = 0. For decays of heavy particles of mass in the range 1.5–5 GeV, the light-cone correlator is shown to systematically overestimate the full correlator, numerically the difference being 10–20%.

  16. Bound state quantum field theory application to atoms and ions

    CERN Document Server

    Sapirstein, Jonathan

    2019-01-01

    Two aspects of the book should appeal to a wide audience. One aspect would be the comprehensive coverage on the latest updates and developments this book provides, besides Bethe and Salpeter's handbook on hydrogen and helium, which is still widely regarded as useful. The other aspect would be that a major part of the book uses “effective field theory”, a way of including quantum electrodynamics (QED) that starts with the familiar Schrödinger equation, and then adds perturbing operators derived in a rather simple manner that incorporates QED. Effective field theory is used in a number of fields including particle physics and nuclear physics, and readership is targeted at these communities too.Additionally, students using this book in conjunction with Peskin's textbook could learn to carry out fairly sophisticated calculations in QED in order to learn the technique, as this book comes with practical calculations.Also included is a very clear exposition of the Bethe–Salpeter equation, which is simply either ...

  17. The Bethe wavefunction

    CERN Document Server

    Gaudin, Michel

    2014-01-01

    Michel Gaudin's book La fonction d'onde de Bethe is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics. Available in English for the first time, this translation brings his classic work to a new generation of graduate students and researchers in physics. It presents a mixture of mathematics interspersed with powerful physical intuition, retaining the author's unmistakably honest tone. The book begins with the Heisenberg spin chain, starting from the coordinate Bethe Ansatz and culminating in a discussion of its thermodynamic properties. Delta-interacting bosons (the Lieb-Liniger model) are then explored, and extended to exactly solvable models associated to a reflection group. After discussing the continuum limit of spin chains, the book covers six- and eight-vertex models in extensive detail, from their lattice definition to their thermodynamics. Later chapters examine advanced topics such as multi-component delta-interacting systems, Gaudin magnets and...

  18. Effective Hamiltonian theory: recent formal results and non-nuclear applications

    International Nuclear Information System (INIS)

    Brandow, B.H.

    1981-01-01

    Effective Hamiltonian theory is discussed from the points of view of the unitary transformation method and degenerate perturbation theory. It is shown that the two approaches are identical term by term. The main features of a formulation of the coupled-cluster method for open-shell systems are outlined. Finally, recent applications of the many-body linked-cluster form of degenerate perturbation theory are described: the derivation of effective spin Hamiltonians in magnetic insulator systems, the derivation and calculation ab initio of effective π-electron Hamiltonians for planar conjugated hydrocarbon molecules, and understanding the so-called valence fluctuation phenomenon exhibited by certain rare earth compounds

  19. Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models

    Science.gov (United States)

    Ghosh, Pijush K.; Sinha, Debdeep

    2018-01-01

    A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occurs in a pairwise fashion. It is also shown that with the choice of a suitable co-ordinate, the Hamiltonian can always be reformulated in the background of a pseudo-Euclidean metric. If the equations of motion of some of the well-known many-body systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion are constructed. The examples include a coupled chain of nonlinear oscillators and a many-particle Calogero-type model with four-body inverse square plus two-body pair-wise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the loss and gain parameter has unbounded upper range. Further, the range of the parameter for which the stable solutions are obtained is independent of the total number of the oscillators. The set of coupled nonlinear equations are solved exactly for the case when the values of all the constants of motions except the Hamiltonian are equal to zero. Exact, analytical classical solutions are presented for all the examples considered.

  20. Off-diagonal Bethe ansatz for exactly solvable models

    CERN Document Server

    Wang, Yupeng; Cao, Junpeng; Shi, Kangjie

    2015-01-01

    This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix.  These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.

  1. Renormalization of Hamiltonians

    International Nuclear Information System (INIS)

    Glazek, S.D.; Wilson, K.G.

    1993-01-01

    This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method

  2. General QED/QCD aspects of simple systems

    International Nuclear Information System (INIS)

    Telegdi, V.L.; Brodsky, S.J.

    1989-09-01

    This paper discusses the following topics: renormalization theory; the Kinoshita-Lee-Nauenberg theorem; the Yennie-Frautschi-Suura relation; scale invariance at large momentum transfer; scaling and scaling violation at large momentum transfers; low-energy theorem in Compton scattering; does the perturbation series in QED converge; renormalization of the weak angle Θ w ; the Nambu-Bethe-Salpeter (NBS) equation; the decay rate of 3 S, positronium; radiative corrections to QCD Born cross section; and progress on the relativistic 2-body equation

  3. The Bethe Wavefunction

    NARCIS (Netherlands)

    Gaudin, M.; Caux, J.-S.

    2014-01-01

    Michel Gaudin's book La fonction d'onde de Bethe is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics. Available in English for the first time, this translation brings his classic work to a new generation of graduate students and researchers

  4. Optical absorption spectra of semiconductors and insulators: ab initio calculation of many-body effects

    International Nuclear Information System (INIS)

    Albrecht, Stefan

    1999-01-01

    A method for the inclusion of self-energy and excitonic effects in first-principle calculations of absorption spectra, within the state-of-the-art plane wave pseudopotential approach, is presented. Starting from a ground state calculation, using density functional theory (DFT) in the local density approximation (LDA), we correct the exchange-correlation potential of DFT-LDA with the self-energy applying Hedin's GW approximation to obtain the physical quasiparticles states. The electron-hole interaction is treated solving an effective two-particle equation, which we derive from Hedin's coupled integral equations, leading to the fundamental Bethe-Salpeter equation in an intermediate step. The interaction kernel contains the screened electron-hole Coulomb interaction and the electron-hole exchange effects, which reflect the microscopic structure of the system and are thus also called local-field effects. We obtain the excitonic eigenstates through diagonalization. This allows us a detailed analysis of the optical properties. The application of symmetry properties enables us to reduce the size of the two-particle Hamiltonian matrix, thus minimizing the computational effort. We apply our method to silicon, diamond, lithium oxide and the sodium tetramer. Good agreement with experiment is obtained for the absorption spectra of Si and diamond, the static dielectric constant of diamond, and for the onset of optical absorption of Li 2 O due to discrete bound excitons. We discuss various approximations of our method and show the strong mixing of independent particle transitions to a bound excitonic state in the Na 4 cluster. The influence of ground state calculations on optical spectra is investigated under particular consideration of the pseudopotential generation and we discuss the use of different Brillouin zone point sampling schemes for spectral calculations. (author) [fr

  5. Comparison of two Minkowski-space approaches to heavy quarkonia

    Energy Technology Data Exchange (ETDEWEB)

    Leitao, Sofia; Biernat, Elmar P. [Universidade de Lisboa, CFTP, Instituto Superior Tecnico, Lisbon (Portugal); Li, Yang [Iowa State University, Department of Physics and Astronomy, Ames, IA (United States); College of William and Mary, Department of Physics, Williamsburg, VA (United States); Maris, Pieter; Vary, James P. [Iowa State University, Department of Physics and Astronomy, Ames, IA (United States); Pena, M.T. [Universidade de Lisboa, CFTP, Instituto Superior Tecnico, Lisbon (Portugal); Universidade de Lisboa, Departamento de Fisica, Instituto Superior Tecnico, Lisbon (Portugal); Stadler, Alfred [Universidade de Lisboa, CFTP, Instituto Superior Tecnico, Lisbon (Portugal); Universidade de Evora, Departamento de Fisica, Evora (Portugal)

    2017-10-15

    In this work we compare mass spectra and decay constants obtained from two recent, independent, and fully relativistic approaches to the quarkonium bound-state problem: the Basis Light-Front Quantization approach, where light-front wave functions are naturally formulated; and, the Covariant Spectator Theory (CST), based on a reorganization of the Bethe-Salpeter equation. Even though conceptually different, both solutions are obtained in Minkowski space. Comparisons of decay constants for more than ten states of charmonium and bottomonium show favorable agreement between the two approaches as well as with experiment where available. We also apply the Brodsky-Huang-Lepage prescription to convert the CST amplitudes into functions of light-front variables. This provides an ideal opportunity to investigate the similarities and differences at the level of the wave functions. Several qualitative features are observed in remarkable agreement between the two approaches even for the rarely addressed excited states. Leading-twist distribution amplitudes as well as parton distribution functions of heavy quarkonia are also analyzed. (orig.)

  6. Construction of Hamiltonians by supervised learning of energy and entanglement spectra

    Science.gov (United States)

    Fujita, Hiroyuki; Nakagawa, Yuya O.; Sugiura, Sho; Oshikawa, Masaki

    2018-02-01

    Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter, nuclear, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely, effective Hamiltonian, is essential. Here, we propose a simple supervised learning algorithm for constructing Hamiltonians from given energy or entanglement spectra. We apply the proposed scheme to the Hubbard model at the half-filling, and compare the obtained effective low-energy spin model with several analytic results based on the high-order perturbation theory, which have been inconsistent with each other. We also show that our approach can be used to construct the entanglement Hamiltonian of a quantum many-body state from its entanglement spectrum as well. We exemplify this using the ground states of the S =1 /2 two-leg Heisenberg ladders. We observe a qualitative difference between the entanglement Hamiltonians of the two phases (the Haldane and the rung singlet phase) of the model due to the different origin of the entanglement. In the Haldane phase, we find that the entanglement Hamiltonian is nonlocal by nature, and the locality can be restored by introducing the anisotropy and turning the ground state into the large-D phase. Possible applications to the model construction from experimental data and to various problems of strongly correlated systems are discussed.

  7. General technique to produce isochronous Hamiltonians

    International Nuclear Information System (INIS)

    Calogero, F; Leyvraz, F

    2007-01-01

    We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra

  8. Hamiltonian description of the ideal fluid

    International Nuclear Information System (INIS)

    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

  9. Part I: quantum fluctuations in chains of Josephson junctions. Part II: directed aggregation on the Bethe lattice

    International Nuclear Information System (INIS)

    Bradley, R.M.

    1985-01-01

    Part I studies the effect of quantum fluctuations of the phase on the low temperature behavior of two models of Josephson junction chains with Coulomb interactions taken into account. The first model, which represents a chain of junctions close to a ground plane, is the Hamiltonian version of the two-dimensional XY model in one space and one time dimension. In the second model, the charging energy for a single junction in the chain is just the parallel-plate capacitor energy. It is shown that quantum fluctuations produce exponential decay of the order parameter correlation junction for any finite value of the junction capacitance. Part II deals with two types of directed aggregation on the Bethe lattice - directed diffusion-limited aggregation DDLA and ballistic aggregation (BA). In the DDLA problem on finite lattices, an exact nonlinear recursion relation is constructed for the probability distribution of the density. The mean density tends to zero as the lattice size is taken into infinity. Using a mapping between the model with perfect adhesion on contact and another model with a particular value of the adhesion probability, it is shown that the adhesion probability is irrelevant over an interval of values

  10. Bayesian extraction of the parton distribution amplitude from the Bethe–Salpeter wave function

    Directory of Open Access Journals (Sweden)

    Fei Gao

    2017-07-01

    Full Text Available We propose a new numerical method to compute the parton distribution amplitude (PDA from the Euclidean Bethe–Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe–Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method (MEM. The Nakanishi weight function as well as the corresponding light-front parton distribution amplitude (PDA can be well determined. We confirm prior work on PDA computations, which was based on different methods.

  11. Meson-baryon interactions in unitarized chiral perturbation theory

    International Nuclear Information System (INIS)

    Garcia Recio, G.; Nieves, J.; Ruiz Arriola, E.; Vicente Vacas, M.

    2003-01-01

    Meson-Baryon Interactions can be successfully described using both Chiral Symmetry and Unitarity. The s-wave meson-baryon scattering amplitude is analyzed in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry in the potential. Two body coupled channel unitarity is exactly preserved. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behavior is parameterized in terms of low energy constants. The relation to the heavy baryon limit is discussed. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths baryonic resonances of the N(1535), N(1670), Λ(1405) and Λ(1670) resonances which compare well with accepted numbers

  12. Professor Hans A Bethe

    Indian Academy of Sciences (India)

    2018-03-06

    Mar 6, 2018 ... These theories formed the deep conceptual foundations of modern ... wrote on nuclear theory in the 1930's, often called 'Bethe's Bible', ... tions to solid state physics, fluid dynamics, shock waves, radar theory and reactor.

  13. The convergence of the binding energy expansion in the Brueckner-Bethe-Goldstone theory of nuclear matter

    International Nuclear Information System (INIS)

    Grange, P.; Lejeune, A.

    1979-01-01

    Two, three- and four-body contributions to the binding energy of nuclear matter are evaluated in the framework of the Bethe-Brueckner expansion. Special attention is devoted to the choice of the auxillary single particle field and to the potential diagrams at the level of three- and four-hole lines present when such a field is different from zero. Two nucleon-nucleon interactions are used: a model interaction V 1 and the Reid soft-core interaction. For V 1 our results are compared with those obtained from variational calculations; this comparison supports the reliability of the perturbative expansion. (Auth.)

  14. Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example

    Science.gov (United States)

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

    1993-07-01

    A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of 150Nd.

  15. Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example

    International Nuclear Information System (INIS)

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

    1993-01-01

    A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of 150 Nd

  16. Quasi-potential approach to the problem of bound states in quantum electrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Rizov, V A; Todorov, I T [Bylgarska Akademiya na Naukite, Sofia. Inst. za Yadrena Izsledvaniya i Yadrena Energetika

    1975-07-01

    The paper reviews two types of quasipotential equations. An equation with a non-local potential is derived from the equations of motion of quantum electrodynamics. It is also related to a Bethe-Salpeter type of equation for the retarded Green function. Most of the paper is devoted to a systematic study of a local version of the Logunov-Tavkhelidze quasipotential approach.

  17. BEC-BCS crossover in a (p+ip)-wave pairing Hamiltonian coupled to bosonic molecular pairs

    International Nuclear Information System (INIS)

    Dunning, Clare; Isaac, Phillip S.; Links, Jon; Zhao, Shao-You

    2011-01-01

    We analyse a (p+ip)-wave pairing BCS Hamiltonian, coupled to a single bosonic degree of freedom representing a molecular condensate, and investigate the nature of the BEC-BCS crossover for this system. For a suitable restriction on the coupling parameters, we show that the model is integrable and we derive the exact solution by the algebraic Bethe ansatz. In this manner we also obtain explicit formulae for correlation functions and compute these for several cases. We find that the crossover between the BEC state and the strong pairing p+ip phase is smooth for this model, with no intermediate quantum phase transition.

  18. Indirect quantum tomography of quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

    2011-01-15

    A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

  19. 'Relativistic' quark model for mesons with flavour-independent potential

    International Nuclear Information System (INIS)

    Kroesen, G.

    1987-01-01

    On the base of the Bethe-Salpeter equation in instantaneous approximation a unified model for the mass spectrum of the mesons was designed. The 'relativistic' structure of the Bethe-Salpeter equation allows a natural inclusion of the spin dependences and an extension of the model to small quark masses. The model contains as essential property two potential contributions where one represents the one-gluon exchange while the other represents the confinement potential. The annihilation of qanti q into gluons was not regarded. The spectrum and the amplitudes of the Bethe-Salpeter equation were solved approximatively in numerical way for the lowest states. The free parameters of the model were determined by a fit of the spectrum to a wellknown part of the meson spectrum. The results yield even at small quark masses a quantitatively good picture for all meson families. The result shows that the spectra of the heavy and light mesons can be described by a flavor-independent potential which contains 5 free parameters. Both the internal spin dependent structure and the absolute position of the families can so correctly be described. Especially the position of the D, D s , and B states and the position of the uanti u, danti d states can be simultaneously described by a constant C in the long-range part of the potential. The constant C is thereby essentially determined by the splitting between the Υ family and the B family repectively Ψ and D family. The 3 S 1- 3 D 1 respectively the 3 P 2 - 3 F 2 configuration mixing was regarded. The results show that this mixing is negligibly small. (orig./HSI) [de

  20. Scaling Universality between Band Gap and Exciton Binding Energy of Two-Dimensional Semiconductors

    Science.gov (United States)

    Jiang, Zeyu; Liu, Zhirong; Li, Yuanchang; Duan, Wenhui

    2017-06-01

    Using first-principles G W Bethe-Salpeter equation calculations and the k .p theory, we unambiguously show that for two-dimensional (2D) semiconductors, there exists a robust linear scaling law between the quasiparticle band gap (Eg) and the exciton binding energy (Eb), namely, Eb≈Eg/4 , regardless of their lattice configuration, bonding characteristic, as well as the topological property. Such a parameter-free universality is never observed in their three-dimensional counterparts. By deriving a simple expression for the 2D polarizability merely with respect to Eg, and adopting the screened hydrogen model for Eb, the linear scaling law can be deduced analytically. This work provides an opportunity to better understand the fantastic consequence of the 2D nature for materials, and thus offers valuable guidance for their property modulation and performance control.

  1. Self-consistent model of confinement

    International Nuclear Information System (INIS)

    Swift, A.R.

    1988-01-01

    A model of the large-spatial-distance, zero--three-momentum, limit of QCD is developed from the hypothesis that there is an infrared singularity. Single quarks and gluons do not propagate because they have infinite energy after renormalization. The Hamiltonian formulation of the path integral is used to quantize QCD with physical, nonpropagating fields. Perturbation theory in the infrared limit is simplified by the absence of self-energy insertions and by the suppression of large classes of diagrams due to vanishing propagators. Remaining terms in the perturbation series are resummed to produce a set of nonlinear, renormalizable integral equations which fix both the confining interaction and the physical propagators. Solutions demonstrate the self-consistency of the concepts of an infrared singularity and nonpropagating fields. The Wilson loop is calculated to provide a general proof of confinement. Bethe-Salpeter equations for quark-antiquark pairs and for two gluons have finite-energy solutions in the color-singlet channel. The choice of gauge is addressed in detail. Large classes of corrections to the model are discussed and shown to support self-consistency

  2. Selected Works Of Hans A Bethe (With Commentary)

    International Nuclear Information System (INIS)

    Bethe, Hans A.

    1997-01-01

    Hans A Bethe received the Nobel Prize for Physics in 1967 for his work on the production of energy in stars. A living legend among the physics community, he helped to shape classical physics into quantum physics and increased the understanding of the atomic processes responsible for the properties of matter and of the forces governing the structures of atomic nuclei. This collection of papers by Prof Bethe dates from 1928, when he received his PhD, to now. It covers several areas and reflects the many contributions in research and discovery made by one of the most important and eminent physicists of all time. Special commentaries have been written by Prof Bethe to complement the selected papers

  3. Treatment of the intrinsic Hamiltonian in particle-number nonconserving theories

    International Nuclear Information System (INIS)

    Hergert, H.; Roth, R.

    2009-01-01

    We discuss the implications of using an intrinsic Hamiltonian in theories without particle-number conservation, e.g., the Hartree-Fock-Bogoliubov approximation, where the Hamiltonian's particle-number dependence leads to discrepancies if one naively replaces the particle-number operator by its expectation value. We develop a systematic expansion that fixes this problem and leads to an a posteriori justification of the widely-used one- plus two-body form of the intrinsic kinetic energy in nuclear self-consistent field methods. The expansion's convergence properties as well as its practical applications are discussed for several sample nuclei.

  4. A diagrammatic construction of formal E-independent model hamiltonian

    International Nuclear Information System (INIS)

    Kvasnicka, V.

    1977-01-01

    A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian

  5. Relativistic two-and three-particle scattering equations using instant and light-front dynamics

    International Nuclear Information System (INIS)

    Adhikari, S.K.; Tomio, L.; Frederico, T.

    1992-01-01

    Starting from the Bethe-Salpeter equation for two particles in the ladder approximation and integrating over the time component of momentum we derive three dimensional scattering integral equations satisfying constraints of unitarity and relativity, both employing the light-front and instant-form variables. The equations we arrive at are those first derived by Weinberg and by Blankenbecler and Sugar, and are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. We extends this procedure to the case of three particles interacting via two-particle separable potentials. Using light-front and instant form variables we suggest a couple of three dimensional three-particle scattering equations satisfying constraints of two and three-particle unitarity and relativity. The three-particle light-front equation is shown to be approximately related by a transformation of variables to one of the instant-form three-particle equations. (author)

  6. A partial Hamiltonian approach for current value Hamiltonian systems

    Science.gov (United States)

    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.

  7. Frenkel and Charge-Transfer Excitations in Donor-acceptor Complexes from Many-Body Green's Functions Theory.

    Science.gov (United States)

    Baumeier, Björn; Andrienko, Denis; Rohlfing, Michael

    2012-08-14

    Excited states of donor-acceptor dimers are studied using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation. For a series of prototypical small-molecule based pairs, this method predicts energies of local Frenkel and intermolecular charge-transfer excitations with the accuracy of tens of meV. Application to larger systems is possible and allowed us to analyze energy levels and binding energies of excitons in representative dimers of dicyanovinyl-substituted quarterthiophene and fullerene, a donor-acceptor pair used in state of the art organic solar cells. In these dimers, the transition from Frenkel to charge transfer excitons is endothermic and the binding energy of charge transfer excitons is still of the order of 1.5-2 eV. Hence, even such an accurate dimer-based description does not yield internal energetics favorable for the generation of free charges either by thermal energy or an external electric field. These results confirm that, for qualitative predictions of solar cell functionality, accounting for the explicit molecular environment is as important as the accurate knowledge of internal dimer energies.

  8. Algebraic Bethe ansatz for the Izergin-Korepin R matrix

    International Nuclear Information System (INIS)

    Tarasov, V.O.

    1989-01-01

    The authors propose a generalization of the algebraic Bethe ansatz for the Izergin-Korepin R matrix - the simplest unstudied odd-dimensional solution of the Yang-Baxter equation - and they discuss some related questions. The first section of the paper is an introduction. In the second they indicate a way of generalizing the algebraic Bethe ansatz to the case of the Izergin-Korepin R matrix. The simplest monodromy matrices (L operators) for this R matrix are described in the third section. The fourth section is devoted to the proof of the proposed generalization of the algebraic Bethe ansatz

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

    International Nuclear Information System (INIS)

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

    2005-01-01

    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

  10. Quantum optics meets quantum many-body theory: coupled cluster studies of the Rabi Hamiltonian

    International Nuclear Information System (INIS)

    Davidson, N.J.; Quick, R.M.; Bishop, R.F.; Van der Walt, D.M.

    1998-01-01

    The Rabi Hamiltonian, which describes the interaction of a single mode of electromagnetic radiation with a two level system, is one of the fundamental models of quantum optics. It is also of wider interest as it provides a generic model for the interaction of bosons and fermions. To allow for a systematic analysis of the strong-coupling behaviour, we have applied the coupled cluster method (CCM) to the Rabi Hamiltonian to calculate its spectrum. We find strong evidence for the existence of a somewhat subtle quantum phase transition. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)

  11. Neutral weak-current two-body contributions in inclusive scattering from {sup 12}C

    Energy Technology Data Exchange (ETDEWEB)

    Lovato, Alessandro [ANL; Gandolfi, Stefano [LANL; Carlson, Joseph [LANL; Pieper, S. C. [ANL; Schiavilla, Rocco [JLAB, ODU

    2014-05-01

    An {\\it ab initio} calculation of the sum rules of the neutral weak response functions in $^{12}$C is reported, based on a realistic Hamiltonian, including two- and three-nucleon potentials, and on realistic currents, consisting of one- and two-body terms. We find that the sum rules of the response functions associated with the longitudinal and transverse components of the (space-like) neutral current are largest and that a significant portion ($\\simeq 30$\\%) of the calculated strength is due to two-body terms. This fact may have implications for the MiniBooNE and other neutrino quasi-elastic scattering data on nuclei.

  12. Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Van Isacker, P., E-mail: isacker@ganil.fr [Grand Accélérateur National d' Ions Lourds, CEA/DSM–CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5 (France); Bouldjedri, A.; Zerguine, S. [Department of Physics, PRIMALAB Laboratory, University of Batna, Avenue Boukhelouf M El Hadi, 05000 Batna (Algeria)

    2015-06-15

    In the context of the interacting boson model with s, d and g bosons, the conditions for obtaining an intrinsic shape with octahedral symmetry are derived for a general Hamiltonian with up to two-body interactions.

  13. Site-occupation embedding theory using Bethe ansatz local density approximations

    Science.gov (United States)

    Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa; Fromager, Emmanuel

    2018-06-01

    Site-occupation embedding theory (SOET) is an alternative formulation of density functional theory (DFT) for model Hamiltonians where the fully interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a noninteracting) one. It provides a rigorous framework for combining wave-function (or Green function)-based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single-impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wave function has been performed with the density-matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

  14. Centenary Birth Anniversary of E. W. Beth (1908-1964)

    Science.gov (United States)

    Bagni, Giorgio T.

    2008-01-01

    Evert Willem Beth (1908-1964) was a Dutch logician, mathematician and philosopher, whose work mainly concerned the foundations of mathematics. Beth was among the founders of the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques and was a member of the Central Committee of the International Commission on…

  15. Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE

    Science.gov (United States)

    Jiang, Yunfeng; Zhang, Yang

    2018-03-01

    In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and powerful tools for understanding the structure of solution space of Bethe ansatz equations. In particular, we find novel efficient methods to count the number of solutions of Bethe ansatz equations based on Gröbner basis and quotient ring. We also develop analytical approach based on companion matrix to perform the sum of on-shell quantities over all physical solutions without solving Bethe ansatz equations explicitly. To demonstrate the power of our method, we revisit the completeness problem of Bethe ansatz of Heisenberg spin chain, and calculate the sum rules of OPE coefficients in planar N=4 super-Yang-Mills theory.

  16. Possible retardation effects of quark confinement on the meson spectrum

    International Nuclear Information System (INIS)

    Qiao, C.; Huang, H.; Chao, K.

    1996-01-01

    The reduced Bethe-Salpeter equation with scalar confinement and vector gluon exchange is applied to quark-antiquark bound states. The so-called intrinsic flaw of the Salpeter equation with static scalar confinement is investigated. The notorious problem of narrow level spacings is found to be remedied by taking into consideration the retardation effect of scalar confinement. A good fit for the mass spectrum of both heavy and light quarkonium states is then obtained. copyright 1996 The American Physical Society

  17. Nonlocality in many-body quantum systems detected with two-body correlators

    Energy Technology Data Exchange (ETDEWEB)

    Tura, J., E-mail: jordi.tura@icfo.es [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); Augusiak, R.; Sainz, A.B. [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); Lücke, B.; Klempt, C. [Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover (Germany); Lewenstein, M.; Acín, A. [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); ICREA—Institució Catalana de Recerca i Estudis Avançats, Lluis Campanys 3, 08010 Barcelona (Spain)

    2015-11-15

    Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, “theorist- and experimentalist-friendly” many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Tura et al., Science 344 (2014) 1256]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states—ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.

  18. Hamiltonian field description of two-dimensional vortex fluids and guiding center plasmas

    International Nuclear Information System (INIS)

    Morrison, P.J.

    1981-03-01

    The equations that describe the motion of two-dimensional vortex fluids and guiding center plasmas are shown to possess underlying field Hamiltonian structure. A Poisson bracket which is given in terms of the vorticity, the physical although noncanonical dynamical variable, casts these equations into Heisenberg form. The Hamiltonian density is the kinetic energy density of the fluid. The well-known conserved quantities are seen to be in involution with respect to this Poisson bracket. Expanding the vorticity in terms of a Fourier-Dirac series transforms the field description given here into the usual canonical equations for discrete vortex motion. A Clebsch potential representation of the vorticity transforms the noncanonical field description into a canonical description

  19. Effect of ladder diagrams on optical absorption spectra in a quasiparticle self-consistent GW framework

    Science.gov (United States)

    Cunningham, Brian; Grüning, Myrta; Azarhoosh, Pooya; Pashov, Dimitar; van Schilfgaarde, Mark

    2018-03-01

    We present an approach to calculate the optical absorption spectra that combines the quasiparticle self-consistent GW method [Phys. Rev. B 76, 165106 (2007), 10.1103/PhysRevB.76.165106] for the electronic structure with the solution of the ladder approximation to the Bethe-Salpeter equation for the macroscopic dielectric function. The solution of the Bethe-Salpeter equation has been implemented within an all-electron framework, using a linear muffin-tin orbital basis set, with the contribution from the nonlocal self-energy to the transition dipole moments (in the optical limit) evaluated explicitly. This approach addresses those systems whose electronic structure is poorly described within the standard perturbative GW approaches with density-functional theory calculations as a starting point. The merits of this approach have been exemplified by calculating optical absorption spectra of a strongly correlated transition metal oxide, NiO, and a narrow gap semiconductor, Ge. In both cases, the calculated spectrum is in good agreement with the experiment. It is also shown that for systems whose electronic structure is well-described within the standard perturbative GW , such as Si, LiF, and h -BN , the performance of the present approach is in general comparable to the standard GW plus Bethe-Salpeter equation. It is argued that both vertex corrections to the electronic screening and the electron-phonon interaction are responsible for the observed systematic overestimation of the fundamental band gap and spectrum onset.

  20. Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice

    Science.gov (United States)

    Chen, Haiyan; Zhang, Fuji

    2013-08-01

    In this paper, we study the sandpile model on the generalized finite Bethe lattice with a particular boundary condition. Using a combinatorial method, we give the exact expressions for all single-site probabilities and some two-site joint probabilities. As a by-product, we prove that the height probabilities of bulk vertices are all the same for the Bethe lattice with certain given boundary condition, which was found from numerical evidence by Grassberger and Manna ["Some more sandpiles," J. Phys. (France) 51, 1077-1098 (1990)], 10.1051/jphys:0199000510110107700 but without a proof.

  1. Relativistic Many-Body Hamiltonian Approach to Mesons

    OpenAIRE

    Llanes-Estrada, Felipe J.; Cotanch, Stephen R.

    2001-01-01

    We represent QCD at the hadronic scale by means of an effective Hamiltonian, $H$, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon app...

  2. Obituary: Beth Brown (1969-2008)

    Science.gov (United States)

    Bregman, Joel

    2011-12-01

    The astronomical community lost one of its most buoyant and caring individuals when Beth Brown died, unexpectedly, at the age of 39 from a pulmonary embolism. Beth Brown was born in Roanoke, Virginia where she developed a deep interest in astronomy, science, and science fiction (Star Trek). After graduating as the valedictorian of William Fleming High School's Class of 1987, she attended Howard University, where she graduated summa cum laude in 1991 with a bachelor's degree in astrophysics. Following a year in the graduate physics program at Howard, she entered the graduate program in the Department of Astronomy at the University of Michigan, the first African-American woman in the program. She received her PhD in 1998, working with X-ray observations of elliptical galaxies from the Röntgen Satellite (ROSAT; Joel Bregman was her advisor). She compiled and analyzed the first large complete sample of such galaxies with ROSAT and her papers in this area made an impact in the field. Following her PhD, Beth Brown held a National Academy of Science & National Research Council Postdoctoral Research Fellowship at NASA's Goddard Space Flight Center. Subsequently, she became a civil servant at the National Space Science Data Center at GSFC, where she was involved in data archival activities as well as education and outreach, a continuing passion in her life. In 2006, Brown became an Astrophysics Fellow at GSFC, during which time she worked as a visiting Assistant Professor at Howard University, where she taught and worked with students and faculty to improve the teaching observatory. At the time of her death, she was eagerly looking forward to a new position at GSFC as the Assistant Director for Science Communications and Higher Education. Beth Brown was a joyous individual who loved to work with people, especially in educating them about our remarkable field. Her warmth and openness was a great aid in making accessible explanations of otherwise daunting astrophysical

  3. Algebraic Bethe ansatz for 19-vertex models with reflection conditions

    International Nuclear Information System (INIS)

    Utiel, Wagner

    2003-01-01

    In this work we solve the 19-vertex models with the use of algebraic Bethe ansatz for diagonal reflection matrices (Sklyanin K-matrices). The eigenvectors, eigenvalues and Bethe equations are given in a general form. Quantum spin chains of spin one derived from the 19-vertex models were also discussed

  4. Overlaps of partial Néel states and Bethe states

    International Nuclear Information System (INIS)

    Foda, O; Zarembo, K

    2016-01-01

    Partial Néel states are generalizations of the ordinary Néel (classical anti-ferromagnet) state that can have arbitrary integer spin. We study overlaps of these states with Bethe states. We first identify this overlap with a partial version of reflecting-boundary domain-wall partition function, and then derive various determinant representations for off-shell and on-shell Bethe states. (paper: quantum statistical physics, condensed matter, integrable systems)

  5. Hybrid mesons with auxiliary fields

    International Nuclear Information System (INIS)

    Buisseret, F.; Mathieu, V.

    2006-01-01

    Hybrid mesons are exotic mesons in which the color field is not in the ground state. Their understanding deserves interest from a theoretical point of view, because it is intimately related to nonperturbative aspects of QCD. Moreover, it seems that some recently detected particles, such as the π 1 (1600) and the Y(4260), are serious hybrid candidates. In this work, we investigate the description of such exotic hadrons by applying the auxiliary fields technique (also known as the einbein field method) to the widely used spinless Salpeter Hamiltonian with appropriate linear confinement. Instead of the usual numerical resolution, this technique allows to find simplified analytical mass spectra and wave functions of the Hamiltonian, which still lead to reliable qualitative predictions. We analyse and compare two different descriptions of hybrid mesons, namely a two-body q system with an excited flux tube, or a three-body qg system. We also compute the masses of the 1 -+ hybrids. Our results are shown to be in satisfactory agreement with lattice QCD and other effective models. (orig.)

  6. Strong Coupling Continuum QCD

    International Nuclear Information System (INIS)

    Pennington, Michael

    2011-01-01

    The Schwinger-Dyson, Bethe-Salpeter system of equations are the link between coloured quarks and gluons, and colourless hadrons and their properties. This talk reviews some aspects of these studies from the infrared behavior of ghosts to the prediction of electromagnetic form-factors.

  7. Zn-VI quasiparticle gaps and optical spectra from many-body calculations.

    Science.gov (United States)

    Riefer, A; Weber, N; Mund, J; Yakovlev, D R; Bayer, M; Schindlmayr, Arno; Meier, C; Schmidt, W G

    2017-06-01

    The electronic band structures of hexagonal ZnO and cubic ZnS, ZnSe, and ZnTe compounds are determined within hybrid-density-functional theory and quasiparticle calculations. It is found that the band-edge energies calculated on the [Formula: see text] (Zn chalcogenides) or GW (ZnO) level of theory agree well with experiment, while fully self-consistent QSGW calculations are required for the correct description of the Zn 3d bands. The quasiparticle band structures are used to calculate the linear response and second-harmonic-generation (SHG) spectra of the Zn-VI compounds. Excitonic effects in the optical absorption are accounted for within the Bethe-Salpeter approach. The calculated spectra are discussed in the context of previous experimental data and present SHG measurements for ZnO.

  8. Experimental observation of Bethe strings

    Science.gov (United States)

    Wang, Zhe; Wu, Jianda; Yang, Wang; Bera, Anup Kumar; Kamenskyi, Dmytro; Islam, A. T. M. Nazmul; Xu, Shenglong; Law, Joseph Matthew; Lake, Bella; Wu, Congjun; Loidl, Alois

    2018-02-01

    Almost a century ago, string states—complex bound states of magnetic excitations—were predicted to exist in one-dimensional quantum magnets. However, despite many theoretical studies, the experimental realization and identification of string states in a condensed-matter system have yet to be achieved. Here we use high-resolution terahertz spectroscopy to resolve string states in the antiferromagnetic Heisenberg-Ising chain SrCo2V2O8 in strong longitudinal magnetic fields. In the field-induced quantum-critical regime, we identify strings and fractional magnetic excitations that are accurately described by the Bethe ansatz. Close to quantum criticality, the string excitations govern the quantum spin dynamics, whereas the fractional excitations, which are dominant at low energies, reflect the antiferromagnetic quantum fluctuations. Today, Bethe’s result is important not only in the field of quantum magnetism but also more broadly, including in the study of cold atoms and in string theory; hence, we anticipate that our work will shed light on the study of complex many-body systems in general.

  9. Particle–hole duality, integrability, and Russian doll BCS model

    Energy Technology Data Exchange (ETDEWEB)

    Bork, L.V. [Center for Fundamental and Applied Research, N. L. Dukhov All-Russia Research Institute of Automatics, 127055 Moscow (Russian Federation); Institute for Theoretical and Experimental Physics, 117218 Moscow (Russian Federation); Pogosov, W.V., E-mail: walter.pogosov@gmail.com [Center for Fundamental and Applied Research, N. L. Dukhov All-Russia Research Institute of Automatics, 127055 Moscow (Russian Federation); Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, 125412 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700 (Russian Federation)

    2015-08-15

    We address a generalized Richardson model (Russian doll BCS model), which is characterized by the breaking of time-reversal symmetry. This model is known to be exactly solvable and integrable. We point out that the Russian doll BCS model, on the level of Hamiltonian, is also particle–hole symmetric. This implies that the same state can be expressed both in the particle and hole representations with two different sets of Bethe roots. We then derive exact relations between Bethe roots in the two representations, which can hardly be obtained staying on the level of Bethe equations. In a quasi-classical limit, similar identities for usual Richardson model, known from literature, are recovered from our results. We also show that these relations for Richardson roots take a remarkably simple form at half-filling and for a symmetric with respect to the middle of the interaction band distribution of one-body energy levels, since, in this special case, the rapidities in the particle and hole representations up to the translation satisfy the same system of equations.

  10. Perturbation theory of effective Hamiltonians

    International Nuclear Information System (INIS)

    Brandow, B.H.

    1975-01-01

    This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)

  11. g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...

    Indian Academy of Sciences (India)

    Keywords. g2 algebra; quasiexactly solvable Hamiltonian; hidden algebra; Poschl–Teller potential. ... space of the polynomials, restricting to a linear transformation on this space, the associ- .... The operators L6 and L7 are the positive root.

  12. Light-Front Hamiltonian Approach to the Bound-State Problem in Quantum Electrodynamics

    Science.gov (United States)

    Jones, Billy D.

    1997-10-01

    Why is the study of the Lamb shift in hydrogen, which at the level of detail found in this paper was largely completed by Bethe in 1947, of any real interest today? While completing such a calculation using new techniques may be very interesting for formal and academic reasons, our primary motivation is to lay groundwork for precision bound-state calculations in QCD. The Lamb shift provides an excellent pedagogical tool for illustrating light-front Hamiltonian techniques, which are not widely known; but more importantly it presents three of the central dynamical and computational problems that we must face to make these techniques useful for solving QCD: How does a constituent picture emerge in a gauge field theory? How do bound-state energy scales emerge non-perturbatively? How does rotational symmetry emerge in a non-perturbative light-front calculation?

  13. Form factor of relativistic two-particle system and covariant hamiltonian formulation of quantum field theory

    International Nuclear Information System (INIS)

    Skachkov, N.; Solovtsov, I.

    1979-01-01

    Based on the hamiltonian formulation of quantum field theory proposed by Kadyshevsky the three-dimensional relativistic approach is developed for describing the form factors of composite systems. The main features of the diagram technique appearing in the covariant hamiltonian formulation of field theory are discussed. The three-dimensional relativistic equation for the vertex function is derived and its connection with that for the quasipotential wave function is found. The expressions are obtained for the form factor of the system through equal-time two-particle wave functions both in momentum and relativistic configurational representations. An explicit expression for the form factor is found for the case of two-particle interaction through the Coulomb potential

  14. Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz

    Directory of Open Access Journals (Sweden)

    Samuel Belliard

    2013-11-01

    Full Text Available We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations formally similar to the ones obtained in the periodic case or with diagonal boundaries.

  15. Periodic trajectories for a two-dimensional nonintegrable Hamiltonian

    International Nuclear Information System (INIS)

    Baranger, M.; Davies, K.T.R.

    1987-01-01

    A numerical study is made of the classical periodic trajectories for the two-dimensional nonintegrable Hamiltonian H = 1/2(p 2 /sub x/+p 2 /sub y/)+(y-1/2x 2 ) 2 +0.05 x 2 . In addition to x--y pictures of the trajectories, E--tau (energy--period) plots of the periodic families are presented. Efforts have been ade to include all trajectories with short periods and all simple branchings of these trajectories. The monodromy matrix has been calculated in all cases, and from it the stability properties are derived. The topology of the E--tau plot has been explored, with the following results. One family may have several stable regions. The plot is not completely connected; there are islands. The plot is not a tree; there are cycles. There are isochronous branchings, period-doublings, and period-multiplyings of higher orders, and examples of each of these are presented. There is often more than one branch issuing from a branch point. Some general empirical rules are inferred. In particular, the existence of isochronous branching is seen to be a consequence of the symmetry of the Hamiltonian. All these results agree with the general classification of possible branchings derived in Ref. [10]. (M. A. M. de Aguiar, C. P. Malta, M. Baranger, and K. T. R. Davies, in preparation). Finally, some nonperiodic trajectories are calculated to illustrate the fact that stable periodic trajectories lie in ''regular'' regions of phase space, while unstable ones lie in ''chaotic'' regions

  16. Relativistic and separable classical hamiltonian particle dynamics

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1981-01-01

    We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light

  17. Generic Local Hamiltonians are Gapless

    Science.gov (United States)

    Movassagh, Ramis

    2017-12-01

    We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian β orthogonal random matrix ensemble. As a corollary, there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal.

  18. Microscopic Fermi liquid approach to disordered narrow band systems

    International Nuclear Information System (INIS)

    Kolley, E.; Kolley, W.

    1977-01-01

    A Fermi liquid approach to tightly bound electrons in disordered systems is proposed to evaluate two-particle correlation functions L at T=0 deg K. Starting with a random Hubbard model and using a local ladder approximation in the particle-particle channel the irreducible particle-hole vertex is derived, being the kernel of the Bethe-Salpeter equation for L. CPA vertex corrections to the electrical conductivity and, for the ordered case, the correlation-enhanced paramagnetic susceptibility are calculated

  19. Heavy baryon transitions and the heavy quark effective theory

    International Nuclear Information System (INIS)

    Hussain, F.

    1992-01-01

    Heavy baryon decays are studied in the context of the Bethe-Salpeter approach to the heavy quark effective theory. A drastic reduction, in the number of independent form factors, is found. Results are presented both for heavy to heavy and heavy to light baryon decays. (orig.)

  20. The {{\\rm{D}}\\bar{{\\rm{D}}}}^{{\\rm{* }}} interaction with isospin zero in an extended hidden gauge symmetry approach

    Science.gov (United States)

    Sun, Bao-Xi; Wan, Da-Ming; Zhao, Si-Yu

    2018-05-01

    The {{{D}}\\bar{{{D}}}}{{* }} interaction via a ρ or ω exchange is constructed within an extended hidden gauge symmetry approach, where the strange quark is replaced by the charm quark in the SU(3) flavor space. With this {{{D}}\\bar{{{D}}}}{{* }} interaction, a bound state slightly lower than the {{{D}}\\bar{{{D}}}}{{* }} threshold is generated dynamically in the isospin zero sector by solving the Bethe-Salpeter equation in the coupled-channel approximation, which might correspond to the X(3872) particle announced by many collaborations. This formulism is also used to study the {{{B}}\\bar{{{B}}}}{{* }} interaction, and a {{{B}}\\bar{{{B}}}}{{* }} bound state with isospin zero is generated dynamically, which has no counterpart listed in the review of the Particle Data Group. Furthermore, the one-pion exchange between the D meson and the {\\bar{{{D}}}}{{* }} is analyzed precisely, and we do not think the one-pion exchange potential need be considered when the Bethe-Salpeter equation is solved.

  1. Bethe states of the trigonometric SU(3) spin chain with generic open boundaries

    Science.gov (United States)

    Sun, Pei; Xin, Zhirong; Qiao, Yi; Wen, Fakai; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Tao; Yang, Wen-Li; Shi, Kangjie

    2018-06-01

    By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU (3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T - Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe-type eigenstates which have well-defined homogeneous limit. This exact solution provides a basis for further analyzing the thermodynamic properties and correlation functions of the anisotropic models associated with higher rank algebras.

  2. Degeneration of Bethe subalgebras in the Yangian of gl_n

    Science.gov (United States)

    Ilin, Aleksei; Rybnikov, Leonid

    2018-04-01

    We study degenerations of Bethe subalgebras B( C) in the Yangian Y(gl_n), where C is a regular diagonal matrix. We show that closure of the parameter space of the family of Bethe subalgebras, which parameterizes all possible degenerations, is the Deligne-Mumford moduli space of stable rational curves \\overline{M_{0,n+2}}. All subalgebras corresponding to the points of \\overline{M_{0,n+2}} are free and maximal commutative. We describe explicitly the "simplest" degenerations and show that every degeneration is the composition of the simplest ones. The Deligne-Mumford space \\overline{M_{0,n+2}} generalizes to other root systems as some De Concini-Procesi resolution of some toric variety. We state a conjecture generalizing our results to Bethe subalgebras in the Yangian of arbitrary simple Lie algebra in terms of this De Concini-Procesi resolution.

  3. On the physical applications of hyper-Hamiltonian dynamics

    International Nuclear Information System (INIS)

    Gaeta, Giuseppe; Rodriguez, Miguel A

    2008-01-01

    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

  4. Internal parity symmetry and degeneracy of Bethe Ansatz strings in the isotropic heptagonal magnetic ring

    Energy Technology Data Exchange (ETDEWEB)

    Milewski, J., E-mail: jsmilew@wp.pl [Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań (Poland); Lulek, B., E-mail: barlulek@amu.edu.pl [East European State Higher School, ul. Tymona Terleckiego 6, 37-700 Przemyśl (Poland); Lulek, T., E-mail: tadlulek@prz.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland); East European State Higher School, ul. Tymona Terleckiego 6, 37-700 Przemyśl (Poland); Łabuz, M., E-mail: labuz@univ.rzeszow.pl [University of Rzeszow, Institute of Physics, Rejtana 16a, 35-959 Rzeszów (Poland); Stagraczyński, R., E-mail: rstag@prz.edu.pl [Rzeszow University of Technology, The Faculty of Mathematics and Applied Physics, Powstańców Warszawy 6, 35-959 Rzeszów (Poland)

    2014-02-01

    The exact Bethe eigenfunctions for the heptagonal ring within the isotropic XXX model exhibit a doubly degenerated energy level in the three-deviation sector at the centre of the Brillouin zone. We demonstrate an explicit construction of these eigenfunctions by use of algebraic Bethe Ansatz, and point out a relation of degeneracy to parity conservation, applied to the configuration of strings for these eigenfunctions. Namely, the internal structure of the eigenfunctions (the 2-string and the 1-string, with opposite quasimomenta) admits generation of two mutually orthogonal eigenfunctions due to the fact that the strings which differ by their length are distinguishable objects.

  5. Hamiltonian Approach to 2+1 Dimensional Gravity

    Science.gov (United States)

    Cantini, L.; Menotti, P.; Seminara, D.

    2002-12-01

    It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.

  6. On the completeness of the set of Bethe-Hulthen solutions of the linear Heisenberg system

    International Nuclear Information System (INIS)

    Caspers, W J; Labuz, M; Wal, A

    2006-01-01

    In this work we formulate the standard form of the solutions of the Heisenberg chain with periodic boundary conditions and show that these solutions can be transformed into the well-known Bethe-Hulthen solutions. The standard form is found by solving the secular problem, separated according to the irreducible representations of the translation group. The relevant parameters exp(ik j ) of the Bethe-Hulthen solutions are found from a set of linear equations with coefficients derived from the standard solutions. This correspondence between standard and Bethe-Hulthen solutions realizes the completeness of the Bethe-Hulthen method

  7. Confinement contains condensates

    DEFF Research Database (Denmark)

    Brodsky, S. J.; Roberts, C. D.; Shrock, R.

    2012-01-01

    been viewed as constant empirical mass scales that fill all space-time, are instead wholly contained within hadrons; i.e., they are a property of hadrons themselves and expressed, e.g., in their Bethe-Salpeter or light-front wave functions. We explain that this paradigm is consistent with empirical...

  8. Successive canonical transformation in model two-body electrodynamics

    International Nuclear Information System (INIS)

    Raha, S.

    1978-10-01

    The possibility is investigated of bypassing the no interaction theorum of Currie, Jordan and Sudarshan for direct action Lagrangians. Starting with the field theoretic description of a two-body electrodynamic problem, the field variable is solved for in terms of the particle variables, which paves the way to write an action-at-a-distance Hamiltonian for the problem. A suitable transformation is found which uncouples the field and the particle variables in the interaction up to order e 2 . It is shown that this transformation leaves the statement of Newton's 2nd law unchanged which also agrees with the standard results of electrodynamics. This allows for the identification of canonical variables for the proper action-at-a-distance problem. 19 references

  9. Colored Quantum Algebra and Its Bethe State

    International Nuclear Information System (INIS)

    Wang Jin-Zheng; Jia Xiao-Yu; Wang Shi-Kun

    2014-01-01

    We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation. (general)

  10. Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity

    Directory of Open Access Journals (Sweden)

    Azat M. Gainutdinov

    2016-08-01

    Full Text Available For generic values of q, all the eigenvectors of the transfer matrix of the Uqsl(2-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA formalism of Sklyanin. However, when q is a root of unity (q=eiπ/p with integer p≥2, the Bethe equations acquire continuous solutions, and the transfer matrix develops Jordan cells. Hence, there appear eigenvectors of two new types: eigenvectors corresponding to continuous solutions (exact complete p-strings, and generalized eigenvectors. We propose general ABA constructions for these two new types of eigenvectors. We present many explicit examples, and we construct complete sets of (generalized eigenvectors for various values of p and N.

  11. Bethe ansatz solution of the closed anisotropic supersymmetric U model with quantum supersymmetry

    International Nuclear Information System (INIS)

    Hibberd, Katrina; Roditi, Itzhak; Links, Jon; Foerster, Angela

    1999-11-01

    The nested algebraic Bethe Ansatz is presented for the anisotropic supersymmetric U model maintaining quantum a supersymmetry. The Bethe Ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for the energy is given. (author)

  12. Discrete Hamiltonian evolution and quantum gravity

    International Nuclear Information System (INIS)

    Husain, Viqar; Winkler, Oliver

    2004-01-01

    We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

  13. Bethe Ansatz and exact form factors of the O(N) Gross Neveu-model

    International Nuclear Information System (INIS)

    Babujian, Hrachya M.; Foerster, Angela; Karowski, Michael

    2016-01-01

    We apply previous results on the O(N) Bethe Ansatz http://dx.doi.org/10.1088/1751-8113/45/5/055207, http://arxiv.org/abs/1204.3479, http://dx.doi.org/10.1007/JHEP11(2013)089 to construct a general form factor formula for the O(N) Gross-Neveu model. We examine this formula for several operators, such as the energy momentum, the spin-field and the current. We also compare these results with the 1/N expansion of this model and obtain full agreement. We discuss bound state form factors, in particular for the three particle form factor of the field. In addition for the two particle case we prove a recursion relation for the K-functions of the higher level Bethe Ansatz.

  14. The Yangians, Bethe ansatz and combinatorics

    International Nuclear Information System (INIS)

    Kirillov, A.N.; Reshetikhin, N.Yu.

    1986-01-01

    An axiomatic definition of a quantum monodromy matrix and the representations of its corresponding Hopf algebra are discussed. The connection between the quantum inverse transform method and the representation theory of a symmetric group is considered. A new approach to the completeness problem of Bethe vectors is also given. (orig.)

  15. Quantum Waveguide Properties of Bethe Lattices with a Ring

    International Nuclear Information System (INIS)

    Zhi-Ping, Lin; Zhi-Lin, Hou; You-Yan, Liu

    2008-01-01

    Based on waveguide theory we investigate electronic transport properties of Bethe lattices with a mesoscopic ring threaded by a magnetic flux. The generalized eigen-function method (GEM) is used to calculate the transmission and reflection coefficients up to the fifth generation of Bethe lattices. The relationships among the transmission coefficient T, magnetic flux φ and wave vector kl are investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux φ are observed and discussed. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

  16. Potential problems with interpolating fields

    Energy Technology Data Exchange (ETDEWEB)

    Birse, Michael C. [The University of Manchester, Theoretical Physics Division, School of Physics and Astronomy, Manchester (United Kingdom)

    2017-11-15

    A potential can have features that do not reflect the dynamics of the system it describes but rather arise from the choice of interpolating fields used to define it. This is illustrated using a toy model of scattering with two coupled channels. A Bethe-Salpeter amplitude is constructed which is a mixture of the waves in the two channels. The potential derived from this has a strong repulsive core, which arises from the admixture of the closed channel in the wave function and not from the dynamics of the model. (orig.)

  17. Supersymmetric quasipotential equations

    International Nuclear Information System (INIS)

    Zaikov, R.P.

    1981-01-01

    A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru

  18. The second RPA description for the decay of the one-phonon nuclear collective states at finite temperature

    International Nuclear Information System (INIS)

    Yannouleas, C.; Jang, S.

    1986-01-01

    The zero-temperature second RPA is generalized to finite temperatures through the use of the method of linearization of the equations of motion. After elimination of the quadruples, for low enough temperatures and within the subspace spanned by the doubles, a proper symmetrization yields an eigenvalue equation which exhibits formal properties like the simple RPA. From this second RPA eigenvalue equation, a closed formula for the spreading width of an isolated collective state is extracted. The second RPA can be recast in the form of a generalized collision term and be compared with the method of the Bethe-Salpeter equation for the two-body Green function. However, the second RPA method (and results) contrasts with the approach (and corresponding results) of the Boltzmann collision term, which is usually viewed as the appropriate agent for nuclear dissipation. (orig.)

  19. A Direct Method of Hamiltonian Structure

    International Nuclear Information System (INIS)

    Li Qi; Chen Dengyuan; Su Shuhua

    2011-01-01

    A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)

  20. The relativistic harmonic oscillator reconsidered

    International Nuclear Information System (INIS)

    Hofsaess, T.

    1978-01-01

    The bound states of scalar quarks interacting through a scalar harmonic oscillator are investigated. In the presence of this interaction the dressed quark propagator differs substantially from the free one. This leads to a Bethe Salpeter equation which does not allow for any stable bound states of positive mass. (orig.) [de

  1. Obituary: Hans Albrecht Bethe, 1906-2005

    NARCIS (Netherlands)

    Wijers, R.

    2007-01-01

    One of the unquestioned giants of physics and astrophysics, Hans Bethe, died on 6 March 2005, at the venerable age of 98, in his home town of Ithaca, New York. Seven decades of contributing to research and a Nobel Prize for his work on stellar hydrogen burning make a listing of his honors

  2. Semi-classical analysis of the inner product of Bethe states

    International Nuclear Information System (INIS)

    Bettelheim, Eldad; Kostov, Ivan

    2014-01-01

    We study the inner product of two Bethe states, one of which is taken on-shell, in an inhomogeneous XXX chain in the Sutherland limit, where the number of magnons is comparable with the length L of the chain and the magnon rapidities arrange in a small number of macroscopically large Bethe strings. The leading order in the large L limit is known to be expressed through a contour integral of a dilogarithm. Here we derive the sub-leading term. Our analysis is based on a new contour-integral representation of the inner product in terms of a Fredholm determinant. We give two derivations of the sub-leading term. Besides a direct derivation by solving a Riemann–Hilbert problem, we give a less rigorous, but more intuitive derivation by field-theoretical methods. For that we represent the Fredholm determinant as an expectation value in a Fock space of chiral fermions and then bosonize. We construct a collective field for the bosonized theory, the short wave-length part of which may be evaluated exactly, while the long wave-length part is amenable to a 1/L expansion. Our treatment thus results in a systematic 1/L expansion of structure factors within the Sutherland limit. (paper)

  3. A generalized AKNS hierarchy and its bi-Hamiltonian structures

    International Nuclear Information System (INIS)

    Xia Tiecheng; You Fucai; Chen Dengyuan

    2005-01-01

    First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator

  4. Hamiltonian representation of divergence-free fields

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1984-11-01

    Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields

  5. Approximate, analytic solutions of the Bethe equation for charged particle range

    OpenAIRE

    Swift, Damian C.; McNaney, James M.

    2009-01-01

    By either performing a Taylor expansion or making a polynomial approximation, the Bethe equation for charged particle stopping power in matter can be integrated analytically to obtain the range of charged particles in the continuous deceleration approximation. Ranges match reference data to the expected accuracy of the Bethe model. In the non-relativistic limit, the energy deposition rate was also found analytically. The analytic relations can be used to complement and validate numerical solu...

  6. On the structure of the two-stream instability–complex G-Hamiltonian structure and Krein collisions between positive- and negative-action modes

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Ruili; Liu, Jian; Xiao, Jianyuan [Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026 (China); Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026 (China); Qin, Hong, E-mail: hongqin@princeton.edu [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026 (China); Davidson, Ronald C. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)

    2016-07-15

    The two-stream instability is probably the most important elementary example of collective instabilities in plasma physics and beam-plasma systems. For a warm plasma with two charged particle species, the instability diagram of the two-stream instability based on a 1D warm-fluid model exhibits an interesting band structure that has not been explained. We show that the band structure for this instability is the consequence of the Hamiltonian nature of the warm two-fluid system. Interestingly, the Hamiltonian nature manifests as a complex G-Hamiltonian structure in wave-number space, which directly determines the instability diagram. Specifically, it is shown that the boundaries between the stable and unstable regions are locations for Krein collisions between eigenmodes with different Krein signatures. In terms of physics, this rigorously implies that the system is destabilized when a positive-action mode resonates with a negative-action mode, and that this is the only mechanism by which the system can be destabilized. It is anticipated that this physical mechanism of destabilization is valid for other collective instabilities in conservative systems in plasma physics, accelerator physics, and fluid dynamics systems, which admit infinite-dimensional Hamiltonian structures.

  7. Hamiltonian formalism at light front for two-dimensional quantum electrodynamics equivalent to lorentz-covariant approach

    CERN Document Server

    Paston, S A; Prokhvatilov, E V

    2002-01-01

    The Hamiltonian, reproducing the results of the two-dimensional quantum electrodynamics in the Lorentz coordinates, is constructed on the light front. The procedure of bosonization and analysis of the boson perturbation theory in all the orders by the fermions mass are applied for this purpose. Besides the common terms, originating by the naive quantization on the light front, the obtained Hamiltonian contains an additional counterterm. It is proportional to the linear combination of the fermion zero modes (multiplied by a certain factor compensating the charge and fermion number). The coefficient before this counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the theta-vacuum and by the small fermion mass is linear by it

  8. Communication: Strong excitonic and vibronic effects determine the optical properties of Li₂O₂

    DEFF Research Database (Denmark)

    García Lastra, Juan Maria; Bass, J. D.; Thygesen, Kristian Sommer

    2011-01-01

    The band structure and optical absorption spectrum of lithium peroxide (Li2O2) is calculated from first-principles using the G0W0 approximation and the Bethe-Salpeter equation, respectively. A strongly localized (Frenkel type) exciton corresponding to the π*→σ* transition on the O2 −2 peroxide ion...

  9. Powerful effective one-electron Hamiltonian for describing many-atom interacting systems

    International Nuclear Information System (INIS)

    Lugo, J.O.; Vergara, L.I.; Bolcatto, P.G.; Goldberg, E.C.

    2002-01-01

    In this paper, we present an alternative way to build the effective one-electron picture of a many-atom interacting system. By simplifying the many-body general problem we present two different options for the bond-pair model Hamiltonian. We have found that the successive approximations in order to achieve the effective description have a dramatic influence on the result. Thus, only the model that introduces the correct renormalization in the diagonal term due to the overlap is able to reproduce, even in a quantitative fashion, the main properties of simple homonuclear diatomic molecules. The success of the model resides in the accurate definitions (free of parametrization) of the Hamiltonian terms, which, therefore, could be used to describe more complex interacting systems such as polyatomic molecules, adsorbed species, or atoms scattered by a surface

  10. Pionierin der Religionspsychologie: Marianne Beth (1890-1984)

    NARCIS (Netherlands)

    Belzen, J.A.

    2010-01-01

    This article deals with the contributions to the psychology of religion made by Dr. Marianne Beth (1890-1984), an almost totally forgotten pioneer of the psychology of religion. The article especially contextualizes her initiative to turn "unbelief" into a topic for research in psychology of

  11. Effective Hamiltonians in quantum physics: resonances and geometric phase

    International Nuclear Information System (INIS)

    Rau, A R P; Uskov, D

    2006-01-01

    Effective Hamiltonians are often used in quantum physics, both in time-dependent and time-independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian

  12. A cluster-bethe-lattice approach to spin-waves in dilute ferromagnets

    International Nuclear Information System (INIS)

    Salzberg, J.B.; Silva, C.E.T.G. da; Falicov, L.M.

    1975-01-01

    The spin-wave spectra of a dilute ferromagnet within the cluster-bethe-lattice approximation is studied. Short range order effects for the alloy are included. A study of finite size clusters connected at their edges to Bethe lattices of the same coordination number allows one to determine:(i) the stability condition for the magnetic system; (ii) the continuum spin-wave local density of states and (iii) the existence of localized states below and above the continuum states

  13. Model of pair aggregation on the Bethe lattice

    DEFF Research Database (Denmark)

    Baillet, M.V.-P.; Pacheco, A.F.; Gómez, J.B.

    1997-01-01

    We extend a recent model of aggregation of pairs of particles, analyzing the case in which the supporting framework is a Bethe lattice. The model exhibits a critical behavior of the percolation theory type....

  14. A class of conservative Hamiltonians with exactly integrable discrete two-dimensional parametric maps

    International Nuclear Information System (INIS)

    Dikande, Alain M; Njumbe, E Epie

    2010-01-01

    A class of discrete conservative Hamiltonians with completely integrable two-dimensional (2D) mappings is constructed whose generic models are three families of non-integrable discrete Hamiltonians with on-site potentials whose double-well shapes vary. Unlike the discrete 2D mappings associated with the generic models, which all display pitchfork bifurcations towards randomly pinned states with chaotic features, for the derived models the pitchfork bifurcation leads to fixed points always surrounded by periodic trajectories. A nonlinear stability analysis reveals a finite crossover on the bifurcation line at which the pitchfork transition takes the maps from regular real periodic trajectories towards a regime dominated by a cluster of periodic point trajectories representing the allowed real solutions. The rich variety of structures displayed by the new class of discrete maps, combined with their complete integrability, offer rich perspectives for theoretical modelling of a wide class of systems undergoing structural instabilities without noticeable chaotic precursors.

  15. Spectra of heavy-light mesons in a relativistic model

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Jing-Bin; Lue, Cai-Dian [Institute of High Energy Physics, Beijing (China)

    2017-05-15

    The spectra and wave functions of heavy-light mesons are calculated within a relativistic quark model which is based on a heavy-quark expansion of the instantaneous Bethe-Salpeter equation by applying the Foldy-Wouthuysen transformation. The kernel we choose is the standard combination of linear scalar and Coulombic vector. The effective Hamiltonian for heavy-light quark-antiquark system is calculated up to order 1/m{sub Q}{sup 2}. Our results are in good agreement with available experimental data except for the anomalous D{sub s0}{sup *}(2317) and D{sub s1}(2460) states. The newly observed heavy-light meson states can be accommodated successfully in the relativistic quark model with their assignments presented. The D{sub sJ}{sup *}(2860) can be interpreted as the vertical stroke 1{sup 3/2}D{sub 1} right angle and vertical stroke 1{sup 5/2}D{sub 3} right angle states being members of the 1D family with J{sup P} = 1{sup -} and 3{sup -}. (orig.)

  16. Necessary conditions for super-integrability of Hamiltonian systems

    Energy Technology Data Exchange (ETDEWEB)

    Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: maria.przybylska@astri.uni.torun.pl; Yoshida, Haruo [National Astronomical Observatory, 2-21-1 Osawa, Mitaka, 181-8588 Tokyo (Japan)], E-mail: h.yoshida@nao.ac.jp

    2008-08-18

    We formulate a general theorem which gives a necessary condition for the maximal super-integrability of a Hamiltonian system. This condition is expressed in terms of properties of the differential Galois group of the variational equations along a particular solution of the considered system. An application of this general theorem to natural Hamiltonian systems of n degrees of freedom with a homogeneous potential gives easily computable and effective necessary conditions for the super-integrability. To illustrate an application of the formulated theorems, we investigate: three known families of integrable potentials, and the three body problem on a line.

  17. Hamiltonian formulation of QCD in the Schwinger gauge

    International Nuclear Information System (INIS)

    Schutte, D.

    1989-01-01

    The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a specially suited framework for the computation of bound-state (hadron) properties. The most important reasons are the manifest rotation invariance, the lack of a Gribov horizon (giving standard many-body techniques a better chance), and the fact that a regularization analogous to the lattice regularization is easily implementable. Some details of the Schwinger-gauge Hamiltonian theory are discussed

  18. On one estimate of glueball mass

    International Nuclear Information System (INIS)

    Boos, E.E.

    1986-01-01

    The Bethe-Salpeter equation for the wave function of the bound state of two gluons is considered. The mass of the glueball 0 ++ , (M gl ∼ 1.3 GeV), is estimated using some expansions in the equation kernel in the spirit of those made in the QCD sum rules method. In the leading approximation, the masses of the glueballs 0 ++ and 2 ++ appear to be degenerate. A possibility to improve the accuracy of estimating the mass by using the expansion in 1/N c is discussed

  19. Sb2Te3 crystal a potential absorber material for broadband photodetector: A first-principles study

    Directory of Open Access Journals (Sweden)

    Abdullahi Lawal

    Full Text Available Antimony telluride (Sb2Te3, a layered semiconductor material, is considered a promising absorbing material for a high-performance optoelectronic device within broadband wavelengths because of remarkable features like strong optical absorbance and the narrow direct band gap. In this work, based on the first-principles approach, we investigate in detail the structural, electronic and optical properties of the hexagonal Sb2Te3 compound. The structural and electronic properties were computed using the first-principles approach, treating exchange–correlation potential with generalized gradient approximation (GGA within density functional theory (DFT. Furthermore, for accurate prediction of the band gap, we go beyond DFT and calculated band structure using GW correction. The optical properties, namely, imaginary and real parts of complex dielectric function, absorption coefficient, refractive index, reflectivity, extinction coefficient, electron energy loss function and optical conductivity are performed by quasi-particle many-body perturbation theory (MBPT via Bethe-Salpeter equation (BSE. The computed structural parameters are in good agreement with available experimental data. The obtained quasi-particle (GW correction band structure show the semiconducting character of Sb2Te3 material with a direct band gap Eg of 0.221 eV, in agreement with previously reported value (Eg = 0.210 eV while the projected density of states indicates (PDOS that the p-orbital of Sb and Te atoms are responsible for material properties near the Fermi level. To our knowledge, our first reported calculations of optical properties, with the inclusion of electron-hole effects are consistent with available experimental measurements. Consistencies of our findings with experimental data validate the effectiveness of electron-hole interaction for theoretical investigation of optical properties. Keywords: DFT, Quasi-particle many-body perturbation theory, Bethe-Salpeter

  20. Origins of Singlet Fission in Solid Pentacene from an ab initio Green's Function Approach

    Science.gov (United States)

    Refaely-Abramson, Sivan; da Jornada, Felipe H.; Louie, Steven G.; Neaton, Jeffrey B.

    2017-12-01

    We develop a new first-principles approach to predict and understand rates of singlet fission with an ab initio Green's-function formalism based on many-body perturbation theory. Starting with singlet and triplet excitons computed from a G W plus Bethe-Salpeter equation approach, we calculate the exciton-biexciton coupling to lowest order in the Coulomb interaction, assuming a final state consisting of two noninteracting spin-correlated triplets with finite center-of-mass momentum. For crystalline pentacene, symmetries dictate that the only purely Coulombic fission decay process from a bright singlet state requires a final state consisting of two inequivalent nearly degenerate triplets of nonzero, equal and opposite, center-of-mass momenta. For such a process, we predict a singlet lifetime of 30-70 fs, in very good agreement with experimental data, indicating that this process can dominate singlet fission in crystalline pentacene. Our approach is general and provides a framework for predicting and understanding multiexciton interactions in solids.

  1. Variational identities and Hamiltonian structures

    International Nuclear Information System (INIS)

    Ma Wenxiu

    2010-01-01

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

  2. From tricritical Ising to critical Ising by thermodynamic Bethe ansatz

    International Nuclear Information System (INIS)

    Zamolodchikov, A.B.

    1991-01-01

    A simple factorized scattering theory is suggested for the massless Goldstone fermions of the trajectory flowing from the tricritical Ising fixed point to the critical Ising one. The thermodynamic Bethe ansatz approach is applied to this scattering theory to support its interpretation both analytically and numerically. As a generalization a sequence of massless TBA systems is proposed which seems relevant for the trajectories interpolating between two successive minimal CFT models M p and M p-1 . (orig.)

  3. On single-time reduction in quantum field theory

    International Nuclear Information System (INIS)

    Arkhipov, A.A.

    1984-01-01

    It is shown, how the causality and spectrality properties in qUantum field theory may help one to carry out a single-time reduction of the Bethe-Salpeter wave fUnction. The single-time reduction technique is not based on any concrete model of the quantum field theory. Axiomatic formulations underline the quantum field theory

  4. Hamiltonian closures in fluid models for plasmas

    Science.gov (United States)

    Tassi, Emanuele

    2017-11-01

    This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and

  5. Quantum group symmetries and completeness for \\boldsymbol {A}_{\\boldsymbol {2n}}^{\\boldsymbol{(2)}} open spin chains

    Science.gov (United States)

    Ahmed, Ibrahim; Nepomechie, Rafael I.; Wang, Chunguang

    2017-07-01

    We argue that the Hamiltonians for A(2)2n open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries Uq(Bn) and Uq(Cn) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

  6. Cluster expansion for ground states of local Hamiltonians

    Directory of Open Access Journals (Sweden)

    Alvise Bastianello

    2016-08-01

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

  7. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

    DEFF Research Database (Denmark)

    Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip

    2016-01-01

    We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...

  8. Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

    Science.gov (United States)

    Bridges, Thomas J.; Reich, Sebastian

    2001-06-01

    The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

  9. Quantum many-body effects in x-ray spectra efficiently computed using a basic graph algorithm

    Science.gov (United States)

    Liang, Yufeng; Prendergast, David

    2018-05-01

    The growing interest in using x-ray spectroscopy for refined materials characterization calls for an accurate electronic-structure theory to interpret the x-ray near-edge fine structure. In this work, we propose an efficient and unified framework to describe all the many-electron processes in a Fermi liquid after a sudden perturbation (such as a core hole). This problem has been visited by the Mahan-Noziéres-De Dominicis (MND) theory, but it is intractable to implement various Feynman diagrams within first-principles calculations. Here, we adopt a nondiagrammatic approach and treat all the many-electron processes in the MND theory on an equal footing. Starting from a recently introduced determinant formalism [Phys. Rev. Lett. 118, 096402 (2017), 10.1103/PhysRevLett.118.096402], we exploit the linear dependence of determinants describing different final states involved in the spectral calculations. An elementary graph algorithm, breadth-first search, can be used to quickly identify the important determinants for shaping the spectrum, which avoids the need to evaluate a great number of vanishingly small terms. This search algorithm is performed over the tree-structure of the many-body expansion, which mimics a path-finding process. We demonstrate that the determinantal approach is computationally inexpensive even for obtaining x-ray spectra of extended systems. Using Kohn-Sham orbitals from two self-consistent fields (ground and core-excited state) as input for constructing the determinants, the calculated x-ray spectra for a number of transition metal oxides are in good agreement with experiments. Many-electron aspects beyond the Bethe-Salpeter equation, as captured by this approach, are also discussed, such as shakeup excitations and many-body wave function overlap considered in Anderson's orthogonality catastrophe.

  10. Manipulating Light with Transition Metal Clusters, Organic Dyes, and Metal Organic Frameworks

    Energy Technology Data Exchange (ETDEWEB)

    Ogut, Serdar [Univ. of Illinois, Chicago, IL (United States)

    2017-09-11

    The primary goals of our research program is to develop and apply state-of-the-art first-principles methods to predict electronic and optical properties of three systems of significant scientific and technological interest: transition metal clusters, organic dyes, and metal-organic frameworks. These systems offer great opportunities to manipulate light for a wide ranging list of energy-related scientific problems and applications. During this grant period, we focused our investigations on the development, implementation, and benchmarking of many-body Green’s function methods (GW approximation and the Bethe-Salpeter equation) to examine excited-state properties of transition metal/transition-metal-oxide clusters and organic molecules that comprise the building blocks of dyes and metal-organic frameworks.

  11. Combining the GW formalism with the polarizable continuum model: A state-specific non-equilibrium approach

    Energy Technology Data Exchange (ETDEWEB)

    Duchemin, Ivan, E-mail: ivan.duchemin@cea.fr [INAC, SP2M/L-Sim, CEA/UJF Cedex 09, 38054 Grenoble (France); Jacquemin, Denis [Laboratoire CEISAM - UMR CNR 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3 (France); Institut Universitaire de France, 1 rue Descartes, 75005 Paris Cedex 5 (France); Blase, Xavier [CNRS, Inst. NÉEL, F-38000 Grenoble (France); Univ. Grenoble Alpes, Inst. NÉEL, F-38000 Grenoble (France)

    2016-04-28

    We have implemented the polarizable continuum model within the framework of the many-body Green’s function GW formalism for the calculation of electron addition and removal energies in solution. The present formalism includes both ground-state and non-equilibrium polarization effects. In addition, the polarization energies are state-specific, allowing to obtain the bath-induced renormalisation energy of all occupied and virtual energy levels. Our implementation is validated by comparisons with ΔSCF calculations performed at both the density functional theory and coupled-cluster single and double levels for solvated nucleobases. The present study opens the way to GW and Bethe-Salpeter calculations in disordered condensed phases of interest in organic optoelectronics, wet chemistry, and biology.

  12. Contact Hamiltonian mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)

    2017-01-15

    In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.

  13. A Political End to a Pioneering Career: Marianne Beth and the Psychology of Religion

    Directory of Open Access Journals (Sweden)

    Jacob A. Belzen

    2011-07-01

    Full Text Available Although forgotten in both Religionswissenschaft (the Science of Religion and psychology, Marianne Beth (1880-1984, initially trained as a lawyer and already in 1928 called a “leading European woman”, must be considered as one of the female pioneers of these fields. She has been active especially in the psychology of religion, a field in which she, together with her husband Karl Beth, founded a research institute, an international organization and a journal. In 1932, the Beths organized in Vienna (where Karl was a professor the largest conference ever in the history of the psychology of religion. Because of her Jewish descent, Marianne Beth fled to the USA when Austria was annexed by Nazi Germany in 1938. This brought an abrupt end to her career as researcher and writer. The article reconstructs Marianne Beth’s path into psychology, analyzes some of her work and puts her achievements in an international perspective.

  14. Introduction to the thermodynamic Bethe ansatz

    Science.gov (United States)

    van Tongeren, Stijn J.

    2016-08-01

    We give a pedagogical introduction to the thermodynamic Bethe ansatz, a method that allows us to describe the thermodynamics of integrable models whose spectrum is found via the (asymptotic) Bethe ansatz. We set the stage by deriving the Fermi-Dirac distribution and associated free energy of free electrons, and then in a similar though technically more complicated fashion treat the thermodynamics of integrable models, focusing first on the one-dimensional Bose gas with delta function interaction as a clean pedagogical example, secondly the XXX spin chain as an elementary (lattice) model with prototypical complicating features in the form of bound states, and finally the {SU}(2) chiral Gross-Neveu model as a field theory example. Throughout this discussion we emphasize the central role of particle and hole densities, whose relations determine the model under consideration. We then discuss tricks that allow us to use the same methods to describe the exact spectra of integrable field theories on a circle, in particular the chiral Gross-Neveu model. We moreover discuss the simplification of TBA equations to Y systems, including the transition back to integral equations given sufficient analyticity data, in simple examples.

  15. Fungible dynamics: There are only two types of entangling multiple-qubit interactions

    International Nuclear Information System (INIS)

    Bremner, Michael J.; Dodd, Jennifer L.; Nielsen, Michael A.; Bacon, Dave

    2004-01-01

    What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? It has been shown that all two-body Hamiltonian evolutions can be simulated using any fixed two-body entangling n-qubit Hamiltonian and fast local unitaries. By entangling we mean that every qubit is coupled to every other qubit, if not directly, then indirectly via intermediate qubits. We extend this study to the case where interactions may involve more than two qubits at a time. We find necessary and sufficient conditions for an arbitrary n-qubit Hamiltonian to be dynamically universal, that is, able to simulate any other Hamiltonian acting on n qubits, possibly in an inefficient manner. We prove that an entangling Hamiltonian is dynamically universal if and only if it contains at least one coupling term involving an even number of interacting qubits. For odd entangling Hamiltonians, i.e., Hamiltonians with couplings that involve only an odd number of qubits, we prove that dynamic universality is possible on an encoded set of n-1 logical qubits. We further prove that an odd entangling Hamiltonian can simulate any other odd Hamiltonian and classify the algebras that such Hamiltonians generate. Thus, our results show that up to local unitary operations, there are only two fundamentally different types of entangling Hamiltonian on n qubits. We also demonstrate that, provided the number of qubits directly coupled by the Hamiltonian is bounded above by a constant, our techniques can be made efficient

  16. Irreducible kernels and nonperturbative expansions in a theory with pure m -> m interaction

    International Nuclear Information System (INIS)

    Iagolnitzer, D.

    1983-01-01

    Recent results on the structure of the S matrix at the m-particle threshold (m>=2) in a simplified m->m scattering theory with no subchannel interaction are extended to the Green function F on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure of F around s=(mμ) 2 depending on the parity of (m-1) (ν-1) (where μ>0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernel U [which is the analogue of the K matrix in the two different parity cases (m-1)(ν-1) odd or even] and related local expansion of F, for (m-1)(ν-1) even, in powers of sigmasup(β)lnsigma(sigma=(mμ) 2 -s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernel U. The links between kernel U and Bethe-Salpeter type kernels G of the theory are exhibited in both parity cases, as also the links between the above expansion of F and local expansions, in the Bethe-Salpeter type framework, of Fsub(lambda) in terms of Feynman-type integrals in which each vertex is a kernel G and which include both dominant and subdominant contributions. (orig.)

  17. Baryon-baryon bound states from first principles in 3+1 lattice QCD with two flavors and strong coupling

    International Nuclear Information System (INIS)

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

    2006-01-01

    We determine baryon-baryon bound states in (3+1)-dimensional SU(3) lattice QCD with two flavors, 4x4 spin matrices, and in an imaginary time formulation. For small hopping parameter κ>0 and large glueball mass (strong coupling), we show the existence of three-quark isospin 1/2 particles (proton and neutron) and isospin 3/2 baryons (delta particles), with asymptotic masses -3lnκ and isolated dispersion curves. Baryon-baryon bound states of isospin zero are found with binding energy of order κ 2 , using a ladder approximation to a lattice Bethe-Salpeter equation. The dominant baryon-baryon interaction is an energy-independent spatial range-one attractive potential with an O(κ 2 ) strength. There is also attraction arising from gauge field correlations associated with six overlapping bonds, but it is counterbalanced by Pauli repulsion to give a vanishing zero-range potential. The overall range-one potential results from a quark, antiquark exchange with no meson exchange interpretation; the repulsive or attractive nature of the interaction depends on the isospin and spin of the two-baryon state

  18. Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

    Science.gov (United States)

    Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan

    2018-02-01

    Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

  19. Relationship of field-theory based single-boson-exchange potentials to static ones

    International Nuclear Information System (INIS)

    Amghar, A.; Desplanques, B.

    2000-01-01

    It is shown that field-theory based single-boson-exchange potentials cannot be identified to those of the Yukawa or Coulomb type that are currently inserted in the Schroedinger equation. The potential which is obtained rather correspond to this current single-boson-exchange potential corrected for the probability that the system under consideration is in a two-body component, therefore missing contributions due to the interaction of these two bodies while bosons are exchanged. The role of these contributions, which involve at least two-boson exchanges, is examined. The conditions that allow one to recover the usual single-boson-exchange potential are given. It is shown that the present results have some relation: (i) to the failure of the Bethe-Salpeter equation in reproducing the Dirac or Klein-Gordon equations in the limit where one of the constituents has a large mass, (ii) to the absence of corrections of relative order α log 1/α to a full calculation of the binding energy in the case of neutral massless bosons or (iii) to large corrections of wave-functions calculated perturbatively in some light-front approaches. Refs. 48 (author)

  20. Quantum entangling power of adiabatically connected Hamiltonians

    International Nuclear Information System (INIS)

    Hamma, Alioscia; Zanardi, Paolo

    2004-01-01

    The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied

  1. On the Relativistic Separable Functions for the Breakup Reactions

    Science.gov (United States)

    Bondarenko, Serge G.; Burov, Valery V.; Rogochaya, Elena P.

    2018-02-01

    In the paper the so-called modified Yamaguchi function for the Bethe-Salpeter equation with a separable kernel is discussed. The type of the functions is defined by the analytic stucture of the hadron current with breakup - the reactions with interacting nucleon-nucleon pair in the final state (electro-, photo-, and nucleon-disintegration of the deuteron).

  2. Relativistic quarkonium dynamics

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1985-06-01

    We present, in the framework of relativistic quantum mechanics of two interacting particles, a general model for quarkonium systems satisfying the following four requirements: confinement, spontaneous breakdown of chiral symmetry, soft explicit chiral symmetry breaking, short distance interactions of the vector type. The model is characterized by two arbitrary scalar functions entering in the large and short distance interaction potentials, respectively. Using relationships with corresponding quantities of the Bethe-Salpeter equation, we also present the normalization condition of the wave functions, as well as the expressions of the meson decay coupling constants. The quark masses appear in this model as free parameters

  3. Evidence of ghost suppression in gluon mass scale dynamics

    Science.gov (United States)

    Aguilar, A. C.; Binosi, D.; Figueiredo, C. T.; Papavassiliou, J.

    2018-03-01

    In this work we study the impact that the ghost sector of pure Yang-Mills theories may have on the generation of a dynamical gauge boson mass scale, which hinges on the appearance of massless poles in the fundamental vertices of the theory, and the subsequent realization of the well-known Schwinger mechanism. The process responsible for the formation of such structures is itself dynamical in nature, and is governed by a set of Bethe-Salpeter type of integral equations. While in previous studies the presence of massless poles was assumed to be exclusively associated with the background-gauge three-gluon vertex, in the present analysis we allow them to appear also in the corresponding ghost-gluon vertex. The full analysis of the resulting Bethe-Salpeter system reveals that the contribution of the poles associated with the ghost-gluon vertex are particularly suppressed, their sole discernible effect being a slight modification in the running of the gluon mass scale, for momenta larger than a few GeV. In addition, we examine the behavior of the (background-gauge) ghost-gluon vertex in the limit of vanishing ghost momentum, and derive the corresponding version of Taylor's theorem. These considerations, together with a suitable Ansatz, permit us the full reconstruction of the pole sector of the two vertices involved.

  4. Thermodynamic Bethe Ansatz for the Spin-1/2 Staggered XXZ- Model

    OpenAIRE

    Mkhitaryan, V. V.; Sedrakyan, A. G.

    2003-01-01

    We develop the technique of Thermodynamic Bethe Ansatz to investigate the ground state and the spectrum in the thermodynamic limit of the staggered $XXZ$ models proposed recently as an example of integrable ladder model. This model appeared due to staggered inhomogeneity of the anisotropy parameter $\\Delta$ and the staggered shift of the spectral parameter. We give the structure of ground states and lowest lying excitations in two different phases which occur at zero temperature.

  5. Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Cao, Junpeng [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Yang, Wen-Li, E-mail: wlyang@nwu.edu.cn [Institute of Modern Physics, Northwest University, Xian 710069 (China); Shi, Kangjie [Institute of Modern Physics, Northwest University, Xian 710069 (China); Wang, Yupeng, E-mail: yupeng@iphy.ac.cn [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)

    2013-10-01

    Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T–Q relation and the Bethe ansatz equations are derived.

  6. Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions

    International Nuclear Information System (INIS)

    Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng

    2013-01-01

    Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T–Q relation and the Bethe ansatz equations are derived

  7. Ab initio calculation of the electronic and optical properties of solid pentacene

    International Nuclear Information System (INIS)

    Tiago, Murilo L.; Northrup, John E.; Louie, Steve G.

    2002-01-01

    The optical and electronic properties of crystalline pentacene are studied, using a first-principles Green's-function approach. The quasiparticle energies are calculated within the GW approximation and the electron-hole excitations are computed by solving the Bethe-Salpeter equation. We investigate the role of polymorphism on the electronic energy gap and linear optical spectrum by studying two different crystalline phases: the solution-phase structure and the vapor-phase structure. charge-transfer excitons are found to dominate the optical spectrum. Excitons with sizable binding energies are predicted for both phases

  8. Hans Bethe, Quantum Mechanics, and the Lamb Shift

    Indian Academy of Sciences (India)

    addressed by Bethe in his own inimitable style: He was returning to ... the solution in the train itself (!), on his return journey ... was a viable atomic model to account for some cru- ... The WS conditions in turn were based on the Hamilton-.

  9. The bi-Hamiltonian structures of the Manin-Radul super KP hierarchy

    International Nuclear Information System (INIS)

    Panda, S.; Roy, S.

    1992-05-01

    We consider the ''even-time'' flow of the Manin-Radul supersymmetric KP hierarchy and show that it possesses bi-Hamiltonian structures by deriving two distinct Gelfand-Dikii brackets corresponding to two successive Hamiltonians of the system. A recursion relation involving them is also obtained. We observe that the first Hamiltonian structure defines a supersymmetric Lie algebra since it is a linear algebra among the super fields appearing in the Lax operator whereas the second Hamiltonian structure is a non-linear algebra and so it does not define a Lie algebra. (author). 25 refs

  10. Hamiltonian Algorithm Sound Synthesis

    OpenAIRE

    大矢, 健一

    2013-01-01

    Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.

  11. Effective hamiltonian within the microscopic unitary nuclear model

    International Nuclear Information System (INIS)

    Avramenko, V.I.; Blokhin, A.L.

    1989-01-01

    Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs

  12. Bethe ansatz solutions of the τ{sub 2}-model with arbitrary boundary fields

    Energy Technology Data Exchange (ETDEWEB)

    Xu, Xiaotian; Hao, Kun; Yang, Tao [Institute of Modern Physics, Northwest University,Xian 710069 (China); Shaanxi Key Laboratory for Theoretical Physics Frontiers,Xian 710069 (China); Cao, Junpeng [Beijing National Laboratory for Condensed Matter Physics,Institute of Physics, Chinese Academy of Sciences,Beijing 100190 (China); Collaborative Innovation Center of Quantum Matter,Beijing (China); School of Physical Sciences, University of Chinese Academy of Sciences,Beijing (China); Yang, Wen-Li [Institute of Modern Physics, Northwest University,Xian 710069 (China); Shaanxi Key Laboratory for Theoretical Physics Frontiers,Xian 710069 (China); Beijing Center for Mathematics and Information Interdisciplinary Sciences,Beijing, 100048 (China); Shi, Kangjie [Institute of Modern Physics, Northwest University,Xian 710069 (China); Shaanxi Key Laboratory for Theoretical Physics Frontiers,Xian 710069 (China)

    2016-11-11

    The quantum τ{sub 2}-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an inhomogeneous T−Q relation, which is based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices. Moreover, the associated Bethe Ansatz equations are also obtained.

  13. Bethe ansatz approach to quantum sine Gordon thermodynamics and finite temperature excitations

    International Nuclear Information System (INIS)

    Zotos, X.

    1982-01-01

    Takahashi and Suzuki (TS) using the Bethe ansatz method developed a formalism for the thermodynamics of the XYZ spin chain. Translating their formalism to the quantum sine-Gordon system, the thermodynamics and finite temperature elementary excitations are analyzed. Criteria imposed by TS on the allowed states simply correspond to the condition of normalizability of the wave functions. A set of coupled nonlinear integral equations for the thermodynamic equilibrium densities for particular values of the coupling constant in the attractive regime is derived. Solving numerically these Bethe ansatz equations, curves of the specific heat as a function of temperature are obtained. The soliton contribution peaks at a temperature of about 0.4 soliton masses shifting downward as the classical limit is approached. The weak coupling regime is analyzed by deriving the Bethe ansatz equations including the charged vacuum excitations. It is shown that they are necessary for a consistent presentation of the thermodynamics

  14. Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator

    International Nuclear Information System (INIS)

    Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.

    1984-01-01

    Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator

  15. Remarks on Hamiltonian structures in G2-geometry

    International Nuclear Information System (INIS)

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

    2013-01-01

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

  16. Modelling chaotic Hamiltonian systems as a Markov Chain ...

    African Journals Online (AJOL)

    The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...

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

    Science.gov (United States)

    Yang, Yongliang; Wunsch, Donald; Yin, Yixin

    2017-08-01

    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.

  18. The Bethe Sum Rule and Basis Set Selection in the Calculation of Generalized Oscillator Strengths

    DEFF Research Database (Denmark)

    Cabrera-Trujillo, Remigio; Sabin, John R.; Oddershede, Jens

    1999-01-01

    Fulfillment of the Bethe sum rule may be construed as a measure of basis set quality for atomic and molecular properties involving the generalized oscillator strength distribution. It is first shown that, in the case of a complete basis, the Bethe sum rule is fulfilled exactly in the random phase...

  19. A hierarchy of Liouville integrable discrete Hamiltonian equations

    Energy Technology Data Exchange (ETDEWEB)

    Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn

    2008-05-12

    Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.

  20. Elastic proton-deuteron backward scattering: relativistic effects and polarization observables

    International Nuclear Information System (INIS)

    Kaptari, L.P.; Semikh, S.S.

    1997-10-01

    The elastic proton-deuteron backward reaction is analyzed within a covariant approach based on the Bethe-Salpeter equation with 000. Lorentz boost and other relativistic effects in the cross section and spin correlation observables, like tensor analyzing power and polarization transfer etc., are investigated in explicit form. Results of numerical calculations for a complete set of polarization observables are presented. (orig.)

  1. Dynamic equations for gauge-invariant wave functions

    International Nuclear Information System (INIS)

    Kapshaj, V.N.; Skachkov, N.B.; Solovtsov, I.L.

    1984-01-01

    The Bethe-Salpeter and quasipotential dynamic equations for wave functions of relative quark motion, have been derived. Wave functions are determined by the gauge invariant method. The V.A. Fock gauge condition is used in the construction. Despite the transl tional noninvariance of the gauge condition the standard separation of variables has been obtained and wave function doesn't contain gauge exponents

  2. On the origin of the pion in confinement schemes

    International Nuclear Information System (INIS)

    Brout, R.; Englert, F.; Frere, J.-M.

    1978-01-01

    It is argued that the 't Hooft one-dimensional gauge model is a good starting point on how to conceive the pion in confinement schemes. The results of Wu on the quark propagator in this model are analyzed in the light of spontaneously broken chiral symmetry and the existence of the pion is deduced. The corresponding Bethe-Salpeter wave function is exhibited. (Auth.)

  3. Fermion-boson scattering in ladder approximation

    International Nuclear Information System (INIS)

    Jafarov, R.G.; Hadjiev, S.A.

    1992-10-01

    A method of calculation of forward scattering amplitude for fermions and scalar bosons with exchanging of scalar particle is suggested. The Bethe-Salpeter ladder equation for the imaginary part of the amplitude is constructed and a solution in Regge asymptotical form is found and the corrections to the amplitude due to the exit from mass shell are calculated. (author). 8 refs

  4. Nonperturbative Aspects of Axial Vector Vertex

    Institute of Scientific and Technical Information of China (English)

    ZONG Hong-Shi; CHEN Xiang-Song; WANG Fan; CHANG Chao-Hsi; ZHAO En-Guang

    2002-01-01

    It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model.Gluon dressing of the axial vector vertex and the quark self-energy functions are described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger Dyson equation in the rainbow approximation,respectively.

  5. On local Hamiltonians and dissipative systems

    Energy Technology Data Exchange (ETDEWEB)

    Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)

    2006-11-15

    We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.

  6. Quantum-mechanical theory for electronic-vibrational-rotational energy transfer in atom--diatom collisions: Analysis of the Hamiltonian

    International Nuclear Information System (INIS)

    Bellum, J.C.; McGuire, P.

    1983-01-01

    We investigate forms of the molecular system Hamiltonian valid for rigorous quantum-mechanical treatments of inelastic atom--diatom collisions characterized by exchange of energy between electronic, vibrational, and rotational degrees of freedom. We analyze this Hamiltonian in terms of various choices of independent coordinates which unambiguously specify the electronic and nuclear positions in the context of space-fixed and body-fixed reference frames. In particular we derive forms of the Hamiltonian in the context of the following four sets of independent coordinates: (1) a so-called space-fixed set, in which both electronic and nuclear positions are relative to the space-fixed frame; (2) a so-called mixed set, in which nuclear positions are relative to the body-fixed frame while electronic positions are relative to the space-fixed frame; (3) a so-called body-fixed set, in which both electronic and nuclear positions are relative to the body-fixed frame; and (4) another mixed set, in which nuclear positions are relative to the space-fixed frame while electronic positions are relative to the body-fixed frame. Based on practical considerations in accounting for electronic structure and nonadiabatic coupling of electronic states of the collision complex we find the forms of the Hamiltonian in the context of coordinate sets (3) and (4) above to be most appropriate, respectively, for body-fixed and space-fixed treatments of nuclear dynamics in collisional transfer of electronic, vibrational, and rotational energies

  7. Many-body forces in nuclear shell-model

    International Nuclear Information System (INIS)

    Rath, P.K.

    1985-01-01

    In the microscopic derivation of the effective Hamiltonian for the nuclear shell model many-body forces between the valence nucleons occur. These many-body forces can be discriminated in ''real'' many-body forces, which can be related to mesonic and internal degrees of freedom of the nucleons, and ''effective'' many-body forces, which arise by the confinement of the nucleonic Hilbert space to the finite-dimension shell-model space. In the present thesis the influences of such three-body forces on the spectra of sd-shell nuclei are studied. For this the two common techniques for shell-model calculations (Oak Ridge-Rochester and Glasgow representation) are extended in such way that a general three-body term in the Hamiltonian can be regarded. The studies show that the repulsive contributions of the considered three-nucleon forces become more important with increasing number of valence nucleons. By this the particle-number dependence of empirical two-nucleon forces can be qualitatively explained. A special kind of effective many-body force occurs in the folded diagram expansion of the energy-dependent effective Hamiltonian for the shell model. Thereby it is shown that the contributions of the folded diagrams with three nucleons are just as important as those with two nucleons. Thus it is to be suspected that the folded diagram expansion contains many-particle terms with arbitrary particle number. The present studies however show that four nucleon effects are neglegible so that the folded diagram expansion can be confined to two- and three-particle terms. In shell-model calculations which extend over several main shells the influences of the spurious center-of-mass motion must be regarded. A procedure is discussed by which these spurious degrees of freedom can be exactly separated. (orig.) [de

  8. Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces

    CERN Document Server

    Jacob, Birgit

    2012-01-01

    This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir

  9. Loop expansion around the Bethe approximation through the M-layer construction

    Science.gov (United States)

    Altieri, Ada; Chiara Angelini, Maria; Lucibello, Carlo; Parisi, Giorgio; Ricci-Tersenghi, Federico; Rizzo, Tommaso

    2017-11-01

    For every physical model defined on a generic graph or factor graph, the Bethe M-layer construction allows building a different model for which the Bethe approximation is exact in the large M limit, and coincides with the original model for M=1 . The 1/M perturbative series is then expressed by a diagrammatic loop expansion in terms of so-called fat diagrams. Our motivation is to study some important second-order phase transitions that do exist on the Bethe lattice, but are either qualitatively different or absent in the corresponding fully connected case. In this case, the standard approach based on a perturbative expansion around the naive mean field theory (essentially a fully connected model) fails. On physical grounds, we expect that when the construction is applied to a lattice in finite dimension there is a small region of the external parameters, close to the Bethe critical point, where strong deviations from mean-field behavior will be observed. In this region, the 1/M expansion for the corrections diverges, and can be the starting point for determining the correct non-mean-field critical exponents using renormalization group arguments. In the end, we will show that the critical series for the generic observable can be expressed as a sum of Feynman diagrams with the same numerical prefactors of field theories. However, the contribution of a given diagram is not evaluated by associating Gaussian propagators to its lines, as in field theories: one has to consider the graph as a portion of the original lattice, replacing the internal lines with appropriate one-dimensional chains, and attaching to the internal points the appropriate number of infinite-size Bethe trees to restore the correct local connectivity of the original model. The actual contribution of each (fat) diagram is the so-called line-connected observable, which also includes contributions from sub-diagrams with appropriate prefactors. In order to compute the corrections near to the critical

  10. An algorithm for finding a similar subgraph of all Hamiltonian cycles

    Science.gov (United States)

    Wafdan, R.; Ihsan, M.; Suhaimi, D.

    2018-01-01

    This paper discusses an algorithm to find a similar subgraph called findSimSubG algorithm. A similar subgraph is a subgraph with a maximum number of edges, contains no isolated vertex and is contained in every Hamiltonian cycle of a Hamiltonian Graph. The algorithm runs only on Hamiltonian graphs with at least two Hamiltonian cycles. The algorithm works by examining whether the initial subgraph of the first Hamiltonian cycle is a subgraph of comparison graphs. If the initial subgraph is not in comparison graphs, the algorithm will remove edges and vertices of the initial subgraph that are not in comparison graphs. There are two main processes in the algorithm, changing Hamiltonian cycle into a cycle graph and removing edges and vertices of the initial subgraph that are not in comparison graphs. The findSimSubG algorithm can find the similar subgraph without using backtracking method. The similar subgraph cannot be found on certain graphs, such as an n-antiprism graph, complete bipartite graph, complete graph, 2n-crossed prism graph, n-crown graph, n-möbius ladder, prism graph, and wheel graph. The complexity of this algorithm is O(m|V|), where m is the number of Hamiltonian cycles and |V| is the number of vertices of a Hamiltonian graph.

  11. Ab initio electronic structure of quasi-two-dimensional materials: A “native” Gaussian–plane wave approach

    Energy Technology Data Exchange (ETDEWEB)

    Trevisanutto, Paolo E. [Graphene Research Centre and CA2DM, National University of Singapore, Singapore 117542, Singapore and Singapore Synchrotron Light Source, National University of Singapore, Singapore 117603 (Singapore); Vignale, Giovanni, E-mail: vignaleg@missouri.edu [Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211 (United States)

    2016-05-28

    Ab initio electronic structure calculations of two-dimensional layered structures are typically performed using codes that were developed for three-dimensional structures, which are periodic in all three directions. The introduction of a periodicity in the third direction (perpendicular to the layer) is completely artificial and may lead in some cases to spurious results and to difficulties in treating the action of external fields. In this paper we develop a new approach, which is “native” to quasi-2D materials, making use of basis function that are periodic in the plane, but atomic-like in the perpendicular direction. We show how some of the basic tools of ab initio electronic structure theory — density functional theory, GW approximation and Bethe-Salpeter equation — are implemented in the new basis. We argue that the new approach will be preferable to the conventional one in treating the peculiarities of layered materials, including the long range of the unscreened Coulomb interaction in insulators, and the effects of strain, corrugations, and external fields.

  12. Effective Hamiltonian for travelling discrete breathers

    Science.gov (United States)

    MacKay, Robert S.; Sepulchre, Jacques-Alexandre

    2002-05-01

    Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

  13. ODE/IM correspondence and Bethe ansatz for affine Toda field equations

    Directory of Open Access Journals (Sweden)

    Katsushi Ito

    2015-07-01

    Full Text Available We study the linear problem associated with modified affine Toda field equation for the Langlands dual gˆ∨, where gˆ is an untwisted affine Lie algebra. The connection coefficients for the asymptotic solutions of the linear problem are found to correspond to the Q-functions for g-type quantum integrable models. The ψ-system for the solutions associated with the fundamental representations of g leads to Bethe ansatz equations associated with the affine Lie algebra gˆ. We also study the A2r(2 affine Toda field equation in massless limit in detail and find its Bethe ansatz equations as well as T–Q relations.

  14. Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

    Science.gov (United States)

    Risser, Steven Michael

    This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb

  15. Generalized Bethe-Negele inequalities for excited states in muonic atoms

    International Nuclear Information System (INIS)

    Klarsfeld, S.

    1976-11-01

    Rigorous upper and lower bounds are derived for the Bethe logarithms in excited states of muonic atoms. Comparison with previous empirical estimates shows that the latter are inadequate in certain cases

  16. Mixed spin-5/2 and spin-2 Ising ferrimagnetic system on the Bethe lattice

    Energy Technology Data Exchange (ETDEWEB)

    Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, PB 63 46000, Safi (Morocco); Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014, Rabat (Morocco); Jabar, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014, Rabat (Morocco); Benyoussef, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)

    2015-11-01

    The magnetic properties of spins-S and σ Ising model on the Bethe lattice have been investigated by using the Monte Carlo simulation. The thermal total magnetization and magnetization of spins S and σ with the different exchange interactions, different external magnetic field and different temperatures have been studied. The critical temperature and compensation temperature have been deduced. The magnetic hysteresis cycle of Ising ferrimagnetic system on the Bethe lattice has been deduced for different values of exchange interactions between the spins S and σ, for different values of crystal field and for different sizes. The magnetic coercive filed has been deduced. - Highlights: • The magnetic properties of Bethe lattice have been investigated. • The critical temperature and compensation temperature have been deduced. • The magnetic coercive filed has been deduced.

  17. The Quantum N-Body Problem and the Auxiliary Field Method

    International Nuclear Information System (INIS)

    Semay, C.; Buisseret, F.; Silvestre-Brac, B.

    2011-01-01

    Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. We first review the method in the case of nonrelativistic two-body problems. A general procedure is then given for N-body systems and applied to the case of baryons in the large-N c limit. (author)

  18. A local inverse spectral theorem for Hamiltonian systems

    International Nuclear Information System (INIS)

    Langer, Matthias; Woracek, Harald

    2011-01-01

    We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients

  19. Ab initio Hamiltonian approach to light nuclei and quantum field theory

    International Nuclear Information System (INIS)

    Vary, James P.

    2009-01-01

    A basis-function approach that has proven successful for solving the nonrelativistic strongly interacting nuclear many-body problem and appears promising for solving relativistic field theory in a light-front Hamiltonian framework is presented. Both conventional nuclear manybody theory and light-front field theory face common issues within the Hamiltonian approach - i.e. how to; (1) define the Hamiltonian; (2) renormalize to a finite space; (3) solve for non-perturbative observables, preserving as many symmetries as possible; and (4) take the continuum limit. Each of these challenges requires a substantial undertaking but appears solvable. Advances in computational physics, both algorithms and parallel computers, have proven essential to the recent progress. I will present results that illustrate the recent advances and indicate the path forward to ever more realistic applications

  20. Thermodynamic Bethe ansatz with Haldane statistics

    International Nuclear Information System (INIS)

    Bytsko, A.G.; Fring, A.

    1998-01-01

    We derive the thermodynamic Bethe ansatz equation for the situation in which the statistical interaction of a multi-particle system is governed by Haldane statistics. We formulate a macroscopical equivalence principle for such systems. Particular CDD ambiguities play a distinguished role in compensating the ambiguity in the exclusion statistics. We derive Y-systems related to generalized statistics. We discuss several fermionic, bosonic and anyonic versions of affine Toda field theories and Calogero-Sutherland type models in the context of generalized statistics. (orig.)

  1. Conformal operator product expansion in the Yukawa model

    International Nuclear Information System (INIS)

    Prati, M.C.

    1983-01-01

    Conformal techniques are applied to the Yukawa model, as an example of a theory with spinor fields. It is written the partial-wave analysis of the 4-point function of two scalars and two spinors in the channel phi psi → phi psi in terms of spinor tensor representations of the conformal group. Using this conformal expansion, it is diagonalized the Bethe-Salpeter equation, which is reduced to algebraic relations among the partial waves. It is shown that in the γ 5 -invariant model, but not in the general case, it is possible to derive dynamically from the expansions of the 4-point function the vacuum operator product phi psi>

  2. Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models

    Directory of Open Access Journals (Sweden)

    Sh. Khachatryan

    2015-10-01

    Full Text Available We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang–Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.

  3. Hamiltonian constraint in polymer parametrized field theory

    International Nuclear Information System (INIS)

    Laddha, Alok; Varadarajan, Madhavan

    2011-01-01

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

  4. Correlation functions of the spin chains. Algebraic Bethe Ansatz approach

    International Nuclear Information System (INIS)

    Kitanine, N.

    2007-09-01

    Spin chains are the basic elements of integrable quantum models. These models have direct applications in condense matter theory, in statistical physics, in quantum optics, in field theory and even in string theory but they are also important because they enable us to solve, in an exact manner, non-perturbative phenomena that otherwise would stay unresolved. The method described in this work is based on the algebraic Bethe Ansatz. It is shown how this method can be used for the computation of null temperature correlation functions of the Heisenberg 1/2 spin chain. The important point of this approach is the solution of the inverse quantum problem given by the XXZ spin chain. This solution as well as a simple formulae for the scalar product of the Bethe states, have enabled us to get the most basic correlation functions under the form of multiple integrals. The formalism of multiple integrals open the way for asymptotic analysis for a few physical quantities like the probability of vacuum formation. It is worth noticing that this formalism can give exact results for two-point functions that are the most important correlation functions for applications. A relationship has been discovered between these multiple integrals and the sum of the form factors. The results have been extended to dynamical correlation functions. (A.C.)

  5. Electrical conductivity in random alloys

    International Nuclear Information System (INIS)

    Mookerjee, A.; Yussouff, M.

    1983-06-01

    Starting from the augmented space formalism by one of us, and the use of the Ward identity and Bethe Salpeter equation, a complete formalism for the calculation of the electrical conductivity in tight-binding models of random binary alloys has been developed. The formalism is practical in the sense that viable calculations may be carried out with its help for realistics models of alloy systems. (author)

  6. Correlation functions of the spin chains. Algebraic Bethe Ansatz approach; Fonctions de correlation des chaines de spin. Approche de l'ansatz de Bethe algebrique

    Energy Technology Data Exchange (ETDEWEB)

    Kitanine, N

    2007-09-15

    Spin chains are the basic elements of integrable quantum models. These models have direct applications in condense matter theory, in statistical physics, in quantum optics, in field theory and even in string theory but they are also important because they enable us to solve, in an exact manner, non-perturbative phenomena that otherwise would stay unresolved. The method described in this work is based on the algebraic Bethe Ansatz. It is shown how this method can be used for the computation of null temperature correlation functions of the Heisenberg 1/2 spin chain. The important point of this approach is the solution of the inverse quantum problem given by the XXZ spin chain. This solution as well as a simple formulae for the scalar product of the Bethe states, have enabled us to get the most basic correlation functions under the form of multiple integrals. The formalism of multiple integrals open the way for asymptotic analysis for a few physical quantities like the probability of vacuum formation. It is worth noticing that this formalism can give exact results for two-point functions that are the most important correlation functions for applications. A relationship has been discovered between these multiple integrals and the sum of the form factors. The results have been extended to dynamical correlation functions. (A.C.)

  7. Calculation of point-contact spectra for a simple heavy-fermion Hamiltonian by two approaches. Comparison of results

    International Nuclear Information System (INIS)

    Kupka, M.; Farkasovsky, P.C.

    1992-01-01

    Point-contact spectra have been calculated for normal metal -heavy-fermion metal system (described by means of a simplified model Hamiltonian). Two approaches are used: one of them states that the differential conductance reflects an energy-dependent quasi-particle density of states, and 2. one drives the differential conductance are compared

  8. "Her mouth is medicine": Beth Brant and Paula Gunn Allen's decolonizing queer erotics.

    Science.gov (United States)

    Burford, Arianne

    2013-01-01

    This article asserts the need to recognize the complexity of the theoretical work of more lesbian Native American writers, focusing specifically Beth Brant (Bay of Quinte Mohawk) and Paula Gunn Allen (Laguna Pueblo). Their poetry and short stories provide a theoretically nuanced analysis of how heteronormativity is intertwined in and dependent on colonialism, and thus a methodology for Queer Theory that requires an understanding of it in relation to colonialism. They reject heteronormative Pocahontas fantasies about Native women, offering a lesbian-based tactic for decolonization through the expression of erotic desire. This article demonstrates the endless possibilities for fierce queer resistance, revolutionary change, and healing from the trauma of genocide and the accompanying colonialist heteropatriarchal disciplining of Native women's bodies.

  9. No-go theorem for one-way quantum computing on naturally occurring two-level systems

    International Nuclear Information System (INIS)

    Chen Jianxin; Chen Xie; Duan Runyao; Ji Zhengfeng; Zeng Bei

    2011-01-01

    The ground states of some many-body quantum systems can serve as resource states for the one-way quantum computing model, achieving the full power of quantum computation. Such resource states are found, for example, in spin-(5/2) and spin-(3/2) systems. It is, of course, desirable to have a natural resource state in a spin-(1/2), that is, qubit system. Here, we give a negative answer to this question for frustration-free systems with two-body interactions. In fact, it is shown to be impossible for any genuinely entangled qubit state to be a nondegenerate ground state of any two-body frustration-free Hamiltonian. What is more, we also prove that every spin-(1/2) frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states. In other words, there cannot be any interesting entanglement features in the ground state of such a qubit Hamiltonian.

  10. Exact smooth classification of Hamiltonian vector fields on symplectic 2-manifolds

    International Nuclear Information System (INIS)

    Krouglikov, B.S.

    1994-10-01

    Complete exact classification of Hamiltonian systems with one degree of freedom and Morse Hamiltonian is carried out. As it is a main part of trajectory classification of integrable Hamiltonian systems with two degrees of freedom, the corresponding generalization is considered. The dual problem of classification of symplectic form together with Morse foliation is carried out as well. (author). 10 refs, 16 figs

  11. Empirical Hamiltonians

    International Nuclear Information System (INIS)

    Peggs, S.; Talman, R.

    1987-01-01

    As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases

  12. Mixed spin-((1)/(2)) and spin-1 Blume-Capel Ising ferrimagnetic system on the Bethe lattice

    International Nuclear Information System (INIS)

    Albayrak, Erhan; Keskin, Mustafa

    2003-01-01

    The mixed spin-((1)/(2)) and spin-1 Blume-Capel Ising ferrimagnetic system is studied on the Bethe lattice by using the exact recursion equations. Exact expressions for the magnetization, the quadrupolar moment, the Curie temperature and the free energy are found and the phase diagrams are constructed on the Bethe lattice with the coordination numbers q=3, 4, 5 and 6. The existence of a tricritical point is investigated for different values of q. The results are compared with those of other approximate methods and with the exact result on the Bethe lattice by using a discrete nonlinear map and also the exact results that are available for the case of the honeycomb lattice

  13. Anisotropic generalization of Stinchcombe's solution for the conductivity of random resistor networks on a Bethe lattice

    Science.gov (United States)

    Semeriyanov, F.; Saphiannikova, M.; Heinrich, G.

    2009-11-01

    Our study is based on the work of Stinchcombe (1974 J. Phys. C: Solid State Phys. 7 179) and is devoted to the calculations of average conductivity of random resistor networks placed on an anisotropic Bethe lattice. The structure of the Bethe lattice is assumed to represent the normal directions of the regular lattice. We calculate the anisotropic conductivity as an expansion in powers of the inverse coordination number of the Bethe lattice. The expansion terms retained deliver an accurate approximation of the conductivity at resistor concentrations above the percolation threshold. We make a comparison of our analytical results with those of Bernasconi (1974 Phys. Rev. B 9 4575) for the regular lattice.

  14. Anisotropic generalization of Stinchcombe's solution for the conductivity of random resistor networks on a Bethe lattice

    International Nuclear Information System (INIS)

    Semeriyanov, F; Saphiannikova, M; Heinrich, G

    2009-01-01

    Our study is based on the work of Stinchcombe (1974 J. Phys. C: Solid State Phys. 7 179) and is devoted to the calculations of average conductivity of random resistor networks placed on an anisotropic Bethe lattice. The structure of the Bethe lattice is assumed to represent the normal directions of the regular lattice. We calculate the anisotropic conductivity as an expansion in powers of the inverse coordination number of the Bethe lattice. The expansion terms retained deliver an accurate approximation of the conductivity at resistor concentrations above the percolation threshold. We make a comparison of our analytical results with those of Bernasconi (1974 Phys. Rev. B 9 4575) for the regular lattice.

  15. Quantum graphs with the Bethe-Sommerfeld property

    Czech Academy of Sciences Publication Activity Database

    Exner, Pavel; Turek, Ondřej

    2017-01-01

    Roč. 8, č. 3 (2017), s. 305-309 ISSN 2220-8054 R&D Projects: GA ČR GA17-01706S Institutional support: RVO:61389005 Keywords : periodic quantum graphs * gap number * delta-coupling * rectangular lattice graph * scale-invariant coupling * Bethe-Sommerfeld conjecture * golden mean Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

  16. Semi-Leptonic weak decay form factors of LAMBDAb and SIGMAb(OMEGAb) to proton

    International Nuclear Information System (INIS)

    Haghigat, M.

    1996-01-01

    The matrix elements of the semi-leptonic weak decays of Λ b and of Σ b Ω b to proton are calculated, in the Bethe-Salpeter formalism. We propose a protonic wave function in terms of its dynamically indistinguishable constituent quarks. We show that there are two universal form factors for Λ b → P and four for Σ b (OMEGA b ) → P decays. They depend, as expected, on the Lorentz scalar Υ 1 .Υ 2 , whereΥ 1 and Υ 2 , are the velocities of the baryons. On the first order perturbation approximation, however, the two and the four form factors degenerate to one expression for each of the two decays. (author). 14 refs

  17. Relativistic description of quark-antiquark bound states. II. Spin-dependent treatment

    International Nuclear Information System (INIS)

    Gara, A.; Durand, B.; Durand, L.

    1990-01-01

    We present the results of a study of light- and heavy-quark--antiquark bound states in the context of the reduced Bethe-Salpeter equation, including the full spin dependence. We obtain good fits to the observed spin splittings in the b bar b and c bar c systems using a short-distance single-gluon-exchange interaction, and a long-distance scalar confining interaction. However, we cannot obtain satisfactory fits to the centers of gravity of the b bar b and c bar c spin multiplets at the same time, and the splittings calculated for q bar Q mesons containing the lighter quarks are very poor. The difficulty appears to be intrinsic to the reduced Salpeter equation for reasons which we discuss

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

    International Nuclear Information System (INIS)

    Doroshin, Anton V.

    2010-01-01

    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.

  19. Competition Between Two Large-Amplitude Motion Models: New Hybrid Hamiltonian Versus Old Pure-Tunneling Hamiltonian

    Science.gov (United States)

    Kleiner, Isabelle; Hougen, Jon T.

    2017-06-01

    In this talk we report on our progress in trying to make the hybrid Hamiltonian competitive with the pure-tunneling Hamiltonian for treating large-amplitude motions in methylamine. A treatment using the pure-tunneling model has the advantages of: (i) requiring relatively little computer time, (ii) working with relatively uncorrelated fitting parameters, and (iii) yielding in the vast majority of cases fits to experimental measurement accuracy. These advantages are all illustrated in the work published this past year on a gigantic v_{t} = 1 data set for the torsional fundamental band in methyl amine. A treatment using the hybrid model has the advantages of: (i) being able to carry out a global fit involving both v_{t} = 0 and v_{t} = 1 energy levels and (ii) working with fitting parameters that have a clearer physical interpretation. Unfortunately, a treatment using the hybrid model has the great disadvantage of requiring a highly correlated set of fitting parameters to achieve reasonable fitting accuracy, which complicates the search for a good set of molecular fitting parameters and a fit to experimental accuracy. At the time of writing this abstract, we have been able to carry out a fit with J up to 15 that includes all available infrared data in the v_{t} = 1-0 torsional fundamental band, all ground-state microwave data with K up to 10 and J up to 15, and about a hundred microwave lines within the v_{t} = 1 torsional state, achieving weighted root-mean-square (rms) deviations of about 1.4, 2.8, and 4.2 for these three categories of data. We will give an update of this situation at the meeting. I. Gulaczyk, M. Kreglewski, V.-M. Horneman, J. Mol. Spectrosc., in Press (2017).

  20. Some general properties of the Floquet states for the two dimensional interacting fermion systems with quadratic form Hamiltonians

    International Nuclear Information System (INIS)

    Lungu, R. P.

    2002-01-01

    A fermion 2-dimensional interacting system that is coupled with an external classical field having a time periodic dependence is considered. In the absence of the external field, the single-particle Hamiltonian is quadratic and linear with respect to the canonical operators and the particles have static, scalar, two-body self-interactions; in addition, each particle interacts with an external classical field and the coupling functions with the canonical operators (both the momenta and the position coordinates) are time periodic. This model is a generalization of the two-dimensional electron gas in the presence of a monochromatic linear or circular polarized electromagnetic field. Using the Second Quantization version of the Floquet formalism, we obtain the solution of the eigenvalue problem for the Floquet Hamiltonian with the time-reducing transformation method. we construct an unitary transform that produces a transformed Floquet Hamiltonian that is not time dependent; then, the transformed eigenvalue equation can be resolved and this solution is closely related to the solution of the energy eigenvalue equation of the same system in the absence of the external field. This solution of the Floquet problem has the following important consequences: - Green functions and the correlation density functions of this system are related to the corresponding quantities of the conservative system, so it is possible to develop a diagrammatic method for the perturbed evaluation of these quantities in a similar manner to the conservative situation; - when the system is invariant with respect to space translations in the absence of the external field, the diagrammatic analysis can be performed using a space-time Fourier transform, and this property leads to great simplifications and close correspondences to the conservative theory; - it is possible to construct a result similar to the Pauli theorem, i.e. the quasi-energy eigenvalue of the interacting system (when the classical

  1. Bäcklund transformations and Hamiltonian flows

    International Nuclear Information System (INIS)

    Zullo, Federico

    2013-01-01

    In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)

  2. Green's function approach to the anisotropic Kondo-necklace lattice

    International Nuclear Information System (INIS)

    Rezania, H.; Langari, A.; Thalmeier, P.

    2007-01-01

    Full text: We have studied the effect of anisotropy on the quantum phase transition of the 2D anisotropic Kondo necklace lattice [1] within a Green's function approach [2]. In the disordered phase the ground state is the product of all singlet bonds between itinerant and localized spins. It is separated by a finite energy gap from the triplet excited states. The quantum phase transition to the antiferromagnetically ordered phase takes place where the gap vanishes. In this approach we use the bond operator formalism introduced in Ref.[3] where each bond is represented by the singlet and triplet operators. The Kondo necklace Hamiltonian in the bond operator representation is composed of the kinetic energy and pairing part (H2), the two particle interaction (H4) of the boson gas and a term which includes three boson operators (H3). In order to ensure that the physical states are either singlets or triplets we impose the hard-core condition by introducing an infinite on-site repulsion between triplet bosons (H U ). The scattering vertex in the ladder approximation satisfies the Bethe-Salpeter equation [4]. By calculating the scattering vertex function we obtain the self energy contribution of the Hamiltonian H U . We have added the second order contribution of the self energy of H3 to the self energy of H U . It should be noted that the non conservation of triplet boson numbers requires the inclusion of the anomalous Green's functions. We treat H 4 in mean-field theory, by splitting the quartic operator into all possible pairs. Finally we obtain the renormalization of coefficients in the H 2 Hamiltonian and calculate the energy gap. Indeed at the critical point a condensation of triplet bosons occurs. We have numerically found the critical point of this model and compared our results with the corresponding mean field values [5]. Moreover, the critical exponent of the energy gap can be obtained more accurately than the mean field results. (authors)

  3. The packing of two species of polygons on the square lattice

    International Nuclear Information System (INIS)

    Dei Cont, David; Nienhuis, Bernard

    2004-01-01

    We decorate the square lattice with two species of polygons under the constraint that every lattice edge is covered by only one polygon and every vertex is visited by both types of polygons. We end up with a 24-vertex model which is known in the literature as the fully packed double loop model (FPL 2 ). In the particular case in which the fugacities of the polygons are the same, the model admits an exact solution. The solution is obtained using coordinate Bethe ansatz and provides a closed expression for the free energy. In particular, we find the free energy of the four-colouring model and the double Hamiltonian walk and recover the known entropy of the Ice model. When both fugacities are set equal to 2 the model undergoes an infinite-order phase transition

  4. Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

    Energy Technology Data Exchange (ETDEWEB)

    Baskan, O.; Clercx, H. J. H [Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Speetjens, M. F. M. [Energy Technology Laboratory, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Metcalfe, G. [Commonwealth Scientific and Industrial Research Organisation, Melbourne, Victoria 3190 (Australia); Swinburne University of Technology, Department of Mechanical Engineering, Hawthorn VIC 3122 (Australia)

    2015-10-15

    Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

  5. Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state.

    Science.gov (United States)

    Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H

    2015-10-01

    Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

  6. NLO renormalization in the Hamiltonian truncation

    Science.gov (United States)

    Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

    2017-09-01

    Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

  7. Noncanonical Hamiltonian methods in plasma dynamics

    International Nuclear Information System (INIS)

    Kaufman, A.N.

    1982-01-01

    A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)

  8. Inquiry for the conversion of the (π+ - π-) bound state into two π0

    International Nuclear Information System (INIS)

    Bunatyan, G.G.

    1998-01-01

    In the work presented, the decay of the pionium, that is the (π + π - ) bound state, into two π 0 is studied, the ππ-interaction causing this transition being described by the underlying Weinberg Lagrangian. The calculation with such a ππ-Lagrangian being carried out, the π-meson size r 0 emerges to be allowed for, and this quantity occurs in the final result. The bound (π + π - )-system itself is presumed to be due to the instantaneous Coulomb interaction and is treated consistently nonrelativistically, the Bethe-Salpeter equation being utilized. When calculating, the terms to the lowest order in the fine structure constant α and the terms ∼ ln (r 0 ) are retained. The obtained pionium lifetime τ is thought to be compatible with the conceivable future experimental data. The dependence of the results on the effective Lagrangian parameters is visualized. The investigation carried out persuades us that it is just the complete form of the genuine ππ-interaction that determines the pionium lifetime , but not much simply the ππ scattering lengths. The inquiry into pionium decaying promotes to specify the validity of the various ππ-interaction descriptions

  9. Families of superintegrable Hamiltonians constructed from exceptional polynomials

    International Nuclear Information System (INIS)

    Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc

    2012-01-01

    We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)

  10. Hamiltonian dynamics

    CERN Document Server

    Vilasi, Gaetano

    2001-01-01

    This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m

  11. The spin-3/2 Blume-Capel model on the Bethe lattice using the recursion method

    International Nuclear Information System (INIS)

    Albayrak, Erhan; Keskin, Mustafa

    2000-01-01

    The spin-3/2 Blume-Capel model is solved on the Bethe lattice using the exact recursion equations. The nature of the variation of the Curie temperature with the ratio of the single-ion anisotropy term to the exchange-coupling constant is studied and the phase diagrams are constructed on the Bethe lattice with the co-ordination numbers q=3 and 6. A comparison is made with the results of the other approximation schemes

  12. The spin-3/2 Blume-Capel model on the Bethe lattice using the recursion method

    CERN Document Server

    Albayrak, E

    2000-01-01

    The spin-3/2 Blume-Capel model is solved on the Bethe lattice using the exact recursion equations. The nature of the variation of the Curie temperature with the ratio of the single-ion anisotropy term to the exchange-coupling constant is studied and the phase diagrams are constructed on the Bethe lattice with the co-ordination numbers q=3 and 6. A comparison is made with the results of the other approximation schemes.

  13. Pessoa em Bethânia: os versos do desassossego na voz do encantamento

    OpenAIRE

    Barros, Andre Luiz Calsone

    2013-01-01

    Pessoa em Bethânia tem por tema a recriação dos versos de Caeiro no espetáculo Rosa dos Ventos O Show Encantado, tendo por intérprete Maria Bethânia. O corpus é o Poema VIII de Alberto Caeiro, heterônimo de Fernando Pessoa, da obra O Guardador de Rebanhos (1911 1912), transformado em roteiro dramáticomusical e tornado performance no espetáculo Rosa dos Ventos. Reinterpretado por meio da voz, do corpo, da música e dos mais variados recursos cênicos, o poema de Fernando ...

  14. Determinantal method for complex angular momenta in potential scattering

    Energy Technology Data Exchange (ETDEWEB)

    Lee, B. W. [University of Pennsylvania, Philadelphia, PA (United States)

    1963-01-15

    In this paper I would like do describe a formulation of the complex angular momenta in potential scattering based on the Lippmann-Schwinger integral equation rather than on the Schrödinger differential equation. This is intended as a preliminary to the paper by SAWYER on the Regge poles and high energy limits in field theory (Bethe-Salpeter amplitudes), where the integral formulation is definitely more advantageous than the differential formulation.

  15. Quarkonia propagation in QGP: study of elastic and inelastic scattering processes

    International Nuclear Information System (INIS)

    Berrehrah, H; Aichelin, J; Gossiaux, P B

    2011-01-01

    We propose to study the quarkonia (φ) propagation in the QGP. We are especially interested in the elastic and inelastic scattering process of these quarkonia in the medium. We developed the Bethe-Salpeter formalism to calculate the elastic cross section (σ elas ) for φ - gluon/hadron. Results obtained in this work show that σ elas (φ - gluon/hadron) might have non negligible effects in the study of Q Q-bar propagation.

  16. Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. Pt. 2

    International Nuclear Information System (INIS)

    Babbitt, D.; Thomas, L.

    1977-01-01

    In its ground state representation, the infinite, spin 1/2 Heisenberg chain provides a model for spin wave scattering, which entails many features of the quantum mechanical N-body problem. Here, we give a complete eigenfunction expansion for the Hamiltonian of the chain in this representation, for all numbers of spin waves. Our results resolve the questions of completeness and orthogonality of the eigenfunctions given by Bethe for finite chains, in the infinite volume limit. (orig.) [de

  17. Renormalization of Hamiltonian QCD

    International Nuclear Information System (INIS)

    Andrasi, A.; Taylor, John C.

    2009-01-01

    We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.

  18. Non-stoquastic Hamiltonians in quantum annealing via geometric phases

    Science.gov (United States)

    Vinci, Walter; Lidar, Daniel A.

    2017-09-01

    We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.

  19. Equivalence of Lagrangian and Hamiltonian BRST quantizations

    International Nuclear Information System (INIS)

    Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.

    1992-01-01

    Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme

  20. Geometry of Hamiltonian chaos

    DEFF Research Database (Denmark)

    Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir

    2007-01-01

    The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...

  1. Magnetic field line Hamiltonian

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1984-03-01

    The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained

  2. Meson-exchange N-N potential

    International Nuclear Information System (INIS)

    Nutt, W.T.

    1976-01-01

    A meson-theoretic model of the intermediate range nucleon-nucleon potential is presented with emphasis placed on the two-pion exchange contribution. The Bethe-Salpeter equation is reduced, by the Blankenbecler-Sugar technique, to a Lippmann-Schwinger equation, from which an approximate nonlocal, energy-dependent potential is obtained. The nucleon-antinucleon pair contribution, which plagues meson-theoretical two-pion calculations, is suppressed by the complex poles of the one-nucleon Green's function. The importance of the retention of the explicit energy dependence of the potential is demonstrated by calculating the off-shell scattering matrices. The potential is presented in a linearized (in energy) form with the core region adjusted to produce a fit to low energy data

  3. Coulomb Fourier transformation: A novel approach to three-body scattering with charged particles

    International Nuclear Information System (INIS)

    Alt, E.O.; Levin, S.B.; Yakovlev, S.L.

    2004-01-01

    A unitary transformation of the three-body Hamiltonian which describes a system of two charged and one neutral particles is constructed such that the Coulomb potential which acts between the charged particles is explicitly eliminated. The transformed Hamiltonian and, in particular, the transformed short-range pair interactions are worked out in detail. Thereby it is found that, after transformation, the short-range potentials acting between the neutral and either one of the charged particles become simply Fourier transformed but, in addition, multiplied by a function that represents the Coulombic three-body correlations originating from the action of the other charged particle on the considered pair. This function which is universal as it does not depend on any property of the short-range interaction is evaluated explicitly and its singularity structure is described in detail. In contrast, the short-range potential between the charged particles remains of two-body type but occurs now in the 'Coulomb representation'. Specific applications to Yukawa and Gaussian potentials are given. Since the Coulomb-Fourier-transformed Hamiltonian does no longer contain the Coulomb potential or any other effective interaction of long range, standard methods of short-range few-body scattering theory are applicable

  4. Long-range psu(2,2|4) Bethe ansatze for gauge theory and strings

    International Nuclear Information System (INIS)

    Beisert, Niklas; Staudacher, Matthias

    2005-01-01

    We generalize various existing higher-loop Bethe ansatze for simple sectors of the integrable long-range dynamic spin chain describing planar N=4 super-Yang-Mills theory to the full psu(2,2|4) symmetry and, asymptotically, to arbitrary loop order. We perform a large number of tests of our conjectured equations, such as internal consistency, comparison to direct three-loop diagonalization and expected thermodynamic behavior. In the special case of the su(1|2) subsector, corresponding to a long-range t-J model, we are able to derive, up to three loops, the S-matrix and the associated nested Bethe ansatz from the gauge theory dilatation operator. We conjecture novel all-order S-matrices for the su(1|2) and su(1,1|2) subsectors, and show that they satisfy the Yang-Baxter equation. Throughout the paper, we muse about the idea that quantum string theory on AdS 5 xS 5 is also described by a psu(2,2|4) spin chain. We propose asymptotic all-order Bethe equations for this putative ''string chain'', which differ in a systematic fashion from the gauge theory equations

  5. Canonical transformations and hamiltonian path integrals

    International Nuclear Information System (INIS)

    Prokhorov, L.V.

    1982-01-01

    Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms

  6. The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice

    Science.gov (United States)

    Heydenreich, Markus; Kolesnikov, Leonid

    2018-04-01

    We consider the ferromagnetic nearest-neighbor Ising model on regular trees (Bethe lattice), which is well-known to undergo a phase transition in the absence of an external magnetic field. The behavior of the model at critical temperature can be described in terms of various critical exponents; one of them is the critical 1-arm exponent ρ which characterizes the rate of decay of the (root) magnetization as a function of the distance to the boundary. The crucial quantity we analyze in this work is the thermal expectation of the root spin on a finite subtree, where the expected value is taken with respect to a probability measure related to the corresponding finite-volume Hamiltonian with a fixed boundary condition. The spontaneous magnetization, which is the limit of this thermal expectation in the distance between the root and the boundary (i.e., in the height of the subtree), is known to vanish at criticality. We are interested in a quantitative analysis of the rate of this convergence in terms of the critical 1-arm exponent ρ. Therefore, we rigorously prove that ⟨σ0⟩ n +, the thermal expectation of the root spin at the critical temperature and in the presence of the positive boundary condition, decays as ⟨σ0 ⟩ n +≈n-1/2 (in a rather sharp sense), where n is the height of the tree. This establishes the 1-arm critical exponent for the Ising model on regular trees (ρ =1/2 ).

  7. Monte Carlo study of alternate mixed spin-5/2 and spin-2 Ising ferrimagnetic system on the Bethe lattice

    Energy Technology Data Exchange (ETDEWEB)

    Jabar, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, PB 63 46000 Safi (Morocco); Benyoussef, A. [Laboratoire de Magnétisme et Physique des Hautes Energies L.M.P.H.E.URAC 12, Université Mohammed V, Faculté des Sciences, B.P. 1014 Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)

    2016-01-01

    The magnetic properties of alternate mixed spin-5/2 and spin-2 Ising model on the Bethe lattice have been studied by using the Monte Carlo simulations. The ground state phase diagrams of alternate mixed spin-5/2 and spin-2 Ising model on the Bethe lattice has been obtained. The thermal total magnetization and magnetization of spins-5/2 and spin-2 with the different exchange interactions, external magnetic field and temperatures have been studied. The critical temperature have been deduced. The magnetic hysteresis cycle on the Bethe lattice has been deduced for different values of exchange interactions, for different values of crystal field and for different sizes. The magnetic coercive field has been deduced. - Highlights: • The alternate mixed spin-5/2 and -2 on the Bethe lattice is studied. • The critical temperature has been deduced. • The magnetic coercive filed has been deduced.

  8. Orbits and variational principles for conservative Hamiltonian systems

    International Nuclear Information System (INIS)

    Torres del Castillo, G.F.

    1989-01-01

    It is shown that for any Hamiltonian system whose Hamiltonian is time-independent the equations that determine the orbits followed by the system, without making reference to time, have the form of Hamilton's equations in a phase space of dimension two units smaller than that of the original phase space. By considering the cases of classical mechanics and of geometrical optics, it is shown that this result amounts, respectively, to Maupertuis' least action principle and to Fermat's principle. (Author)

  9. Perspective: Quantum Hamiltonians for optical interactions

    Science.gov (United States)

    Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

    2018-01-01

    The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

  10. Hamiltonian boundary term and quasilocal energy flux

    International Nuclear Information System (INIS)

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

    2005-01-01

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

  11. On the topological entropy of an optical Hamiltonian flow

    OpenAIRE

    Niche, Cesar J.

    2000-01-01

    In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the exponential growth rate of the average of the determinant of the differential of the flow, restricted to the Lagrangian distribution or to a proper modification.

  12. Origins of extreme broadening mechanisms in near-edge x-ray spectra of nitrogen compounds

    Science.gov (United States)

    Vinson, John; Jach, Terrence; Elam, W. T.; Denlinger, J. D.

    2014-11-01

    We demonstrate the observation of many-body lifetime effects in valence-band x-ray emission. A comparison of the N K α emission of crystalline ammonium nitrate to molecular-orbital calculations revealed an unexpected, extreme broadening of the NO σ recombination—so extensively as to virtually disappear. GW calculations establish that this disappearance is due to a large imaginary component of the self-energy associated with the NO σ orbitals. Building upon density-functional theory, we have calculated radiative transitions from the nitrogen 1 s level of ammonium nitrate and ammonium chloride using a Bethe-Salpeter method to include electron-hole interactions. The absorption and emission spectra of both crystals evince large, orbital-dependent sensitivity to molecular dynamics. We demonstrate that many-body effects as well as thermal and zero-point motion are vital for understanding observed spectra. A computational approach using average atomic positions and uniform broadening to account for lifetime and phonon effects is unsatisfactory.

  13. Notch filters for port-Hamiltonian systems

    NARCIS (Netherlands)

    Dirksz, D.A.; Scherpen, J.M.A.; van der Schaft, A.J.; Steinbuch, M.

    2012-01-01

    In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the

  14. Noncanonical Hamiltonian methods in plasma dynamics

    International Nuclear Information System (INIS)

    Kaufman, A.N.

    1981-11-01

    A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions

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

    International Nuclear Information System (INIS)

    Tassi, E

    2014-01-01

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

  16. Theory of collective Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Qingying

    1982-02-01

    Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.

  17. Hadronic bound states in SU(2) from Dyson-Schwinger equations

    Energy Technology Data Exchange (ETDEWEB)

    Vujinovic, Milan [Karl-Franzens-Universitaet Graz, Institut fuer Physik, Graz (Austria); Williams, Richard [Justus-Liebig-Universitaet Giessen, Institut fuer Theoretische Physik, Giessen (Germany)

    2015-03-01

    By using the Dyson-Schwinger/Bethe-Salpeter formalism in Euclidean spacetime, we calculate the ground state spectrum of J ≤ 1 hadrons in an SU(2) gauge theory with two fundamental fermions. We show that the rainbow-ladder truncation, commonly employed in QCD studies, is unsuitable for a description of an SU(2) theory. This we remedy by truncating at the level of the quark-gluon vertex Dyson-Schwinger equation in a diagrammatic expansion. Results obtained within this novel approach show good agreement with lattice studies. These findings emphasize the need to use techniques more sophisticated than rainbow-ladder when investigating generic strongly interacting gauge theories. (orig.)

  18. Magnons and BFKL

    International Nuclear Information System (INIS)

    Gomez, Cesar; Gunnesson, Johan; Hernandez, Rafael

    2008-01-01

    We extract from the double logarithmic contributions to DGLAP anomalous dimensions for twist-two operators up to three-loops the magnon dispersion relation for planar N = 4 supersymmetric Yang-Mills. Perturbatively the magnon dispersion relation agrees with the expansion of the anomalous dimension for spin-one as well as with the non-collinear double logarithmic contributions to the BFKL anomalous dimensions analytically extended to negative spin. The all-loop expression for the magnon dispersion relation is determined by the double logarithmic resummation of the corresponding Bethe-Salpeter equation. A potential map relating the spin chain magnon to BFKL eigenfunctions in the double logarithm approximation is suggested.

  19. Dipole moments of the rho meson

    International Nuclear Information System (INIS)

    Hecht, M.B.; McKellar, B.H.P.

    1997-04-01

    The electric and magnetic dipole moments (EDM) of the rho meson are calculated using the propagators and vertices derived from the quantum chromodynamics Dyson-Schwinger equations. Results obtained from using the Bethe-Salpeter amplitude studied by Chappell, Mitchell et. al., and Pichowsky and Lee, are compared. The rho meson EDM is generated through the inclusion of a quark electric dipole moment, which is left as a free variable. These results are compared to the perturbative results to obtain a measure of the effects of quark interactions and confinement. The two dipole moments are also calculated using the phenomenological MIT bag model to provide a further basis for comparison

  20. Periodic quantum graphs from the Bethe-Sommerfeld perspective

    Czech Academy of Sciences Publication Activity Database

    Exner, Pavel; Turek, Ondřej

    2017-01-01

    Roč. 50, č. 45 (2017), č. článku 455201. ISSN 1751-8113 R&D Projects: GA ČR GA17-01706S Institutional support: RVO:61389005 Keywords : quantum graphs * Bethe-Sommerfeld conjecture * vertex coupling * Diophantine approximation * periodic structure Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.857, year: 2016

  1. On the domain of the Nelson Hamiltonian

    Science.gov (United States)

    Griesemer, M.; Wünsch, A.

    2018-04-01

    The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.

  2. Muonium hyperfine structure : An analytical solution to perturbative calculations

    International Nuclear Information System (INIS)

    Wotzasek, C.J.; Gregorio, M.A.; Reinecke, S.

    1982-01-01

    The purely coulombian contribution to the terms of order E sub(F) (α 2 m sub(e)/m sub(μ))ln α - 1 of the hyperfine splitting of muonium is computed. Results agree with those of other authors. The goal of the work was twofold: first, to confirm that contribution; second, and perhaps more important, to check the analytic solution of the relativistic coulombian problem of the Bethe-Salpeter equation with instantaneous kernel. (Author) [pt

  3. Aspects of open-flavour mesons in a comprehensive DSBSE study

    Energy Technology Data Exchange (ETDEWEB)

    Hilger, T. [University of Graz, NAWI Graz, Institute of Physics, Graz (Austria); Austrian Academy of Sciences, Institute of High Energy Physics, Vienna (Austria); Gomez-Rocha, M. [ECT*, Villazzano (Trento) (Italy); Krassnigg, A. [University of Graz, NAWI Graz, Institute of Physics, Graz (Austria); Lucha, W. [Austrian Academy of Sciences, Institute of High Energy Physics, Vienna (Austria)

    2017-10-15

    Open-flavour meson studies are the necessary completion to any comprehensive investigation of quarkonia. We extend recent studies of quarkonia in the Dyson-Schwinger-Bethe-Salpeter equation approach to explore their results for all possible flavour combinations. Within the inherent limitations of the setup, we present the most comprehensive results for meson masses and leptonic decay constants currently available and put them in perspective with respect to experiment and other approaches. (orig.)

  4. Geometry of quantal adiabatic evolution driven by a non-Hermitian Hamiltonian

    International Nuclear Information System (INIS)

    Wu Zhaoyan; Yu Ting; Zhou Hongwei

    1994-01-01

    It is shown by using a counter example, which is exactly solvable, that the quantal adiabatic theorem does not generally hold for a non-Hermitian driving Hamiltonian, even if it varies extremely slowly. The condition for the quantal adiabatic theorem to hold for non-Hermitian driving Hamiltonians is given. The adiabatic evolutions driven by a non-Hermitian Hamiltonian provide examples of a new geometric structure, that is the vector bundle in which the inner product of two parallelly transported vectors generally changes. A new geometric concept, the attenuation tensor, is naturally introduced to describe the decay or flourish of the open quantum system. It is constructed in terms of the spectral projector of the Hamiltonian. (orig.)

  5. Geometric Hamiltonian structures and perturbation theory

    International Nuclear Information System (INIS)

    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

  6. Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

    OpenAIRE

    Kaneko, Yuta; Yoshida, Zensho

    2014-01-01

    Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term -{\\Delta}Q, just representing the current density (Q is a Clebsch variable, and {\\Delta} is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensi...

  7. Anisotropic generalization of Stinchcombe's solution for the conductivity of random resistor networks on a Bethe lattice

    Energy Technology Data Exchange (ETDEWEB)

    Semeriyanov, F; Saphiannikova, M; Heinrich, G [Leibniz Institute of Polymer Research Dresden, Hohe str. 6, 01069 Dresden (Germany)], E-mail: fsemeriyanov@yahoo.de

    2009-11-20

    Our study is based on the work of Stinchcombe (1974 J. Phys. C: Solid State Phys. 7 179) and is devoted to the calculations of average conductivity of random resistor networks placed on an anisotropic Bethe lattice. The structure of the Bethe lattice is assumed to represent the normal directions of the regular lattice. We calculate the anisotropic conductivity as an expansion in powers of the inverse coordination number of the Bethe lattice. The expansion terms retained deliver an accurate approximation of the conductivity at resistor concentrations above the percolation threshold. We make a comparison of our analytical results with those of Bernasconi (1974 Phys. Rev. B 9 4575) for the regular lattice.

  8. Hamiltonian mechanics and divergence-free fields

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1986-08-01

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

  9. Quantum-circuit model of Hamiltonian search algorithms

    International Nuclear Information System (INIS)

    Roland, Jeremie; Cerf, Nicolas J.

    2003-01-01

    We analyze three different quantum search algorithms, namely, the traditional circuit-based Grover's algorithm, its continuous-time analog by Hamiltonian evolution, and the quantum search by local adiabatic evolution. We show that these algorithms are closely related in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This makes it possible to implement the two Hamiltonian-evolution algorithms on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm. It also clarifies the link between the adiabatic search algorithm and Grover's algorithm

  10. Time dependent drift Hamiltonian

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1982-04-01

    The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)

  11. Two pairs of Lie algebras and the integrable couplings as well as the Hamiltonian structure of the Yang hierarchy

    International Nuclear Information System (INIS)

    Zhang Yufeng; Guo Fukui

    2007-01-01

    Two types of Lie algebras, which are the subalgebras of the Lie algebra A 2 , A 3 respectively, are presented. The resulting loop algebras are following. As their applications, two different integrable couplings of the Yang hierarchy are obtained, called them the double integrable couplings. The Hamiltonian structure of one of them is worked out by a proper linear isomorphic transformation and the quadratic-form identity

  12. Symplectic and Hamiltonian structures of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Dorfman, I.Y.

    1993-01-01

    A Hamiltonian structure on a finite-dimensional manifold can be introduced either by endowing it with a (pre)symplectic structure, or by describing the Poisson bracket with the help of a tensor with two upper indices named the Poisson structure. Under the assumption of nondegeneracy, the Poisson structure is nothing else than the inverse of the symplectic structure. Also in the degenerate case the distinction between the two approaches is almost insignificant, because both presymplectic and Poisson structures split into symplectic structures on leaves of appropriately chosen foliations. Hamiltonian structures that arise in the theory of evolution equations demonstrate something new in this respect: trying to operate in local terms, one is induced to develop both approaches independently. Hamiltonian operators, being the infinite-dimensional counterparts of Poisson structures, were the first to become the subject of investigations. A considerable period of time passed before the papers initiated research in the theory of symplectic operators, being the counterparts of presymplectic structures. In what follows, we focus on the main achievements in this field

  13. Generalized TBA and generalized Gibbs

    NARCIS (Netherlands)

    Mossel, J.; Caux, J.-S.

    2012-01-01

    We consider the extension of the thermodynamic Bethe Ansatz to cases in which additional terms involving higher conserved charges are added to the Hamiltonian, or in which a distinction is made between the Hamiltonian used for time evolution and that used for defining the density matrix. Writing

  14. Magnetic field line Hamiltonian

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1985-02-01

    The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined

  15. The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach

    International Nuclear Information System (INIS)

    Baseilhac, Pascal

    2006-01-01

    The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite-dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order q-difference equation (or its degenerate discrete version). In the algebraic sector associated with polynomial eigenfunctions (or their discrete analogues), Bethe equations naturally appear. Beyond this sector, where the Bethe ansatz approach is not applicable in related massive quantum integrable models, the eigenfunctions are also described. The spin-half XXZ open spin chain with general integrable boundary conditions is reconsidered in light of this approach: all the eigenstates are constructed. In the algebraic sector which corresponds to special relations among the parameters, known results are recovered

  16. Single-particle dynamics - Hamiltonian formulation

    International Nuclear Information System (INIS)

    Montague, B.W.

    1977-01-01

    In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)

  17. Multiphonon states in even-even spherical nuclei. Pt. 2. Calculation of the matrix elements of one and two body operators

    International Nuclear Information System (INIS)

    Piepenbring, R.; Protasov, K.V.; Silvestre-Brac, B.

    1995-01-01

    Matrix elements of one and two body operators, which appear in a general hamiltonian and in electromagnetic transitions are derived in a subspace spanned by multiphonon states. The method is illustrated for a single j-shell, where phonons built with one type of particles are introduced. The eigenvalues obtained within the space spanned by the phonons of lowest angular momentum are compared to those of the full space. In such a method, the Pauli principle is fully and properly taken into account. ((orig.))

  18. Electronic structure of disordered binary alloys with short range correlation in Bethe lattice

    International Nuclear Information System (INIS)

    Moreno, I.F.

    1987-01-01

    The determination of the electronic structure of a disordered material along the tight-binding model when applied to a Bethe lattice. The diagonal as well as off-diagonal disorder, are considered. The coordination number on the Bethe is fixed lattice to four (Z=4) that occurs in most compound semiconductors. The main proposal was to study the conditions under which a relatively simple model of a disordered material, i.e, a binary alloy, could account for the basic properties of transport or more specifically for the electronic states in such systems. By using a parametrization of the pair probability the behaviour of the electronic density of states (DOS) for different values of the short range order parameter, σ, which makes possible to treat the segregated, random and alternating cases, was analysed. In solving the problem via the Green function technique in the Wannier representation a linear chain of atoms was considered and using the solution of such a 1-D system the problem of the Bethe lattice which is constructed using such renormalized chains as elements, was solved. The results indicate that the obtained DOS are strongly dependent on the correlation assumed for the occupancy in the lattice. (author) [pt

  19. Toy models for wrapping effects

    International Nuclear Information System (INIS)

    Penedones, Joao; Vieira, Pedro

    2008-01-01

    The anomalous dimensions of local single trace gauge invariant operators in N = 4 supersymmetric Yang-Mills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of a perturbative asymptotic Bethe ansatz. This formalism breaks down when the number of fields of the composite operator is smaller than the range of the Hamiltonian which coincides with the order in perturbation theory at study. We analyze two spin chain toy models which might shed some light on the physics behind these wrapping effects. One of them, the Hubbard model, is known to be closely related to N = 4 SYM. In this example, we find that the knowledge of the effective spin chain description is insufficient to reconstruct the finite size effects of the underlying electron theory. We compute the wrapping corrections for generic states and relate them to a Luscher like approach. The second toy models are long range integrable Hamiltonians built from the standard algebraic Bethe ansatz formalism. This construction is valid for any symmetry group. In particular, for non-compact groups it exhibits an interesting relation between wrapping interactions and transcendentality.

  20. Weak KAM for commuting Hamiltonians

    International Nuclear Information System (INIS)

    Zavidovique, M

    2010-01-01

    For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax–Oleinik semi-groups, a result of Barles and Tourin (2001 Indiana Univ. Math. J. 50 1523–44), using a direct geometrical method (Stoke's theorem). We also obtain a 'generalization' of a theorem of Maderna (2002 Bull. Soc. Math. France 130 493–506). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton–Jacobi equation) for G and for H are the same. As a corollary we obtain the equality of the Aubry sets and of the Peierls barrier. This is also related to works of Sorrentino (2009 On the Integrability of Tonelli Hamiltonians Preprint) and Bernard (2007 Duke Math. J. 136 401–20)

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

    Science.gov (United States)

    Chen, Yunjie; Kale, Seyit; Weare, Jonathan; Dinner, Aaron R; Roux, Benoît

    2016-04-12

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

  2. The Hamiltonian of QED. Zero mode

    International Nuclear Information System (INIS)

    Zastavenko, L.G.

    1990-01-01

    We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs

  3. Dissipative systems and Bateman's Hamiltonian

    International Nuclear Information System (INIS)

    Pedrosa, I.A.; Baseia, B.

    1983-01-01

    It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt

  4. Diagonalization of Hamiltonian; Diagonalization of Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Garrido, L M; Pascual, P

    1960-07-01

    We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.

  5. Phase transitions in the Hubbard Hamiltonian

    International Nuclear Information System (INIS)

    Chaves, C.M.; Lederer, P.; Gomes, A.A.

    1977-05-01

    Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed

  6. Port-Hamiltonian Systems on Open Graphs

    NARCIS (Netherlands)

    Schaft, A.J. van der; Maschke, B.M.

    2010-01-01

    In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac

  7. Squeezed states from a quantum deformed oscillator Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)

    2016-03-11

    The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.

  8. The Beer/Bethe/Uexküll paper (1899) and misinterpretations surrounding 'vitalistic behaviorism'.

    Science.gov (United States)

    Mildenberger, Florian

    2006-01-01

    In the history of behaviorism the paper of the three physiologists Theodor Beer, Albrecht Bethe and Jakob von Uexküll from 1899 plays an important role. Many researchers were influenced by this paper and identified it as fundamental for objective psychological research. But during the period of its adoption (1900-1925) psychologists did not notice that Beer, Bethe and Uexküll had distanced themselves from their own paper, because it had been ignored in physiological and biological discussions. Moreover, one of the three (Beer) had to resign from the scientific community because of private scandal and another one (Uexküll) changed all of his views and left the base of objective science for subjective vitalism. However, this did not change his adoption of behaviorism.

  9. Large-scale stochasticity in Hamiltonian systems

    International Nuclear Information System (INIS)

    Escande, D.F.

    1982-01-01

    Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)

  10. Meson-exchange Hamiltonian for NN scattering and isobar-nucleus dynamics

    International Nuclear Information System (INIS)

    Lee, T.S.H.

    1983-01-01

    We have constructed a meson-exchange Hamiltonian for π, N, Δ and N* for NN scattering up to 2 GeV. The model gives good descriptions of the Arndt phase-shifts up to 1 GeV in both the T = 0 and T = 1 channels. The calculated total cross sections sigma/sup tot/, Δsigma/sub L//sup tot/ and Δsigma/sub T//sup tot/ agree to a large extent with the data in both the magnitudes and the signs. The present calculation gives a sound starting point for future refinements. Among them, a large-scale three-body calculation could be needed to investigate the energy dependence of the effect due to NN interactions in the πNN channel. Until this effect is carefully studied, it is premature to extract information on dibaryon resonances, if they exist, from the data. Our model also gives definite predictions of np scattering. Precise np polarization measurements at higher energy > 0.6 GeV are needed to have a complete test of our model. Finally, the present model Hamiltonian can be used to carry our many-body calculations

  11. Explicit treatment of N-body correlations within a density-matrix formalism

    International Nuclear Information System (INIS)

    Shun-Jin, W.; Cassing, W.

    1985-01-01

    The nuclear many-body problem is reformulated in the density-matrix approach such that n-body correlations are separated out from the reduced density matrix rho/sub n/. A set of equations for the time evolution of the n-body correlations c/sub n/ is derived which allows for physically transparent truncations with respect to the order of correlations. In the stationary limit (c/sub n/ = 0) a restriction to two-body correlations yields a generalized Bethe-Goldstone equation a restriction to body correlations yields generalized Faddeev equations in the density-matrix formulation. Furthermore it can be shown that any truncation of the set of equations (c/sub n/ = 0, n>m) is compatible with conservation laws, a quality which in general is not fulfilled if higher order correlations are treated perturbatively

  12. Lattice QCD studies on baryon interactions in the strangeness -2 sector with physical quark masses

    Science.gov (United States)

    Sasaki, Kenji; Aoki, Sinya; Doi, Takumi; Gongyo, Shinya; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Iritani, Takumi; Ishii, Noriyoshi; Miyamoto, Takaya

    2018-03-01

    We investigate baryon-baryon (BB) interactions in the strangeness S = -2 sector via the coupled-channel HAL QCD method which enables us to extract the scattering observables from Nambu-Bethe-Salpeter (NBS) wave function on the lattice. The simulations are performed with (almost) physical quark masses (mπ = 146MeV) and a huge lattice volume of La = 8.1fm. We discuss the fate of H-dibaryon state through the ΛΛ and NΞ coupled-channel scatterings

  13. The chiral Ward-Takahashi identity in the ladder approximation

    International Nuclear Information System (INIS)

    Kugo, Taichiro; Mitchard, M.G.

    1992-01-01

    We show that the ladder approximation to the Schwinger-Dyson and Bethe-Salpeter equations preserves the Ward-Takahashi identity for the axial vector vertex if and only if we use the gluon momentum as the argument of the running coupling constant. However, in the usual Landau gauge this is inconsistent with the vector Ward identity. We propose a new method for making the ladder approximation scheme consistent with both vector and axial vector Ward identities. (orig.)

  14. LSZ asymptotic condition and dynamic equations in quantum field theory

    International Nuclear Information System (INIS)

    Arkhipov, A.A.; Savrin, V.I.

    1983-01-01

    Some techniques that may be appropriate for the derivation of dynamic equations in quantum field theory are considered. A new method of deriving equations based on the use of LSZ asymptotic condition is described. It is proved that with the help of this method it becomes possible to obtain equations for wave functions both of scattering and bound states. Work is described in several papers under the dame title. The first paper is devoted to the Bethe-Salpeter equation

  15. On the dynamic polarizability of atoms

    International Nuclear Information System (INIS)

    Nuroh, K.; Zaremba, E.

    1989-04-01

    The positive frequency dependent polarizability of atoms is discussed in terms of the particle-hole polarization propagator. It is considered in the simplest approximation defined by the Bethe-Salpeter equation which includes a subset of particle-hole interactions to all orders in the Coulomb potential. Its solution is used to show the relationship between different formulations of atomic photoabsorption via the effective dipole matrix element (Fermi's 'golden rule'), the TDLDA and the reaction matrix. (author). 21 refs, 7 figs

  16. Squeezed condensate and confinement in a scalar model

    International Nuclear Information System (INIS)

    Blaschke, D.; Pavel, H.P.; Roepke, G.; Peradze, G.; Pervushin, V.N.

    1996-01-01

    The generating functional of a free scalar field theory is generalized to the case of a squeezed vacuum. The squeezed vacuum is prepared by macroscopically populating the original vacuum with pairs of zero energy particles. It is shown that the corresponding quark propagator has no poles on the real-k 2 axis which can be interpreted as quark confinement. In contrast, a scalar meson-like bound state exists as solution of the corresponding Bethe-Salpeter equation. 20 refs

  17. Quantum Hamiltonian reduction in superspace formalism

    International Nuclear Information System (INIS)

    Madsen, J.O.; Ragoucy, E.

    1994-02-01

    Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs

  18. Small traveling clusters in attractive and repulsive Hamiltonian mean-field models.

    Science.gov (United States)

    Barré, Julien; Yamaguchi, Yoshiyuki Y

    2009-03-01

    Long-lasting small traveling clusters are studied in the Hamiltonian mean-field model by comparing between attractive and repulsive interactions. Nonlinear Landau damping theory predicts that a Gaussian momentum distribution on a spatially homogeneous background permits the existence of traveling clusters in the repulsive case, as in plasma systems, but not in the attractive case. Nevertheless, extending the analysis to a two-parameter family of momentum distributions of Fermi-Dirac type, we theoretically predict the existence of traveling clusters in the attractive case; these findings are confirmed by direct N -body numerical simulations. The parameter region with the traveling clusters is much reduced in the attractive case with respect to the repulsive case.

  19. Nonlinear Quantum Metrology of Many-Body Open Systems

    Science.gov (United States)

    Beau, M.; del Campo, A.

    2017-07-01

    We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k -body Hamiltonian and p -body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N-[k -(p /2 )], surpassing the shot-noise limit for 2 k >p +1 . Metrology equivalence between initial product states and maximally entangled states is established for p ≥1 . We further show that one can estimate the system-environment coupling parameter with precision N-(p /2 ), while many-body decoherence enhances the precision to N-k in the noise-amplitude estimation of a fluctuating k -body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.

  20. The front form of relativistic Lagrangian dynamics in the two-dimensional space-time and its connection with the Hamiltonian description

    International Nuclear Information System (INIS)

    Sokolov, S.N.; Tret'yak, V.I.

    1985-01-01

    The Lagrangian relativistic theory in the two-dimensional space-time in the front form of dynamics is formulated and its connections with the predictive mechanics, with the Hamiltonian description, and with the Fokker-type action theory are established. The relations are found in a closed form without using formal expansions. The existence of mathematical limitations on a magnitude of Lagrangians of two-particle interactions is shown

  1. Solution of the effective Hamiltonian of impurity hopping between two sites in a metal

    Science.gov (United States)

    Ye, Jinwu

    1997-07-01

    We analyze in detail all the possible fixed points of the effective Hamiltonian of a nonmagnetic impurity hopping between two sites in a metal obtained by Moustakas and Fisher (MF). We find a line of non-Fermi liquid fixed points which continuously interpolates between the two-channel Kondo fixed point (2CK) and the one-channel, two-impurity Kondo (2IK) fixed point. There is one relevant direction with scaling dimension 12 and one leading irrelevant operator with dimension 32. There is also one marginal operator in the spin sector moving along this line. The marginal operator, combined with the leading irrelevant operator, will generate the relevant operator. For the general position on this line, the leading low-temperature exponents of the specific heat, the hopping susceptibility and the electron conductivity Cimp,χhimp,σ(T) are the same as those of the 2CK, but the finite-size spectrum depends on the position on the line. No universal ratios can be formed from the amplitudes of the three quantities except at the 2CK point on this line where the universal ratios can be formed. At the 2IK point on this line, σ(T)~2σu(1+aT3/2), no universal ratio can be formed either. The additional non-Fermi-liquid fixed point found by MF has the same symmetry as the 2IK, it has two relevant directions with scaling dimension 12, and is therefore also unstable. The leading low-temperature behaviors are Cimp~T,χhimp~lnT,σ(T)~2σu(1+aT3/2) no universal ratios can be formed. The system is shown to flow to a line of Fermi-liquid fixed points which continuously interpolates between the noninteracting fixed point and the two-channel spin-flavor Kondo fixed point discussed by the author previously. The effect of particle-hole symmetry breaking is discussed. The effective Hamiltonian in the external magnetic field is analyzed. The scaling functions for the physical measurable quantities are derived in the different regimes; their predictions for the experiments are given. Finally

  2. Bethe-Salpeter dynamics and the constituent mass concept for heavy quark mesons

    International Nuclear Information System (INIS)

    Souchlas, N.; Stratakis, D.

    2010-01-01

    The definition of a quark as heavy requires a comparison of its mass with the nonperturbative chiral symmetry breaking scale which is about 1 GeV (Λ χ ∼1 GeV) or with the scale Λ QCD ∼0.2 GeV that characterizes the distinction between perturbative and nonperturbative QCD. For quark masses significantly larger than these scales, nonperturbative dressing effects, or equivalently nonperturbative self-energy contributions, and relativistic effects are believed to be less important for physical observables. We explore the concept of a constituent mass for heavy quarks in the Dyson-Schwinger equations formalism, for light-heavy and heavy-heavy quark mesons by studying their masses and electroweak decay constants.

  3. Intriguing solutions of the Bethe-Salpeter equation for radially excited pseudoscalar charmonia

    Czech Academy of Sciences Publication Activity Database

    Šauli, Vladimír

    2014-01-01

    Roč. 90, č. 1 (2014), 016005 ISSN 1550-7998 Institutional support: RVO:61389005 Keywords : quantum chromodynamics * confinement * quarks * gluons Subject RIV: BE - Theoretical Physics Impact factor: 4.643, year: 2014

  4. Generalized oscillator representations for Calogero Hamiltonians

    International Nuclear Information System (INIS)

    Tyutin, I V; Voronov, B L

    2013-01-01

    This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)

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

    International Nuclear Information System (INIS)

    Molique, H.; Dudek, J.

    1997-01-01

    A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian H pair =summation αβ G αβ c α † c bar α † c bar β c β with an arbitrary set of matrix elements G αβ . Symmetries of the Hamiltonians on the many-body level are discussed using the language of P symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of P symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to p∼40 particles on n∼80 levels and for several dozens of lowest lying states with precision ∼(1 endash 2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority s=0 solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei. copyright 1997 The American Physical Society

  6. Constructing Dense Graphs with Unique Hamiltonian Cycles

    Science.gov (United States)

    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…

  7. Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

    Science.gov (United States)

    Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

    2018-03-01

    We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

  8. Three-body forces: a status report

    International Nuclear Information System (INIS)

    Coon, S.A.

    1976-01-01

    Real three-body forces due to meson exchange are distinguished from effective three-body interactions of a nuclear Hamiltonian. The long-range part of the real three-body force is proportional to the off-mass-shell sup(PI)N scattering amplitude. Its contribution to the binding energy of nuclear matter is quite dependent upon the treatment of correlations (due to the two-body potential) in the three-body wave function. A recent improvemrnt in the amplitude implies a very small contribution. But, a recent improvement in the treatment of correlations implies a large contribution. Work towards including both these improvements in a single calculation is in progress. (author)

  9. Symmetry and resonance in Hamiltonian systems

    NARCIS (Netherlands)

    Tuwankotta, J.M.; Verhulst, F.

    2000-01-01

    In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After giving a sharp estimate of the resonance domain, we

  10. Symmetry and resonance in Hamiltonian systems

    NARCIS (Netherlands)

    Tuwankotta, J.M.; Verhulst, F.

    1999-01-01

    In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After determining the size of the resonance domain, we

  11. Multi-Hamiltonian formulations and stability of higher-derivative extensions of 3d Chern-Simons

    Energy Technology Data Exchange (ETDEWEB)

    Abakumova, V.A.; Kaparulin, D.S.; Lyakhovich, S.L. [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)

    2018-02-15

    Most general third-order 3d linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the canonical energy-momentum being a particular representative of the series. For a certain range of the model parameters, the series of conserved tensors include bounded quantities. This makes the dynamics classically stable, though the canonical energy is unbounded in all the instances. The free third-order equations are shown to admit constrained multi-Hamiltonian form with the 00-components of conserved tensors playing the roles of corresponding Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's one, which is unbounded. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. This means, the theory admits inequivalent quantizations at the free level. Covariant interactions are included with spinor fields such that the higher-derivative dynamics remains stable at interacting level if the bounded conserved quantity exists in the free theory. In the first-order formalism, the interacting theory remains Hamiltonian and therefore it admits quantization, though the vertices are not necessarily Lagrangian in the third-order field equations. (orig.)

  12. O(N)-matrix difference equations and a nested Bethe ansatz

    International Nuclear Information System (INIS)

    Babujian, Hrachya M; Foerster, Angela; Karowski, Michael

    2012-01-01

    A system of O(N)-matrix difference equations is solved by means of the off-shell version of the nested algebraic Bethe ansatz. In the nesting process, a new object, the Π-matrix, is introduced to overcome the complexities of the O(N)-group structure. The highest weight property of the solutions is proved and some explicit examples are discussed. (paper)

  13. Morphology of Laplacian growth processes and statistics of equivalent many-body systems

    International Nuclear Information System (INIS)

    Blumenfeld, R.

    1994-01-01

    The authors proposes a theory for the nonlinear evolution of two dimensional interfaces in Laplacian fields. The growing region is conformally mapped onto the unit disk, generating an equivalent many-body system whose dynamics and statistics are studied. The process is shown to be Hamiltonian, with the Hamiltonian being the imaginary part of the complex electrostatic potential. Surface effects are introduced through the Hamiltonian as an external field. An extension to a continuous density of particles is presented. The results are used to study the morphology of the interface using statistical mechanics for the many-body system. The distribution of the curvature and the moments of the growth probability along the interface are calculated exactly from the distribution of the particles. In the dilute limit, the distribution of the curvature is shown to develop algebraic tails, which may, for the first time, explain the origin of fractality in diffusion controlled processes

  14. New integrable structures in large-N QCD

    International Nuclear Information System (INIS)

    Ferretti, Gabriele; Heise, Rainer; Zarembo, Konstantin

    2004-01-01

    We study the anomalous dimensions of single trace operators composed of field strengths F μν in large-N QCD. The matrix of anomalous dimensions is the Hamiltonian of a compact spin chain with two spin one representations at each vertex corresponding to the self-dual and anti-self-dual components of F μν . Because of the special form of the interaction it is possible to study separately renormalization of purely self-dual components. In this sector the Hamiltonian is integrable and can be exactly solved by Bethe ansatz. Its continuum limit is described by the level two SU(2) Wess-Zumino-Witten model

  15. Effective Hamiltonian for protected edge states in graphene

    International Nuclear Information System (INIS)

    Winkler, R.; Deshpande, H.

    2017-01-01

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

  16. Lepton-pair production of a light pseudoscalar particle via the Bethe-Heitler process

    International Nuclear Information System (INIS)

    Kim, B.R.; Stamm, C.

    1983-01-01

    Bethe-Heitler processes of light pseudoscalar particles off nuclei are at present very important experimentally. For these processes we present our results which seem to differ from previous theoretical calculations found in the literature. (orig.)

  17. Oscillator representations for self-adjoint Calogero Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)

    2011-10-21

    In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

  18. Oscillator representations for self-adjoint Calogero Hamiltonians

    International Nuclear Information System (INIS)

    Gitman, D M; Tyutin, I V; Voronov, B L

    2011-01-01

    In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

  19. Quasiparticle and optical properties of strained stanene and stanane.

    Science.gov (United States)

    Lu, Pengfei; Wu, Liyuan; Yang, Chuanghua; Liang, Dan; Quhe, Ruge; Guan, Pengfei; Wang, Shumin

    2017-06-20

    Quasiparticle band structures and optical properties of two dimensional stanene and stanane (fully hydrogenated stanene) are studied by the GW and GW plus Bethe-Salpeter equation (GW-BSE) approaches, with inclusion of the spin-orbit coupling (SOC). The SOC effect is significant for the electronic and optical properties in both stanene and stanane, compared with their group IV-enes and IV-anes counterparts. Stanene is a semiconductor with a quasiparticle band gap of 0.10 eV. Stanane has a sizable band gap of 1.63 eV and strongly binding exciton with binding energy of 0.10 eV. Under strain, the quasiparticle band gap and optical spectrum of both stanene and stanane are tunable.

  20. EMR-related problems at the interface between the crystal field Hamiltonians and the zero-field splitting Hamiltonians

    Directory of Open Access Journals (Sweden)

    Rudowicz Czesław

    2015-07-01

    Full Text Available The interface between optical spectroscopy, electron magnetic resonance (EMR, and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF (or equivalently ligand field (LF Hamiltonians, and the effective spin Hamiltonians (SH, which include the zero-field splitting (ZFS Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA. Survey of recent literature has revealed that this interface, denoted CF (LF ↔ SH (ZFS, has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF, SH (ZFS, and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF ↔ SH (ZFS interface with the focus on the EMR-related problems for transition ions.

  1. Quadratic Hamiltonians on non-symmetric Poisson structures

    International Nuclear Information System (INIS)

    Arribas, M.; Blesa, F.; Elipe, A.

    2007-01-01

    Many dynamical systems may be represented in a set of non-canonical coordinates that generate an su(2) algebraic structure. The topology of the phase space is the one of the S 2 sphere, the Poisson structure is the one of the rigid body, and the Hamiltonian is a parametric quadratic form in these 'spherical' coordinates. However, there are other problems in which the Poisson structure losses its symmetry. In this paper we analyze this case and, we show how the loss of the spherical symmetry affects the phase flow and parametric bifurcations for the bi-parametric cases

  2. Electromagnetic reactions of few-body systems with the Lorentz integral transform method

    International Nuclear Information System (INIS)

    Leidemann, W.

    2007-01-01

    Various electromagnetic few-body break-up reactions into the many-body continuum are calculated microscopically with the Lorentz integral transform (LIT) method. For three- and four-body nuclei the nuclear Hamiltonian includes two- and three-nucleon forces, while semirealistic interactions are used in case of six- and seven-body systems. Comparisons with experimental data are discussed. In addition various interesting aspects of the 4 He photodisintegration are studied: investigation of a tetrahedrical symmetry of 4 He and a test of non-local nuclear force models via the induced two-body currents

  3. Superconductivity a new approach based on the Bethe-Salpeter equation in the mean-field approximation

    CERN Document Server

    Malik, G P

    2016-01-01

    Given the Debye temperature of an elemental superconductor (SC) and its Tc, BCS theory enables one to predict the value of its gap 0 at T = 0, or vice versa. This monograph shows that non-elemental SCs can be similarly dealt with via the generalized BCS equations (GBCSEs) which, given any two parameters of the set {Tc, 10, 20 > 10}, enable one to predict the third. Also given herein are new equations for the critical magnetic field and critical current density of an elemental and a non-elemental SC — equations that are derived directly from those that govern pairing in them. The monograph includes topics that are usually not covered in any one text on superconductivity, e.g., BCS-BEC crossover physics, the long-standing puzzle posed by SrTiO3, and heavy-fermion superconductors — all of which are still imperfectly understood and therefore continue to avidly engage theoreticians. It suggests that addressing the Tcs, s and other properties (e.g., number densities of charge carriers) of high-Tc SCs via GBCSE...

  4. Physics over easy Breakfasts with Beth and physics

    CERN Document Server

    Azaroff, L V

    2010-01-01

    During a sequence of meals, the author relates the principal features of physics in easy-to-understand conversations with his wife Beth. Beginning with the studies of motion by Galileo and Newton through to the revolutionary theories of relativity and quantum mechanics in the 20th century, all important aspects of electricity, energy, magnetism, gravity and the structure of matter and atoms are explained and illustrated. The second edition similarly recounts the more recent application of these theories to nanoparticles, Bose-Einstein condensates, quantum entanglement and quantum computers. By

  5. Lie transforms and their use in Hamiltonian perturbation theory

    International Nuclear Information System (INIS)

    Cary, J.R.

    1978-06-01

    A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here

  6. Derivation of Hamiltonians for accelerators

    Energy Technology Data Exchange (ETDEWEB)

    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.

  7. Purely non-local Hamiltonian formalism, Kohno connections and ∨-systems

    International Nuclear Information System (INIS)

    Arsie, Alessandro; Lorenzoni, Paolo

    2014-01-01

    In this paper, we extend purely non-local Hamiltonian formalism to a class of Riemannian F-manifolds, without assumptions on the semisimplicity of the product ○ or on the flatness of the connection ∇. In the flat case, we show that the recurrence relations for the principal hierarchy can be re-interpreted using a local and purely non-local Hamiltonian operators and in this case they split into two Lenard-Magri chains, one involving the even terms, the other involving the odd terms. Furthermore, we give an elementary proof that the Kohno property and the ∨-system condition are equivalent under suitable assumptions and we show how to associate a purely non-local Hamiltonian structure to any ∨-system, including degenerate ones

  8. Long-time correlation for the chaotic orbit in the two-wave Hamiltonian

    International Nuclear Information System (INIS)

    Hatori, Tadatsugu; Irie, Haruyuki.

    1987-03-01

    The time correlation function of velocity is found to decay with the power law for the orbit governed by a Hamiltonian, H = v 2 /2-M cos x - P cos[k(x - t)]. The renormalization group technique can predict the power of decay for the correlation function defined by the ensemble average. The power spectrum becomes the 1/f-type for a special case. (author)

  9. Chain and ladder models with two-body interactions and analytical ground states

    Science.gov (United States)

    Manna, Sourav; Nielsen, Anne E. B.

    2018-05-01

    We consider a family of spin-1 /2 models with few-body, SU(2)-invariant Hamiltonians and analytical ground states related to the one-dimensional (1D) Haldane-Shastry wave function. The spins are placed on the surface of a cylinder, and the standard 1D Haldane-Shastry model is obtained by placing the spins with equal spacing in a circle around the cylinder. Here, we show that another interesting family of models with two-body exchange interactions is obtained if we instead place the spins along one or two lines parallel to the cylinder axis, giving rise to chain and ladder models, respectively. We can change the scale along the cylinder axis without changing the radius of the cylinder. This gives us a parameter that controls the ratio between the circumference of the cylinder and all other length scales in the system. We use Monte Carlo simulations and analytical investigations to study how this ratio affects the properties of the models. If the ratio is large, we find that the two legs of the ladder decouple into two chains that are in a critical phase with Haldane-Shastry-like properties. If the ratio is small, the wave function reduces to a product of singlets. In between, we find that the behavior of the correlations and the Renyi entropy depends on the distance considered. For small distances the behavior is critical, and for long distances the correlations decay exponentially and the entropy shows an area law behavior. The distance up to which there is critical behavior gets larger as the ratio increases.

  10. Relativistic non-Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2010-01-01

    Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.

  11. Chromatic roots and hamiltonian paths

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2000-01-01

    We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...

  12. Hamiltonian structure of the Lotka-Volterra equations

    Science.gov (United States)

    Nutku, Y.

    1990-03-01

    The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

  13. Boson mapping and the microscopic collective nuclear Hamiltonian

    International Nuclear Information System (INIS)

    Dobes, J.; Ivanova, S.P.; Dzholos, R.V.; Pedrosa, R.

    1990-01-01

    Starting with the mapping of the quadrupole collective states in the fermion space onto the boson space, the fermion nuclear problem is transformed into the boson one. The boson images of the bifermion operators and of the fermion Hamiltonian are found. Recurrence relations are used to obtain approximately the norm matrix which appears in the boson-fermion mapping. The resulting boson Hamiltonian contains terms which go beyond the ordinary SU(6) symmetry Hamiltonian of the interacting boson model. Calculations, however, suggest that on the phenomenological level the differences between the mapped Hamiltonian and the SU(6) Hamiltonian are not too important. 18 refs.; 2 figs

  14. The pion form factor from first principles

    International Nuclear Information System (INIS)

    Heide, J. van der

    2004-01-01

    We calculate the electromagnetic form factor of the pion in quenched lattice QCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is used together with the O(a) improved current. We calculate form factor for pion masses down to mπ = 380 MeV. We compare the mean square radius for the pion extracted from our form factors to the value obtained from the 'Bethe Salpeter amplitude'. Using (quenched) chiral perturbation theory, we extrapolate our results towards the physical pion mass

  15. SU(N)-QCD2 meson equation in next-to-leading order

    International Nuclear Information System (INIS)

    Durgut, M.; Pak, N.K.

    1982-08-01

    We compute the 1/N corrections to the meson equation in the regular cut-off scheme. We illustrate that although the quark and gluon self energy and vertex corrections do not vanish explicitly as in the singular cut-off scheme, their contributions to the meson Bethe-Salpeter equation get cancelled within the whole set of contributing diagrams. We also argue that 0(1/N) corrections to the meson equation remove the massless boson from the spectrum in accordance with the Coleman theorem. (author)

  16. Lattice QCD studies on baryon interactions in the strangeness -2 sector with physical quark masses

    Directory of Open Access Journals (Sweden)

    Sasaki Kenji

    2018-01-01

    Full Text Available We investigate baryon-baryon (BB interactions in the strangeness S = −2 sector via the coupled-channel HAL QCD method which enables us to extract the scattering observables from Nambu-Bethe-Salpeter (NBS wave function on the lattice. The simulations are performed with (almost physical quark masses (mπ = 146MeV and a huge lattice volume of La = 8.1fm. We discuss the fate of H-dibaryon state through the ΛΛ and NΞ coupled-channel scatterings

  17. On integrable Hamiltonians for higher spin XXZ chain

    International Nuclear Information System (INIS)

    Bytsko, Andrei G.

    2003-01-01

    Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to (3/2) are given. Relations between Hamiltonians for some U q (sl 2 )-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U q (sl 2 )-symmetric Hamiltonian for an open chain

  18. Hamiltonian ABC

    NARCIS (Netherlands)

    Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.

    2015-01-01

    Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of

  19. Blocking Radial Diffusion in a Double-Waved Hamiltonian Model

    International Nuclear Information System (INIS)

    Martins, Caroline G L; De Carvalho, R Egydio; Marcus, F A; Caldas, I L

    2011-01-01

    A non-twist Hamiltonian system perturbed by two waves with particular wave numbers can present Robust Tori, barriers created by the vanishing of the perturbing Hamiltonian at some defined positions. When Robust Tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. We analyze the breaking up of the RT as well the transport dependence on the wave numbers and on the wave amplitudes. Moreover, we report the chaotic web formation in the phase space and how this pattern influences the transport.

  20. Constraints and Hamiltonian in light-front quantized field theory

    International Nuclear Information System (INIS)

    Srivastava, P.P.

    1993-01-01

    Self-consistent hamiltonian formulation of scalar theory on the null plane is constructed and quantized following the Dirac procedure. The theory contains also constraint equations which would give, if solved, to a nonlocal Hamiltonian. In contrast to the equal-time formulation we obtain a different description of the spontaneous symmetry breaking in the continuum and the symmetry generators are found to annihilate the light-front vacuum. Two examples are given where the procedure cannot be applied self-consistently. The corresponding theories are known to be ill-defined from the equal-time quantization. (author)

  1. Accuracy of the Bethe approximation for hyperparameter estimation in probabilistic image processing

    International Nuclear Information System (INIS)

    Tanaka, Kazuyuki; Shouno, Hayaru; Okada, Masato; Titterington, D M

    2004-01-01

    We investigate the accuracy of statistical-mechanical approximations for the estimation of hyperparameters from observable data in probabilistic image processing, which is based on Bayesian statistics and maximum likelihood estimation. Hyperparameters in statistical science correspond to interactions or external fields in the statistical-mechanics context. In this paper, hyperparameters in the probabilistic model are determined so as to maximize a marginal likelihood. A practical algorithm is described for grey-level image restoration based on a Gaussian graphical model and the Bethe approximation. The algorithm corresponds to loopy belief propagation in artificial intelligence. We examine the accuracy of hyperparameter estimation when we use the Bethe approximation. It is well known that a practical algorithm for probabilistic image processing can be prescribed analytically when a Gaussian graphical model is adopted as a prior probabilistic model in Bayes' formula. We are therefore able to compare, in a numerical study, results obtained through mean-field-type approximations with those based on exact calculation

  2. Decay constants of pseudoscalar mesons in Bethe–Salpeter framework with generalized structure of hadron-quark vertex

    International Nuclear Information System (INIS)

    Bhatnagar, Shashank; Li, Shiyuan

    2009-01-01

    We employ the framework of Bethe–Salpeter equation under Covariant Instantaneous Ansatz to study the leptonic decays of pseudoscalar mesons. The Dirac structure of hadron-quark vertex function Γ is generalized to include various Dirac covariants besides γ5 from their complete set. The covariants are incorporated in accordance with a power counting rule, order-by-order in powers of the inverse of the meson mass. The decay constants are calculated with the incorporation of leading order covariants. Most of the results are dramatically improved. (author)

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

    International Nuclear Information System (INIS)

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

    2011-01-01

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

  4. Mathematical Modeling of Constrained Hamiltonian Systems

    NARCIS (Netherlands)

    Schaft, A.J. van der; Maschke, B.M.

    1995-01-01

    Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the

  5. Lagrangian and Hamiltonian dynamics

    CERN Document Server

    Mann, Peter

    2018-01-01

    An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...

  6. Painlevé IV Hamiltonian systems and coherent states

    International Nuclear Information System (INIS)

    Bermudez, D; Contreras-Astorga, A; Fernández C, D J

    2015-01-01

    Schrödinger Hamiltonians with third-order differential ladder operators are linked to the Painlevé IV equation. Some of these appear from applying SUSY QM to the harmonic oscillator. Departing from them, we will build coherent states as eigenstates of the annihilation operator, then as displaced versions of the extremal states, both involving the third-order ladder operators, and finally as displaced extremal states using linearized ladder operators. To each Hamiltonian corresponds two families of coherent states for fixed ladder operators: one in the infinite dimension subspace associated with the oscillator spectrum and another in the finite dimension one generated by the eigenstates created by SUSY QM. (paper)

  7. Phase transition in the non-degenerate Hubbard Hamiltonian

    International Nuclear Information System (INIS)

    Chaves, C.M.; Lederer, P.; Gomes, A.A.

    1976-01-01

    Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques, using the epsilon = 4 - d expansion to first order in epsilon, is studied. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. The possibility of tricritical behavior then emerges. The effects of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed

  8. Relativistic magnetohydrodynamics as a Hamiltonian system

    International Nuclear Information System (INIS)

    Holm, D.D.; Kupershmidt, A.

    1985-01-01

    The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr

  9. Many-body localization proximity effects in platforms of coupled spins and bosons

    Science.gov (United States)

    Marino, J.; Nandkishore, R. M.

    2018-02-01

    We discuss the onset of many-body localization in a one-dimensional system composed of a XXZ quantum spin chain and a Bose-Hubbard model linearly coupled together. We consider two complementary setups, depending whether spatial disorder is initially imprinted on spins or on bosons; in both cases, we explore the conditions for the disordered portion of the system to localize by proximity of the other clean half. Assuming that the dynamics of one of the two parts develops on shorter time scales than the other, we can adiabatically eliminate the fast degrees of freedom, and derive an effective Hamiltonian for the system's remainder using projection operator techniques. Performing a locator expansion on the strength of the many-body interaction term or on the hopping amplitude of the effective Hamiltonian thus derived, we present results on the stability of the many-body localized phases induced by proximity effect. We also briefly comment on the feasibility of the proposed model through modern quantum optics architectures, with the long-term perspective to realize experimentally, in composite open systems, Anderson or many-body localization proximity effects.

  10. Noncanonical Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Litteljohn, R.G.

    1986-01-01

    Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)

  11. Supersymmetric Extension of Non-Hermitian su(2 Hamiltonian and Supercoherent States

    Directory of Open Access Journals (Sweden)

    Omar Cherbal

    2010-12-01

    Full Text Available A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2 generators in the form H=ωJ_3+αJ_−+βJ_+, α≠β, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.

  12. An integrable Hamiltonian hierarchy and its constrained flows with generalized Hamiltonian regular representations, as well as its expanding integrable system

    International Nuclear Information System (INIS)

    Zhang Yufeng

    2003-01-01

    A new subalgebra of loop algebra A-tilde 2 is first constructed. It follows that an isospectral problem is established. Using Tu-pattern gives rise to a new integrable hierarchy, which possesses bi-Hamiltonian structure. As its reduction cases, the well-known standard Schrodinger equation and MKdV equation are presented, respectively. Furthermore, by making use of bi-symmetry constraints, generalized Hamiltonian regular representations for the hierarchy are obtained. At last, we obtain an expanding integrable system of this hierarchy by applying a scalar transformation between two isospectral problems and constructing a five-dimensional loop algebra G-tilde. In particular, the expanding integrable models of Schrodinger equation and MKdV equation are presented, respectively

  13. Spontaneous symmetry breaking and neutral stability in the noncanonical Hamiltonian formalism

    International Nuclear Information System (INIS)

    Morrison, P.J.; Eliezer, S.

    1985-10-01

    The noncanonical Hamiltonian formalism is based upon a generalization of the Poisson bracket, a particular form of which is possessed by continuous media fields. Associated with this generalization are special constants of motion called Casimirs. These are constants that can be viewed as being built into the phase space, for they are invariant for all Hamiltonians. Casimirs are important because when added to the Hamiltonian they yield an effective Hamiltonian that produces equilibrium states upon variation. The stability of these states can be ascertained by a second variation. Goldstone's theorem, in its usual context, determines zero eigenvalues of the mass matrix for a given vacuum state, the equilibrium with minimum energy. Here, since for fluids and plasmas the vacuum state is uninteresting, we examine symmetry breaking for general equilibria. Broken symmetries imply directions of neutral stability. Two examples are presented: the nonlinear Alfven wave of plasma physics and the Korteweg-de Vries soliton. 46 refs

  14. Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

    Science.gov (United States)

    Yuzbashyan, Emil A.

    2018-05-01

    We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

  15. Regge trajectories for heavy quarkonia from the quadratic form of the spinless Salpeter-type equation

    Science.gov (United States)

    Chen, Jiao-Kai

    2018-03-01

    In this paper, we present one new form of the Regge trajectories for heavy quarkonia which is obtained from the quadratic form of the spinless Salpeter-type equation (QSSE) by employing the Bohr-Sommerfeld quantization approach. The obtained Regge trajectories take the parameterized form M^2={β }({c_l}l+{π }n_r+c_0)^{2/3}+c_1, which are different from the present Regge trajectories. Then we apply the obtained Regge trajectories to fit the spectra of charmonia and bottomonia. The fitted Regge trajectories are in good agreement with the experimental data and the theoretical predictions.

  16. Quantum gates by inverse engineering of a Hamiltonian

    Science.gov (United States)

    Santos, Alan C.

    2018-01-01

    Inverse engineering of a Hamiltonian (IEH) from an evolution operator is a useful technique for the protocol of quantum control with potential applications in quantum information processing. In this paper we introduce a particular protocol to perform IEH and we show how this scheme can be used to implement a set of quantum gates by using minimal quantum resources (such as entanglement, interactions between more than two qubits or auxiliary qubits). Remarkably, while previous protocols request three-qubit interactions and/or auxiliary qubits to implement such gates, our protocol requires just two-qubit interactions and no auxiliary qubits. By using this approach we can obtain a large class of Hamiltonians that allow us to implement single and two-qubit gates necessary for quantum computation. To conclude this article we analyze the performance of our scheme against systematic errors related to amplitude noise, where we show that the free parameters introduced in our scheme can be useful for enhancing the robustness of the protocol against such errors.

  17. A simple global representation for second-order normal forms of Hamiltonian systems relative to periodic flows

    International Nuclear Information System (INIS)

    Avendaño-Camacho, M; Vallejo, J A; Vorobjev, Yu

    2013-01-01

    We study the determination of the second-order normal form for perturbed Hamiltonians relative to the periodic flow of the unperturbed Hamiltonian H 0 . The formalism presented here is global, and can be easily implemented in any computer algebra system. We illustrate it by means of two examples: the Hénon–Heiles and the elastic pendulum Hamiltonians. (paper)

  18. Almost periodic Hamiltonians: an algebraic approach

    International Nuclear Information System (INIS)

    Bellissard, J.

    1981-07-01

    We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians

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

    International Nuclear Information System (INIS)

    Huang, Qing-Guo; Zhang, Ke-Chao; Zhou, Shuang-Yong

    2013-01-01

    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''

  20. Scattering theory for Stark Hamiltonians

    International Nuclear Information System (INIS)

    Jensen, Arne

    1994-01-01

    An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs