Landau levels from the Bethe Ansatz equations
Hoshi, K.; Hatsugai, Y.
2000-01-01
The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak-field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.
Landau Levels from the Bethe Ansatz Equations
Hoshi, K.; Hatsugai, Y.
1999-01-01
The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.
Levkovich-Maslyuk, Fedor
2016-08-01
We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S-matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU(2) chiral Gross–Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU(3) chiral Gross–Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU(3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completely different setting, namely for the 1D oscillator in quantum mechanics.
Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field
Hatsugai, Yasuhiro; Kohmoto, Mahito; Wu, Yong-Shi
1994-01-01
For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations of Wiegmann and Zabrodin. When the magnetic flux per plaquette is 1 / Q with Q an odd integer, distribution of the roots of the Bethe ansatz equation is uniform except at two points on the unit circle in the complex plane. For the semiclassical limit Q→∞, the wave function is
On the algebraic Bethe ansatz for the XXX spin chain: creation operators 'beyond the equator'
International Nuclear Information System (INIS)
Considering the XXX spin-1/2 chain in the framework of the algebraic Bethe ansatz, we make the following short comment: the product of the creation operators corresponding to the recently found solution of the Bethe equations 'on the wrong side of the equator' is just zero (not only its action on the pseudovacuum). (author). Letter-to-the-editor
Levkovich-Maslyuk, Fedor
2016-01-01
We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S-matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU(2) chiral Gross-Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU(3) chiral Gross-Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU(3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completley different setting, namely for the 1d oscillator in quantum mechani...
ODE/IM correspondence and Bethe ansatz for affine Toda field equations
Ito, Katsushi
2015-01-01
We study the linear problem associated with modified affine Toda field equation for the Langlands dual $\\hat{\\mathfrak{g}}^\\vee$, where $\\hat{\\mathfrak{g}}$ is an untwisted affine Lie algebra. The connection coefficients for the asymptotic solutions of the linear problem correspond to the Q-functions for $\\mathfrak{g}$-type quantum integrable models. The $\\psi$-system for the solutions associated with the fundamental representations of $\\mathfrak{g}$ leads to Bethe ansatz equations associated with the affine Lie algebra $\\hat{\\mathfrak{g}}$. We also study the $A^{(2)}_{2r}$ affine Toda field equation in massless limit in detail and find its Bethe ansatz equations as well as T-Q relations.
ODE/IM correspondence and Bethe ansatz for affine Toda field equations
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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.
Analysis of the Bethe-ansatz equations of the chiral-invariant Gross-Neveu model
International Nuclear Information System (INIS)
The Bethe-ansatz equations of the chiral-invariant Gross-Neveu model are reduced to a simple form in which the parameters of the vacuum solution have been eliminated. The resulting system of equations involves only the rapidities of physical particles and a minimal set of complex parameters needed to distinguish the various internal symmetry states of these particles. The analysis is performed without invoking the time-honored assumption that the solutions of the Bethe-ansatz equations, in the infinite-volume limit, are comprised entirely of strings ('bound states'). Surprisingly, it is found that the correct description of the n-particle states involves no strings of length greater than two (except for special values of the momenta). (orig.)
Bethe-ansatz equations for quantum Heisenberg chains with elliptic exchange
Inozemtsev, V. I.
1999-01-01
The eigenvectors of the Hamiltonian ${\\cal H}_{N}$ of $N$-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.
osp (1 vertical bar 2) off-shell Bethe ansatz equations
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The semiclassical limit of the algebraic quantum inverse scattering method is used to solve the theory of the Gaudin model. Via Off-shell Bethe ansatz equations of an integrable representation of the graded osp(1 vertical bar 2) vertex model we find the spectrum of the N - 1 independents Hamiltonians of Gaudin. Integral representations of the N-point correlators are presented as solutions of the Knizhnik-Zamolodchikov equation. These results are extended for highest representations of the osp (1 vertical bar 2) Gaudin algebra
Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field
Hatsugai, Yasuhiro; Kohmoto, Mahito; Wu, Yong-Shi
1994-01-01
For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations recently proposed by Wiegmann and Zabrodin. When the magnetic flux per plaquette is $1/Q$ where $Q$ is an odd integer, distribution of the roots is uniform on the unit circle in the complex plane. For the semi-classical limit, $ Q\\rightarrow\\infty$, the wavefunction obeys the power low and is given by $|\\psi(x)|^2=(2/ \\sin \\pi x)$ which is critical and unnormal...
Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz
Le Doussal, Pierre
2014-04-01
We show how our previous result based on the replica Bethe ansatz for the Kardar-Parisi-Zhang (KPZ) equation with the ‘half-flat’ initial condition leads to the Airy2 to Airy1 (i.e. GUE (Gaussian unitary ensemble) to GOE (Gaussian orthogonal ensemble)) universal crossover one-point height distribution in the limit of large time. It involves a ‘decoupling assumption’ in that limit, validated by the result. Equivalently, we obtain the distribution of the free energy of a long directed polymer (DP) in a random potential with one fixed endpoint and the other one on a half-line. We generalize to a DP when each endpoint is free on its own half-line. This yields, in the large time limit, a conjecture for the distribution of the maximum of the transition process Airy2→1 (minus a half-parabola) on a half-line.
Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz
International Nuclear Information System (INIS)
We show how our previous result based on the replica Bethe ansatz for the Kardar–Parisi–Zhang (KPZ) equation with the ‘half-flat’ initial condition leads to the Airy2 to Airy1 (i.e. GUE (Gaussian unitary ensemble) to GOE (Gaussian orthogonal ensemble)) universal crossover one-point height distribution in the limit of large time. It involves a ‘decoupling assumption’ in that limit, validated by the result. Equivalently, we obtain the distribution of the free energy of a long directed polymer (DP) in a random potential with one fixed endpoint and the other one on a half-line. We generalize to a DP when each endpoint is free on its own half-line. This yields, in the large time limit, a conjecture for the distribution of the maximum of the transition process Airy2→1 (minus a half-parabola) on a half-line. (paper)
Energy Technology Data Exchange (ETDEWEB)
Bracken, Anthony J.; Ge Xiangyu; Gould, Mark D.; Links, Jon; Zhou Huanqiang [Centre for Mathematical Physics, University of Queensland, Brisbane, QLD (Australia)
2001-06-01
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method. (author)
Kitanine, N; Niccoli, G
2014-01-01
We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to be equivalent to the known separation of variable (SOV) representation hence proving that it defines a complete characterization of the transfer matrix spectrum. The polynomial character of the Q-function allows us then to show that a finite system of equations of generalized Bethe type can be similarly used to describe the complete transfer matrix spectru...
Off-diagonal Bethe ansatz for exactly solvable models
International Nuclear Information System (INIS)
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.
Introduction to the thermodynamic Bethe ansatz
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.
Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
Gombor, Tamas
2015-01-01
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the particle rapidities and the accompanying Bethe Ansatz equations are derived.
International Nuclear Information System (INIS)
The exactly integrable isotropic Heisenberg chain of N spins s is studied, and numerical solutions to the Bethe ansatz equations corresponding to the antiferromagnetic vacuum (for sN ≤ 128) and the simplest excitations have been obtained. For s = 1, a complete set of states for N = 6 is given, and the vacuum solution for finite N is estimated analytically. The deviations from the string picture at large N are discussed
Matrix coordinate Bethe Ansatz: applications to XXZ and ASEP models
International Nuclear Information System (INIS)
We present the construction of the full set of eigenvectors of the open asymmetric simple exclusion process (ASEP) and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. This 'matrix coordinate Bethe Ansatz' can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing in the matrix Ansatz. (paper)
Bethe ansatz for the Temperley–Lieb spin chain with integrable open boundaries
International Nuclear Information System (INIS)
In this paper we study the spectrum of the spin-1 Temperley–Lieb spin chain with integrable open boundary conditions. We obtain the eigenvalue expressions as well as its associated Bethe ansatz equations by means of the coordinate Bethe ansatz. These equations provide the complete description of the spectrum of the model. (paper)
Introduction to the thermodynamic Bethe ansatz
van Tongeren, Stijn J
2016-01-01
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 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 ...
Bethe ansatz solution of the open XX spin chain with non-diagonal boundary terms
International Nuclear Information System (INIS)
We consider the integrable open XX quantum spin chain with non-diagonal boundary terms. We derive an exact inversion identity, by which we obtain the eigenvalues of the transfer matrix and the Bethe ansatz equations. For generic values of the boundary parameters, the Bethe ansatz solution is formulated in terms of the Jacobian elliptic functions. (author)
Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
Cao, Junpeng; Shi, Kangjie; Wang, Yupeng
2013-01-01
With 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.
Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
International Nuclear Information System (INIS)
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
Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
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.
Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices
International Nuclear Information System (INIS)
By means of an algebraic Bethe ansatz approach, we study the Zamolodchikov–Fateev and Izergin–Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors are used to diagonalize the associated transfer matrix. The eigenvalues as well as the Bethe equations are presented. (paper)
Algebraic Bethe Ansatz for Open XXX Model with Triangular Boundary Matrices
Belliard, Samuel; Crampé, Nicolas; Ragoucy, Eric
2013-05-01
We consider an open XXX spin chain with two general boundary matrices whose entries obey a relation, which is equivalent to the possibility to put simultaneously the two matrices in a upper-triangular form. We construct Bethe vectors by means of a generalized algebraic Bethe ansatz. As usual, the method uses Bethe equations and provides transfer matrix eigenvalues.
Algebraic Bethe ansatz for the gl(1|2) generalized model: II. the three gradings
International Nuclear Information System (INIS)
The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same R-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe ansatz for all models with 9 x 9, rational, gl(1|2) invariant R-matrix and all three possibilities of choosing the grading. Our Bethe ansatz solution applies, for instance, to the supersymmetric t-J model, the supersymmetric U model and a number of interesting impurity models. It may be extended to obtain the quantum transfer matrix spectrum for this class of models. The properties of a specific model enter the Bethe ansatz solution (i.e. the expression for the transfer matrix eigenvalue and the Bethe ansatz equations) through the three pseudo vacuum eigenvalues of the diagonal elements of the monodromy matrix which in this context are called the parameters of the model
Matrix coordinate Bethe Ansatz: applications to XXZ and ASEP models
Energy Technology Data Exchange (ETDEWEB)
Crampe, N [Laboratoire Charles Coulomb, UMR 5221, Universite Montpellier 2, F-34095 Montpellier (France); Ragoucy, E [Laboratoire de Physique Theorique LAPTH, CNRS and Universite de Savoie, 9 chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux Cedex (France); Simon, D, E-mail: nicolas.crampe@univ-montp2.fr, E-mail: ragoucy@lapp.in2p3.fr, E-mail: damien.simon@upmc.fr [LPMA, Universite Pierre et Marie Curie, Case Courrier 188, 4 place Jussieu, 75252 Paris Cedex 05 (France)
2011-10-07
We present the construction of the full set of eigenvectors of the open asymmetric simple exclusion process (ASEP) and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. This 'matrix coordinate Bethe Ansatz' can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing in the matrix Ansatz. (paper)
Cyclotomic Gaudin Models: Construction and Bethe Ansatz
Vicedo, Benoît; Young, Charles
2016-05-01
To any finite-dimensional simple Lie algebra g and automorphism {σ: gto g we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of {U(g)^{⊗ N}} generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case {σ =id}. We go on to construct joint eigenvectors and their eigenvalues for this hierarchy of cyclotomic Gaudin Hamiltonians, in the case of a spin chain consisting of a tensor product of Verma modules. To do so we generalize an approach to the Bethe ansatz due to Feigin, Frenkel and Reshetikhin involving vertex algebras and the Wakimoto construction. As part of this construction, we make use of a theorem concerning cyclotomic coinvariants, which we prove in a companion paper. As a byproduct, we obtain a cyclotomic generalization of the Schechtman-Varchenko formula for the weight function.
Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models
Khachatryan, Sh.; Ferraz, A.; Klümper, A.; Sedrakyan, A.
2015-10-01
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.
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.
Algebraic Bethe ansatz for Q-operators: the Heisenberg spin chain
Frassek, Rouven
2015-07-01
We diagonalize Q-operators for rational homogeneous {sl}(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we demonstrate that the Q-operators act diagonally on the Bethe vectors if the Bethe equations are satisfied. In this way we provide a direct proof that the eigenvalues of the Q-operators studied here are given by Baxter's Q-functions.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
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.
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.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
International Nuclear Information System (INIS)
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
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
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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.
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
Belliard, Samuel; Crampé, Nicolas
2013-11-01
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.
Heisenberg XXX model with general boundaries: Eigenvectors from Algebraic Bethe ansatz
Belliard, S
2013-01-01
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.
Bethe ansatz solution of the $\\tau_2$-model with arbitrary boundary fields
Xu, Xiaotian; Yang, Tao; Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie
2016-01-01
The quantum $\\tau_2$-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.
Spin-1/2 XYZ model revisit: General solutions via off-diagonal Bethe ansatz
Energy Technology Data Exchange (ETDEWEB)
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); Cui, Shuai [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); Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048 (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); Collaborative Innovation Center of Quantum Matter, Beijing (China)
2014-09-15
The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the inhomogeneous T–Q relations, which allow us to treat both the even N (the number of lattice sites) and odd N cases simultaneously in a unified approach.
Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain
Nepomechie, Rafael I
2016-01-01
We use the algebraic Bethe ansatz to obtain the eigenvalues and eigenvectors of the spin-1 Temperley-Lieb open quantum chain with "free" boundary conditions. We exploit the associated reflection algebra in order to prove the off-shell equation satisfied by the Bethe vectors.
Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
Belliard, Samuel
2015-01-01
The spectral problem of the Heisenberg XXZ spin-$\\frac{1}{2}$ chain on the segment is investigated within a modified algebraic Bethe ansatz framework. We consider in this work the most general boundaries allowed by integrability. The eigenvalues and the eigenvectors are obtained. They are characterised by a set of Bethe roots with cardinality equal to $N$, the length of the chain, and which satisfies a set of Bethe equations with an additional term.
Bethe Ansatz for the Ruijsenaars Model of BC_1-Type
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Oleg Chalykh
2007-02-01
Full Text Available We consider one-dimensional elliptic Ruijsenaars model of type $BC_1$. It is given by a three-term difference Schrödinger operator $L$ containing 8 coupling constants. We show that when all coupling constants are integers, $L$ has meromorphic eigenfunctions expressed by a variant of Bethe ansatz. This result generalizes the Bethe ansatz formulas known in the $A_1$-case.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
António, N Cirilo; Salom, I
2014-01-01
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 corresponding Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the Bethe vectors through the so-called quasi-classical limit.
Large and small density approximations to the thermodynamic Bethe ansatz
International Nuclear Information System (INIS)
We provide analytical solutions to the thermodynamic Bethe ansatz equations in the large and small density approximations. We extend results previously obtained for leading order behaviour of the scaling function of affine Toda field theories related to simply laced Lie algebras to the non-simply laced case. The comparison with semi-classical methods shows perfect agreement for the simply laced case. We derive the Y-systems for affine Toda field theories with real coupling constant and employ them to improve the large density approximations. We test the quality of our analysis explicitly for the sinh-Gordon model and the (G2(1),D4(3)) -affine Toda field theory
Hofstadter problem on the honeycomb and triangular lattices: Bethe ansatz solution
Kohmoto, M.; Sedrakyan, A.
2006-06-01
We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with 2πp/q flux per cell. It is shown that the problem factorizes to two triangular lattices. Treating magnetic translations as a Heisenberg-Weyl group and by the use of its irreducible representation on the space of theta functions, we find a nested set of Bethe equations, which determine the eigenstates and energy spectrum. The Bethe equations have simple form which allows us to consider them further in the limit p,q→∞ by the technique of thermodynamic Bethe ansatz and analyze the Hofstadter problem for the irrational flux.
Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
International Nuclear Information System (INIS)
We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S
On the algebraic Bethe ansatz: Periodic boundary conditions
Lima-Santos, A.
2006-01-01
In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to present explicit expressions for the eigenvectors and eigenvalues of the respective transfer matrices.
Coordinate Bethe Ansatz for Spin s XXX Model
Nicolas Crampé; Eric Ragoucy; Ludovic Alonzi
2010-01-01
We compute the eigenfunctions and eigenvalues of the periodic integrable spin s XXX model using the coordinate Bethe ansatz. To do so, we compute explicitly the Hamiltonian of the model. These results generalize what has been obtained for spin 1/2 and spin 1 chains.
Characters in Conformal Field Theories from Thermodynamic Bethe Ansatz
Kuniba, A.; Nakanishi, T; Suzuki, J.
1993-01-01
We propose a new $q$-series formula for a character of parafermion conformal field theories associated to arbitrary non-twisted affine Lie algebra $\\widehat{g}$. We show its natural origin from a thermodynamic Bethe ansatz analysis including chemical potentials.
The Yangians, Bethe ansatz and combinatorics
International Nuclear Information System (INIS)
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.)
Wiegmann, P. B.; Zabrodin, A. V.
1993-01-01
We present a new approach to the problem of Bloch electrons in magnetic field,\\\\ by making explicit a natural relation between magnetic translations and the\\\\quantum group $U_{q}(sl_2)$. The approach allows to express the spectrum and\\\\\\ the Bloch function as solutions of the Bethe-Ansatz equations typical for com\\\\pletely integrable quantum systems
Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary
António, N Cirilo; Ragoucy, E; Salom, I
2015-01-01
Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations.
Universal Bethe ansatz solution for the Temperley-Lieb spin chain
Nepomechie, Rafael I
2016-01-01
We consider the Temperley-Lieb (TL) open quantum spin chain with "free" boundary conditions associated with the spin-$s$ representation of quantum-deformed $sl(2)$. We construct the transfer matrix, and determine its eigenvalues and the corresponding Bethe equations using analytical Bethe ansatz. We show that the transfer matrix has quantum group symmetry, and we propose explicit formulas for the number of solutions of the Bethe equations and the degeneracies of the transfer-matrix eigenvalues. We propose an algebraic Bethe ansatz construction of the off-shell Bethe states, and we conjecture that the on-shell Bethe states are highest-weight states of the quantum group. We also propose a determinant formula for the scalar product between an off-shell Bethe state and its on-shell dual, as well as for the square of the norm. We find that all of these results, except for the degeneracies and a constant factor in the scalar product, are universal in the sense that they do not depend on the value of the spin. In an...
Nested Bethe ansatz for "all" closed spin chains
Belliard, S.; Ragoucy, E.
2008-01-01
We present in an unified and detailed way the Nested Bethe Ansatz for closed spin chains based on Y(gl(n)), Y(gl(m|n)), U_q(gl(n)) or U_q(gl(m|n)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain. In particular, the case of indecomposable representations of superalgebras is studied. The construction extends and unifies the results already obtained for spin chains based on Y(gl(n)) or U_q(gl(n)) and for some particular super-spin chains. We give the Beth...
International Nuclear Information System (INIS)
The asymmetric simple exclusion process with open boundaries, which is a very simple model of out-of-equilibrium statistical physics, is known to be integrable. In particular, its spectrum can be described in terms of Bethe roots. The large deviation function of the current can be obtained as well by diagonalizing a modified transition matrix, which is still integrable: the spectrum of this new matrix can also be described in terms of Bethe roots for special values of the parameters. However, due to the algebraic framework used to write the Bethe equations in previous works, the nature of the excitations and the full structure of the eigenvectors remained unknown. This paper explains why the eigenvectors of the modified transition matrix are physically relevant, gives an explicit expression for the eigenvectors and applies it to the study of atypical currents. It also shows how the coordinate Bethe ansatz developed for the excitations leads to a simple derivation of the Bethe equations and of the validity conditions of this ansatz. All the results obtained by de Gier and Essler are recovered and the approach gives a physical interpretation of the exceptional points. The overlap of this approach with other tools such as the matrix ansatz is also discussed. The method that is presented here may be not specific to the asymmetric exclusion process and may be applied to other models with open boundaries to find similar exceptional points
How algebraic Bethe ansatz works for integrable model
Fadeev, L
1996-01-01
I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific details are given. Several parameters, appearing in these generalizations: spin s, anisotropy parameter \\ga, shift \\om in the alternating chain, allow to include in our treatment most known examples of soliton theory, including relativistic model of Quantum Field Theory.
Bethe ansatz for higher spin eight vertex models
Takebe, T
1995-01-01
A generalization of the eight vertex model by means of higher spin representations of the Sklyanin algebra is investigated by the quantum inverse scattering method and the algebraic Bethe Ansatz. Under the well-known string hypothesis low-lying excited states are considered and scattering phase shifts of two physical particles are calculated. The S matrix of two particle states is shown to be proportional to the Baxter's elliptic R matrix with a different elliptic modulus from the original one.
Bethe ansatz solvable multi-chain quantum systems
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In this article we review recent developments in the one-dimensional Bethe ansatz solvable multi-chain quantum models. The algebraic version of the Bethe ansatz (the quantum inverse scattering method) permits us to construct new families of integrable Hamiltonians using simple generalizations of the well known constructions of the single-chain model. First we consider the easiest example ('basic' model) of this class of models: the antiferromagnetic two-chain spin-1/2 model with the nearest-neighbour and next-nearest-neighbour spin-frustrating interactions (zigzag chain). We show how the algebra of the quantum inverse scattering method works for this model, and what are the important features of the Hamiltonian (which reveal the topological properties of two dimensions together with the one-dimensional properties). We consider the solution of the Bethe ansatz for the ground state (in particular, commensurate-incommensurate quantum phase transitions present due to competing spin-frustrating interactions are discussed) and construct the thermal Bethe ansatz (in the form of the 'quantum transfer matrix') for this model. Then possible generalizations of the basic model are considered: an inclusion of a magnetic anisotropy, higher-spin representations (including the important case of a quantum ferrimagnet), the multi-chain case, internal degrees of freedom of particles at each site, etc. We observe the similarities and differences between this class of models and related exactly solvable models: other groups of multi-chain lattice models, quantum field theory models and magnetic impurity (Kondo-like) models. Finally, the behaviour of non-integrable (less constrained) multi-chain quantum models is discussed. (author)
Hierarchical Structure of Azbel-Hofstader Problem: Strings and loose ends of Bethe Ansatz
Abanov, A. G.; Talstra, J. C.; Wiegmann, P. B.
1997-01-01
We present numerical evidence that solutions of the Bethe Ansatz equations for a Bloch particle in an incommensurate magnetic field (Azbel-Hofstadter or AH model), consist of complexes-"strings". String solutions are well-known from integrable field theories. They become asymptotically exact in the thermodynamic limit. The string solutions for the AH model are exact in the incommensurate limit, where the flux through the unit cell is an irrational number in units of the elementary flux quantu...
Bethe Ansatz Solutions of the Bose-Hubbard Dimer
Directory of Open Access Journals (Sweden)
Jon Links
2006-12-01
Full Text Available The Bose-Hubbard dimer Hamiltonian is a simple yet effective model for describing tunneling phenomena of Bose-Einstein condensates. One of the significant mathematical properties of the model is that it can be exactly solved by Bethe ansatz methods. Here we review the known exact solutions, highlighting the contributions of V.B. Kuznetsov to this field. Two of the exact solutions arise in the context of the Quantum Inverse Scattering Method, while the third solution uses a differential operator realisation of the su(2 Lie algebra.
G/G gauged WZW model and Bethe Ansatz for the phase model
Okuda, Satoshi
2012-01-01
We investigate the G/G gauged Wess-Zumino-Witten model on a Riemann surface from the point of view of the algebraic Bethe Ansatz for the phase model. After localization procedure is applied to the G/G gauged Wess-Zumino-Witten model, the diagonal components for group elements satisfy Bethe Ansatz equations for the phase model. We show that the partition function of the G/G gauged Wess-Zumino-Witten model is identified as the summation of norms with respect to all the eigenstates of the Hamiltonian with the fixed number of particles in the phase model. We also consider relations between the Chern-Simons theory on $S^1\\times\\Sigma_h$ and the phase model.
Spectral Theory for Interacting Particle Systems Solvable by Coordinate Bethe Ansatz
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro
2015-11-01
We develop spectral theory for the q-Hahn stochastic particle system introduced recently by Povolotsky. That is, we establish a Plancherel type isomorphism result that implies completeness and biorthogonality statements for the Bethe ansatz eigenfunctions of the system. Owing to a Markov duality with the q-Hahn TASEP (a discrete-time generalization of TASEP with particles' jump distribution being the orthogonality weight for the classical q-Hahn orthogonal polynomials), we write down moment formulas that characterize the fixed time distribution of the q-Hahn TASEP with general initial data. The Bethe ansatz eigenfunctions of the q-Hahn system degenerate into eigenfunctions of other (not necessarily stochastic) interacting particle systems solvable by the coordinate Bethe ansatz. This includes the ASEP, the (asymmetric) six-vertex model, and the Heisenberg XXZ spin chain (all models are on the infinite lattice). In this way, each of the latter systems possesses a spectral theory, too. In particular, biorthogonality of the ASEP eigenfunctions, which follows from the corresponding q-Hahn statement, implies symmetrization identities of Tracy and Widom (for ASEP with either step or step Bernoulli initial configuration) as corollaries. Another degeneration takes the q-Hahn system to the q-Boson particle system (dual to q-TASEP) studied in detail in our previous paper (2013). Thus, at the spectral theory level we unify two discrete-space regularizations of the Kardar-Parisi-Zhang equation/stochastic heat equation, namely, q-TASEP and ASEP.
Bethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory
M. Kormos; G. Mussardo; B. Pozsgay
2010-01-01
We show that the matrix elements of integrable models computed by the algebraic Bethe ansatz (BA) can be put in direct correspondence with the form factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe ansatz model can be regarded as a suitable non-relativistic
Twist-three at five loops, Bethe ansatz and wrapping
Beccaria, Matteo; Forini, Valentina; Łukowski, Tomasz; Zieme, Stefan
2009-03-01
We present a formula for the five-loop anomalous dimension of Script N = 4 SYM twist-three operators in the fraktur sfraktur l(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Lüscher formalism, considering scattering processes of spin chain magnons with virtual particles that travel along the cylinder. The complete result respects the expected large spin scaling properties and passes non-trivial tests including reciprocity constraints. We analyze the pole structure and find agreement with a conjectured resummation formula. In analogy with the twist-two anomalous dimension at four-loops wrapping effects are of order (log2M/M2) for large values of the spin.
Correlation functions of the spin chains. Algebraic Bethe Ansatz approach
International Nuclear Information System (INIS)
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.)
Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Azbel-Hofstadter Problem
Wiegmann, P. B.; Zabrodin, A. V.
1993-01-01
We present a new approach to the problem of Bloch electrons in magnetic ( sometimes called Azbel-Hofstadter problem) field, by making explicit a natural relation between the group of magnetic translations and the quantum group $U_{q}(sl_2)$. The approach allows us to express the "mid" band spectrum of the model and the Bloch wave function as solutions of the Bethe-Ansatz equations typical for completely integrable quantum systems. The zero mode wave functions are found explicitly in terms of ...
Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field
Hatsugai, Y.; Kohmoto, M.; Wu, Y.-S.
1995-01-01
The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group $U_q(sl_2)$. A linear combination of its generators gives the Hamiltonian. We obtain analytical and numerical solutions for the wave functions by solving the Bethe Ansatz equations, proposed by Wiegmann and Zabrodin on the basis of above observation. The semi-classical case with the flux per plaquette $\\phi=1/Q$ is ...
Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity
Gainutdinov, Azat M
2016-01-01
For generic values of q, all the eigenvectors of the transfer matrix of the U_q sl(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=exp(i pi/p) with integer p>1), 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.
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.
Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity
Gainutdinov, Azat M.; Nepomechie, Rafael I.
2016-08-01
For generic values of q, all the eigenvectors of the transfer matrix of the Uq sl (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 =e iπ / 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.
Functional Bethe ansatz methods for the open XXX chain
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We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of variables or, equivalently, from the fusion of transfer matrices. For generic boundary conditions the eigenvalues cannot be obtained from the solution of finitely many algebraic Bethe equations. Based on careful finite size studies of the analytic properties of the underlying hierarchy of transfer matrices we devise two approaches to analyze the functional equations. First we introduce a truncation method leading to Bethe-type equations determining the energy spectrum of the spin chain. In a second approach, the hierarchy of functional equations is mapped to an infinite system of nonlinear integral equations of TBA type. The two schemes have complementary ranges of applicability and facilitate an efficient numerical analysis for a wide range of boundary parameters. Some data are presented on the finite-size corrections to the energy of the state which evolves into the antiferromagnetic ground state in the limit of parallel boundary fields.
Quantum integrability and Bethe ansatz solution for interacting matter-radiation systems
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A unified integrable system, generating a new series of interacting matter-radiation models with interatomic coupling and different atomic frequencies, is constructed and exactly solved through an algebraic Bethe ansatz. Novel features in Rabi oscillation and vacuum Rabi splitting are shown on the example of an integrable two-atom Buck-Sukumar model with resolution of some important controversies in the Bethe ansatz solution including its possible degeneracy for such models. (letter to the editor)
Algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models
Belliard, S; Ragoucy, E; Slavnov, N A
2012-01-01
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for particular case of scalar products of Bethe vectors. This representation can be used for the calculation of form factors and correlation functions of XXX SU(3)-invariant Heisenberg chain.
Masoero, Davide; Raimondo, Andrea; Valeri, Daniele
2016-06-01
We study the ODE/IM correspondence for ODE associated to {widehat{mathfrak{g}}}-valued connections, for a simply-laced Lie algebra {mathfrak{g}}. We prove that subdominant solutions to the ODE defined in different fundamental representations satisfy a set of quadratic equations called {Ψ}-system. This allows us to show that the generalized spectral determinants satisfy the Bethe Ansatz equations.
Twisted Bethe equations from a twisted S-matrix
Ahn, Changrim; Bombardelli, Diego; Nepomechie, Rafael I
2010-01-01
All-loop asymptotic Bethe equations for a 3-parameter deformation of AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld twist of the AdS5/CFT4 S-matrix, together with c-number diagonal twists of the boundary conditions, from which we derive these Bethe equations. Although the undeformed S-matrix factorizes into a product of two su(2|2) factors, the deformed S-matrix cannot be so factored. Diagonalization of the corresponding transfer matrix requires a generalization of the conventional algebraic Bethe ansatz approach, which we first illustrate for the simpler case of the twisted su(2) principal chiral model. We also demonstrate that the same twisted Bethe equations can alternatively be derived using instead untwisted S-matrices and boundary conditions with operatorial twists.
Masoero, Davide; Valeri, Daniele
2015-01-01
We assess the ODE/IM correspondence for the quantum $\\mathfrak{g}$-KdV model, for a non-simply laced Lie algebra $\\mathfrak{g}$. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra ${\\mathfrak{g}}^{(1)}$, and constructing the relevant $\\Psi$-system among subdominant solutions. We then use the $\\Psi$-system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum $\\mathfrak{g}$-KdV model. We also consider generalized Airy functions for twisted Kac--Moody algebras and we construct new explicit solutions to the Bethe Ansatz equations. The paper is a continuation of our previous work on the ODE/IM correspondence for simply-laced Lie algebras.
Instantaneous Bethe-Salpeter equation
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We present a systematic algebraic and numerical investigation of the instantaneous Beth-Salpeter equation. Emphasis is placed on confining interaction kernels of the Lorentz scalar, time component vector, and full vector-types. We explore the stability of the solutions and Regge behavior for each of these interactions, and conclude that only time component vector confinement leads to normal Regge structure and stable solutions for all quark masses
Particle-hole symmetry in algebraic Bethe Ansatz for the XXX model
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It is well known that the space of all quantum states of the XXX model for a magnetic ring of N nodes, each with the spin 1/2, decomposes into sectors with r spin deviations, r = 0,1, 2,..., N [1, 2, 3, 4]. The sectors r and N - r are related mutually by the particle-hole transformation which exchanges the signs + and - on each node. We discuss here effects of this transformation on the formalism of algebraic Bethe Ansatz, in particular on the form of the monodromy matrix, the main tool of this formalism. We derive explicitly appropriate transformation rules for CN- orbits of magnetic configurations and the corresponding Fourier transformations within the bases of wavelets. In particular, we point out some important phase relations between orbits on both sides of the equator.
Bethe Ansatz and exact form factors of the O(N) Gross Neveu-model
Babujian, Hrachya M; Karowski, Michael
2015-01-01
We apply the algebraic nested O(N) Bethe Ansatz 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.
Bethe Ansatz and exact form factors of the O ( N) Gross Neveu-model
Babujian, Hrachya M.; Foerster, Angela; Karowski, Michael
2016-02-01
We apply previous results on the O ( N) Bethe Ansatz [1-3] 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.
Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
Kormos, M.; Mussardo, G.; Pozsgay, B.
2010-01-01
We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic limit of the S-matrix of a field theory, and when there is a well-defined mapping between the Hilbert spaces and operators of the two theories. This correspondence provides an efficient method to compu...
Integrable achiral D5-brane reflections and asymptotic Bethe equations
Correa, Diego H; Young, Charles A S
2011-01-01
We study the reflection of magnons from a D5-brane in the framework of the AdS/CFT correspondence. We consider two possible orientations of the D5-brane with respect to the reference vacuum state, namely vacuum states aligned along "vertical" and "horizontal" directions. We show that the reflections are of the achiral type. We also show that the reflection matrices satisfy the boundary Yang-Baxter equations for both orientations. In the horizontal case the reflection matrix can be interpreted in terms of a bulk S-matrix, S(p, -p), and factorizability of boundary scattering therefore follows from that of bulk scattering. Finally, we solve the nested coordinate Bethe ansatz for the system in the vertical case to find the Bethe equations. In the horizontal case, the Bethe equations are of the same form as those for the closed string.
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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.
Massless Lüscher terms and the limitations of the AdS3 asymptotic Bethe ansatz
Abbott, Michael C.; Aniceto, Inês
2016-05-01
In AdS5/CFT4 integrability the Bethe ansatz gives the spectrum of long strings, accurate up to exponentially small corrections. This is no longer true in three-dimensional anti-de Sitter (AdS3 ) space, as we demonstrate here by studying Lüscher F-terms with a massless particle running in the loop. We apply this to the classic test of Hernández and López, in which the s u (2 ) sector Bethe equations (including the one-loop dressing phase) should match the semiclassical string theory result for a circular spinning string. These calculations do not agree in AdS3×S3×T4 , and we show that the sum of all massless Lüscher F-terms can reproduce the difference.
Generalized Coordinate Bethe Ansatz for open spin chains with non-diagonal boundaries
International Nuclear Information System (INIS)
We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work with N. Crampe (L2C) and D. Simon (LPMA), see arXiv:1009.4119, arXiv:1105.4119 and arXiv:1106.3264.
Yang-Baxter algebras, integrable theories and Bethe Ansatz
International Nuclear Information System (INIS)
This paper presents the Yang-Baxter algebras (YBA) in a general framework stressing their power to exactly solve the lattice models associated to them. The algebraic Behe Ansatz is developed as an eigenvector construction based on the YBA. The six-vertex model solution is given explicitly. The generalization of YB algebras to face language is considered. The algebraic BA for the SOS model of Andrews, Baxter and Forrester is described using these face YB algebras. It is explained how these lattice models yield both solvable massive QFT and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. This approach permit to define and solve rigorously massive QFT as an appropriate continuum limit of gapless vertex models. The deep links between the YBA and Lie algebras are analyzed including the quantum groups that underlay the trigonometric/hyperbolic YBA. Braid and quantum groups are derived from trigonometric/hyperbolic YBA in the limit of infinite spectral parameter. To conclude, some recent developments in the domain of integrable theories are summarized
Algebraic and geometric properties of Bethe Ansatz eigenfunctions on a pentagonal magnetic ring
International Nuclear Information System (INIS)
The exact solution of the eigenproblem of the Heisenberg Hamiltonian for the XXX model in the case of a magnetic ring with N=5 nodes is presented in a closed algebraic form. It is demonstrated that the eigenproblem itself is expressible within the extension of the prime field Q of rationals by the primitive fifth root of unity, whereas the associated Bethe parameters, i.e. pseudomomenta, phases of scattering, and spectral parameters, require some finite field extensions, such that the nonlinearity remains algebraic rather than transcendental. Classification of exact Bethe Ansatz eigenstates in terms of rigged string configurations is presented. -- Research Highlights: → The eigenproblem is expressed in a finite extension of the field Q. → The Galois symmetry gives rise to operators which reproduce the energy band structure. → Original Bethe parameters can be derived by the inverse BA problem. → String hypothesis, expected to work as N goes to infinity, is almost satisfied for N=5.
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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.)
Bethe ansatz solvability and supersymmetry of the M2 model of single fermions and pairs
International Nuclear Information System (INIS)
A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice N=2 supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified. The relation between this manifold and the existence of additional, so-called dynamic, supersymmetries is discussed. The ground states are analysed with the help of cohomology techniques, and their exact finite-size Bethe roots are found. Moreover, through analytical and numerical studies it is argued that the model provides a lattice version of the N=1 super-sine-Gordon model at a particular coupling where an additional N=(2,2) supersymmetry is present. The dynamic supersymmetry is shown to allow an exact determination of the gap scaling function of the model. (paper)
Algebraic Bethe ansatz for the six vertex model with upper triangular K-matrices
International Nuclear Information System (INIS)
We consider a formulation of the algebraic Bethe ansatz for the six vertex model with non-diagonal open boundaries. Specifically, we study the case where both left and right K-matrices have an upper triangular form. We show that the main difficulty entailed by those forms of the K-matrices is the construction of the excited states. However, it is possible to treat this problem with the aid of an auxiliary transfer matrix and by means of a generalized creation operator. (paper)
A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons
Hibberd, K. E.; Dunning, C.; Links, J.
2006-08-01
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 Schrödinger operators. For the solution we derive here the potential of the Schrödinger 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.
A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons
Energy Technology Data Exchange (ETDEWEB)
Hibberd, K.E. [Centre for Mathematical Physics, University of Queensland, 4072 (Australia); Dunning, C. [Institute of Mathematics, Statistics and Actuarial Science, University of Kent (United Kingdom); Links, J. [Centre for Mathematical Physics, University of Queensland, 4072 (Australia)]. E-mail: jrl@maths.uq.edu.au
2006-08-07
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.
Kundu, Anjan
2016-01-01
Integrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a novel quantum field model in quasi-two dimensions involving interacting fields. The Yang-Baxter integrability is proved for the model by finding a new kind of commutation rule for its basic fields, representing nonstandard scalar fields along the transverse direction. In spite of a close link with the quantum Landau-Lifshitz equation, the present model differs widely from it, in its content and the result obtained. Using further the algebraic Bethe ansatz we solve exactly the eigenvalue problem of this quantum field model for all its higher conserved operators. The idea presented here should instigate the construction of a novel class of integrable field and lattice models and exploration of a new type of underlying algebras.
Log-gamma directed polymer with fixed endpoints via the replica Bethe Ansatz
International Nuclear Information System (INIS)
We study the model of a discrete directed polymer (DP) on a square lattice with homogeneous inverse gamma distribution of site random Boltzmann weights, introduced by Seppalainen (2012 Ann. Probab. 40 19–73). The integer moments of the partition sum, Zn-bar , are studied using a transfer matrix formulation, which appears as a generalization of the Lieb–Liniger quantum mechanics of bosons to discrete time and space. In the present case of the inverse gamma distribution the model is integrable in terms of a coordinate Bethe Ansatz, as discovered by Brunet. Using the Brunet-Bethe eigenstates we obtain an exact expression for the integer moments of Zn-bar for polymers of arbitrary lengths and fixed endpoint positions. Although these moments do not exist for all integer n, we are nevertheless able to construct a generating function which reproduces all existing integer moments and which takes the form of a Fredholm determinant (FD). This suggests an analytic continuation via a Mellin–Barnes transform and we thereby propose a FD ansatz representation for the probability distribution function (PDF) of Z and its Laplace transform. In the limit of a very long DP, this ansatz yields that the distribution of the free energy converges to the Gaussian unitary ensemble (GUE) Tracy-Widom distribution up to a non-trivial average and variance that we calculate. Our asymptotic predictions coincide with a result by Borodin et al (2013 Commun. Math. Phys. 324 215–32) based on a formula obtained by Corwin et al (2011 arXiv:1110.3489) using the geometric Robinson–Schensted–Knuth (gRSK) correspondence. In addition we obtain the dependence on the endpoint position and the exact elastic coefficient at a large time. We argue the equivalence between our formula and that of Borodin et al. As we will discuss, this provides a connection between quantum integrability and tropical combinatorics. (paper)
Log-gamma directed polymer with fixed endpoints via the replica Bethe Ansatz
Thiery, Thimothée; Le Doussal, Pierre
2014-10-01
We study the model of a discrete directed polymer (DP) on a square lattice with homogeneous inverse gamma distribution of site random Boltzmann weights, introduced by Seppalainen (2012 Ann. Probab. 40 19-73). The integer moments of the partition sum, \\overline{Z^n} , are studied using a transfer matrix formulation, which appears as a generalization of the Lieb-Liniger quantum mechanics of bosons to discrete time and space. In the present case of the inverse gamma distribution the model is integrable in terms of a coordinate Bethe Ansatz, as discovered by Brunet. Using the Brunet-Bethe eigenstates we obtain an exact expression for the integer moments of \\overline{Z^n} for polymers of arbitrary lengths and fixed endpoint positions. Although these moments do not exist for all integer n, we are nevertheless able to construct a generating function which reproduces all existing integer moments and which takes the form of a Fredholm determinant (FD). This suggests an analytic continuation via a Mellin-Barnes transform and we thereby propose a FD ansatz representation for the probability distribution function (PDF) of Z and its Laplace transform. In the limit of a very long DP, this ansatz yields that the distribution of the free energy converges to the Gaussian unitary ensemble (GUE) Tracy-Widom distribution up to a non-trivial average and variance that we calculate. Our asymptotic predictions coincide with a result by Borodin et al (2013 Commun. Math. Phys. 324 215-32) based on a formula obtained by Corwin et al (2011 arXiv:1110.3489) using the geometric Robinson-Schensted-Knuth (gRSK) correspondence. In addition we obtain the dependence on the endpoint position and the exact elastic coefficient at a large time. We argue the equivalence between our formula and that of Borodin et al. As we will discuss, this provides a connection between quantum integrability and tropical combinatorics.
Twisting singular solutions of Bethe's equations
Nepomechie, Rafael I
2014-01-01
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 be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.
Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution
Kohmoto, M.; Sedrakyan, A.
2006-01-01
We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with $2 \\pi p/q$ flux per cell. It is shown that the problem factorizes to two triangular lattices. Treating magnetic translations as Heisenberg-Weyl group and by the use of its irreducible representation on the space of theta functions, we find a nested set of Bethe equations, which determine the eigenstates and energy spectrum. The Bethe equations have simple form which allows to consider them further in the...
Bethe Ansatz for Supersymmetric Model Constructed from Uq[osp(2|2)(2)] R-Matrix
Institute of Scientific and Technical Information of China (English)
YANG Wen-Li; ZHEN Yi
2001-01-01
Using the algebraic Bethe ansatz method, we obtain the eigenvalues of transfer matrix of the supersymmetric model constructed from the R-matrix of the twisted affine superalgebra Uq[osp(2|2)(2)] in periodic boundary condition and twisted boundary condition.``
Gaudin-type models, non-skew-symmetric classical r-matrices and nested Bethe ansatz
Directory of Open Access Journals (Sweden)
T. Skrypnyk
2015-02-01
Full Text Available We consider quantum integrable systems associated with the Lie algebra gl(n and Cartan-invariant non-dynamical non-skew-symmetric classical r-matrices. We describe the sub-class of Cartan-invariant non-skew-symmetric r-matrices for which exists the standard procedure of the nested Bethe ansatz associated with the chain of embeddings gl(n⊃gl(n−1⊃gl(n−2⊃⋯⊃gl(1. We diagonalize the corresponding quantum integrable systems by its means. We illustrate the obtained results by the examples of the generalized Gaudin systems with and without external magnetic field associated with three classes of non-dynamical non-skew-symmetric classical r-matrices.
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.
Bethe-salpeter equation from many-body perturbation theory
International Nuclear Information System (INIS)
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.
RPA equations and the instantaneous Bethe-Salpeter equation
Resag, J
1993-01-01
We give a derivation of the particle-hole RPA equations for an interacting multi-fermion system by applying the instantaneous approximation to the amputated two-fermion propagator of the system. In relativistic field theory the same approximation leads from the fermion-antifermion Bethe-Salpeter equation to the Salpeter equation. We show that RPA equations and Salpeter equation are indeed equivalent.
International Nuclear Information System (INIS)
We extend the exact periodic Bethe ansatz solution for one-dimensional bosons and fermions with δ-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground-state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground-state energy in the weak and strong coupling limits
Energy Technology Data Exchange (ETDEWEB)
Choudhury, A.G.; Chowdhury, A.R. [Jadavpur Univ., Calcutta (India)
1996-08-01
Intertwining relations for the quantum R-matrix of the SU{sub p,q}(2) invariant spin chain are obtained and the corresponding face model is deduced. An important difference is seen to arise due to the asymmetry generated by the parameters p and q, which leads to a asymmetric face model. An algebraic Bethe ansatz is set up and solved with the help of these intertwining vectors.
Energy Technology Data Exchange (ETDEWEB)
Oelkers, N; Batchelor, M T; Bortz, M; Guan, X-W [Department of Theoretical Physics, Research School of Physical Sciences and Engineering and Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200 (Australia)
2006-02-03
We extend the exact periodic Bethe ansatz solution for one-dimensional bosons and fermions with {delta}-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground-state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground-state energy in the weak and strong coupling limits.
International Nuclear Information System (INIS)
We consider the problem of consistence between the Bethe ansatz (BA) wave function and the multiparticle (more than two) scattering in one-dimensional δ-function interacting SU(4) fermions, which the approach of BA does not explicitly take into account. We find the scattering conditions of three and four particles located at the same position and show that the conditions can be fulfilled by the two-particle connection conditions of the BA wave function. So the definition of the BA wave function can be exactly extended to those cases with multiple occupancies. The inconsistence between the BA and multiparticle interacting on a same site in the degenerate Hubbard model, which makes the BA fail for the model, is shown to vanish in the limit of small site spacing. A correspondence relation of the BA equation and SU(4) symmetry of the system is also indicated for the fermions. The degeneracy of state with BA eigenenergy is given. Singlet lies in the case when there are equal numbers of particles in each inner component
Gainutdinov, A M; Nepomechie, Rafael I; Sommese, Andrew J
2015-01-01
We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of dimensions of irreducible representations of the Temperley-Lieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)_q-modules. These formulas include corrections that appear if two or more tilting modules are spectrum-degenerate. For the XX case (q=exp(i pi/2)), we give explicit formulas for the number of admissible solutions and degeneracies. We also consider the cases of generic q and the isotropic (q->1) limit. Numerical solutions of the Bethe equations up to N=8 are presented. Our results are consistent with the Bethe ansatz solution being complete.
Two-body bound states & the Bethe-Salpeter equation
Energy Technology Data Exchange (ETDEWEB)
Pichowsky, M. [Argonne National Lab., IL (United States); Kennedy, M. [Univ. of New Hampshire, Durham, NH (United States). Physics Dept.; Strickland, M. [Duke Univ., Durham, NC (United States)
1995-01-18
The Bethe-Salpeter formalism is used to study two-body bound states within a scalar theory: two scalar fields interacting via the exchange of a third massless scalar field. The Schwinger-Dyson equation is derived using functional and diagrammatic techniques, and the Bethe-Salpeter equation is obtained in an analogous way, showing it to be a two-particle generalization of the Schwinger-Dyson equation. The authors also present a numerical method for solving the Bethe-Salpeter equation without three-dimensional reduction. The ground and first excited state masses and wavefunctions are computed within the ladder approximation and space-like form factors are calculated.
Colored Quantum Algebra and Its Bethe State
International Nuclear Information System (INIS)
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)
International Nuclear Information System (INIS)
The same-position scattering (SPS) of more than two electrons in a one-dimensional model of two-band electrons with spin-exchange interaction is discussed. The boundary conditions of three- and four-particle SPS are given. It is shown that the conditions can be fulfilled by the two-particle boundary conditions for the Bethe ansatz (BA) wavefunction. Consequently, the definition of the BA wavefunction can be extended to those cases of more than two particles occupying the same position. Therefore, unlike the case in lattice models in which configurations with more than two particles at one site are excluded in applying the approach, the BA is valid without the exclusion of multi-particle SPS in the spin-exchange model. A relation between the SU(2)xSU(2) symmetry and the BA equation is also indicated. (author)
Bethe states of the integrable spin-s chain with generic open boundaries
International Nuclear Information System (INIS)
Based on the inhomogeneous T –Q relation and the associated Bethe ansatz equations obtained via the off-diagonal Bethe ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries by employing certain orthogonal basis of the Hilbert space. (paper)
Glueball properties from the Bethe-Salpeter equation
International Nuclear Information System (INIS)
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.)
Castro-Alvaredo, Olalla; Doyon, Benjamin; Hoogeveen, Marianne
2013-01-01
We evaluate the exact energy current and scaled cumulant generating function (related to the large-deviation function) in non-equilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of D. Bernard and B. Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures $T_l$, $T_r$, and waiting for a long time. We evaluate the current $J(T_l,T_r)$ using the exact QFT density matrix describing these non-equilibrium steady states and using Al.B. Zamolodchikov's method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the high-temperature limit. We analyze numerically our non-equilibrium steady-...
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
Fast analytic solver of rational Bethe equations
Marboe, Christian
2016-01-01
In this note we propose an approach for a fast analytic determination of all possible eigenstates of rational GL(N|M) integrable spin chains of given not too large length, in terms of Baxter Q-functions. We observe that all exceptional solutions, if any, are automatically correctly accounted. The key intuition behind the approach is that the equations on the Q-functions are determined solely by the Young diagram, and not by the choice of the rank of the GL symmetry. Hence we can choose arbitrary N and M that accommodate the desired representation. Then we consider all distinguished Q-functions at once, not only those following a certain Kac-Dynkin path.
Bethe vectors in GL(3)-based quantum integrable models
Pakuliak, S; Slavnov, N A
2015-01-01
We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable models we prove a formula for the Bethe vectors of composite model. We show that this representation is a particular case of general coproduct property of the weight functions (Bethe vectors) found in the theory of the deformed Knizhnik--Zamolodchokov equation.
Bethe-Salpeter equation for elastic nucleon-nucleon scattering
International Nuclear Information System (INIS)
The Bethe-Salpeter equation for NN scattering with one-boson exchange is investigated for the case in which the pion-nucleon coupling is described by axial-vector theory. In contrast to the results with pseudoscalar coupling, good agreement with the experimental data can be obtained for all partial waves. Also, the deviations from the Blankenbecler-Sugar equation are not as large as they are for pseudoscalar coupling. In addition, cancellations between the direct and the crossed box graph with pseudoscalar πN coupling are investigated for the 3S1 phase shift in the framework of the variational operator Pade approximation
Hutsalyuk, A; Pakuliak, S Z; Ragoucy, E; Slavnov, N A
2016-01-01
We study integrable models with $\\mathfrak{gl}(2|1)$ symmetry and solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for scalar products of Bethe vectors, when the Bethe parameters obey some relations weaker than the Bethe equations. This representation allows us to find the norms of on-shell Bethe vectors and obtain determinant formulas for form factors of the diagonal entries of the monodromy matrix.
Bethe states of the XXZ spin-12 chain with arbitrary boundary fields
Directory of Open Access Journals (Sweden)
Xin Zhang
2015-04-01
Full Text Available Based on the inhomogeneous T−Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-12 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge transformations, proper generators and reference state for constructing Bethe vectors can be obtained respectively. Given an inhomogeneous T−Q relation for an eigenvalue, it is proven that the resulting Bethe state is an eigenstate of the transfer matrix, provided that the parameters of the generators satisfy the associated Bethe Ansatz equations.
Excited charmonium states from Bethe-Salpeter equation
Sauli, Vladimir
2011-01-01
We solve the Bethe-Salpeter equation for a system of a heavy quark-antiquark pair interacting with a screened linear confining potential. First we show the spinless QFT model is inadequate and fail to describe even gross feature of the quarkonia spectrum. In order to get reliable description the spine degrees of freedom has to be considered. Within the approximation employed we reasonably reproduce known radial excitation of vector charmonium. The BSE favors relatively large string breaking scale $\\mu\\simeq 350MeV$ . Using free charm quark propagators we observe that $J/\\Psi$ is the only charmonium left bellow naive quark-antiquark threshold $2m_c$, while the all excited states are situated above this threshold. Within the numerical method we overcome obstacles related with threshold singularity and discuss the consequences of the use of free propagators for calculation of excited states above the threshold.
A systematic approach to sketch Bethe-Salpeter equation
Qin, Si-xue
2016-01-01
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 symm...
Two-body bound states ampersand the Bethe-Salpeter equation
International Nuclear Information System (INIS)
The Bethe-Salpeter formalism is used to study two-body bound states within a scalar theory: two scalar fields interacting via the exchange of a third massless scalar field. The Schwinger-Dyson equation is derived using functional and diagrammatic techniques, and the Bethe-Salpeter equation is obtained in an analogous way, showing it to be a two-particle generalization of the Schwinger-Dyson equation. The authors also present a numerical method for solving the Bethe-Salpeter equation without three-dimensional reduction. The ground and first excited state masses and wavefunctions are computed within the ladder approximation and space-like form factors are calculated
Skrypnyk, T.
2016-09-01
We consider quantum integrable models based on the Lie algebra gl(n) and non-skew-symmetric classical r-matrices associated with Z 2-gradings of gl(n) of the following type: {gl}(n)={gl}{(n)}\\bar{0}+{gl}{(n)}\\bar{1}, where {gl}{(n)}\\bar{0}={gl}({n}1)\\oplus {gl}(n-{n}1). Among the considered models are Gaudin-type models with an external magnetic field, used in nuclear physics to produce proton–neutron Bardeen–Cooper–Schrieer-type models, n-level many-mode Jaynes–Cummings–Dicke-type models of quantum optics, matrix generalization of Bose–Hubbard dimers, etc. We diagonalize the constructed models by means of the ‘generalized’ nested Bethe ansatz.
Bethe's quantum numbers and rigged configurations
Directory of Open Access Journals (Sweden)
Anatol N. Kirillov
2016-04-01
Full Text Available We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model under the periodic boundary condition. Our method is based on the observation that the sums of Bethe's quantum numbers within each string behave particularly nicely. We confirm our procedure for all solutions for length 12 chain (totally 923 solutions.
Bethe's quantum numbers and rigged configurations
Kirillov, Anatol N.; Sakamoto, Reiho
2016-01-01
We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model under the periodic boundary condition. Our method is based on the observation that the sums of Bethe's quantum numbers within each string behave particularly nicely. We confirm our procedure for all solutions for length 12 chain (totally 923 solutions).
Efficient implementation of core-excitation Bethe Salpeter equation calculations
Gilmore, K; Shirley, E L; Prendergast, D; Pemmaraju, C D; Kas, J J; Vila, F D; Rehr, J J
2016-01-01
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) [Phys. Rev. B 83, 115106 (2011)]. Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previous...
Scattering solutions of Bethe-Salpeter equation in Minkowski and Euclidean spaces
Carbonell, J
2016-01-01
We shortly review different methods to obtain the scattering solutions of the Bethe-Salpeter equation in Minkowski space. We emphasize the possibility to obtain the zero energy observables in terms of the Euclidean scattering amplitude.
Light Pseudoscalar Mesons in Bethe-Salpeter Equation with Instantaneous Interaction
Lucha, Wolfgang
2015-01-01
The light pseudoscalar mesons play a twofold role: they may or have to be regarded both as low-lying bound states of the fundamental degrees of freedom of quantum chromodynamics as well as the (pseudo-) Goldstone bosons of the spontaneously broken chiral symmetries of quantum chromodynamics. We interrelate these aspects in a single quantum-field-theoretic approach relying on the Bethe-Salpeter formalism in instantaneous approximation by very simple means: the shape of the pseudoscalar-meson Bethe-Salpeter wave function dictated by chiral symmetry is used in Bethe-Salpeter equations for bound states of vanishing mass, in order to deduce analytically the interactions which govern the bound states under study. In this way, we obtain exact Bethe-Salpeter solutions for pseudoscalar mesons, in the sense of establishing the rigorous relationship between, on the one hand, the relevant interactions and, on the other hand, the Bethe-Salpeter amplitudes that characterize the bound states.
Use of the Bethe equation for inner-shell ionization by electron impact
Powell, Cedric J.; Llovet, Xavier; Salvat, Francesc
2016-05-01
We analyzed calculated cross sections for K-, L-, and M-shell ionization by electron impact to determine the energy ranges over which these cross sections are consistent with the Bethe equation for inner-shell ionization. Our analysis was performed with K-shell ionization cross sections for 26 elements, with L-shell ionization cross sections for seven elements, L3-subshell ionization cross sections for Xe, and M-shell ionization cross sections for three elements. The validity (or otherwise) of the Bethe equation could be checked with Fano plots based on a linearized form of the Bethe equation. Our Fano plots, which display theoretical cross sections and available measured cross sections, reveal two linear regions as predicted by de Heer and Inokuti [in Electron Impact Ionization, edited by T. D. Märk and G. H. Dunn, (Springer-Verlag, Vienna, 1985), Chap. 7, pp. 232-276]. For each region, we made linear fits and determined values of the two element-specific Bethe parameters. We found systematic variations of these parameters with atomic number for both the low- and the high-energy linear regions of the Fano plots. We also determined the energy ranges over which the Bethe equation can be used.
Bethe states for the two-site Bose-Hubbard model: a binomial approach
Santos, Gilberto; Foerster, Angela; Roditi, Itzhak
2015-01-01
We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix for the two-site Bose-Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
Solution of the Bethe-Goldstone Equation without Partial Wave Decomposition
White, L; Sammarruca, F.
2013-01-01
We present a method for solving the nucleon-nucleon scattering equation without the use of a partial wave expansion of the scattering amplitude. After verifying the accuracy of the numerical solutions, we proceed to apply the method to the in-medium scattering equation (the Bethe-Goldstone equation) in three dimensions. A focal point is a study of Pauli blocking effects calculated in the (angle-dependent) three-dimensional formalism as compared to the usual spherical approximation. We discuss...
Normalization and perturbation theory for tightly bound states of the spinor Bethe-Salpeter equation
L.G. Suttorp
1976-01-01
The normalisation integrals for the tightly-bound-state solutions of the spinor Bethe-Salpeter equation that have been derived recently are evaluated. Ghost states are found to appear when the continuous parameters characterising the type of fermion-boson interaction reach a critical value. Perturba
Exact solutions of the spinor Bethe-Salpeter equation for tightly bound states
L.G. Suttorp
1975-01-01
Exact solutions are obtained for the spinor Bethe-Salpeter equation that describes tightly bound states of spin-/sup 1///sub 2/ fermions with massless-boson exchange. The corresponding coupling constants form a discrete spectrum that depends continuously on the parameters characterizing the type of
Calculation of Spin Observables for Proton-Neutron Elastic Scattering in the Bethe-Salpeter Equation
Kinpara, Susumu
2016-01-01
Bethe-Salpeter equation is applied to $p$-$n$ elastic scattering. The spin observables are calculated by the M matrix similar to $p$-$p$ case. The parameters of the meson-exchange model are used with the cut-off for the pion exchange interaction. Change of the M matrix indicates breaking of the charge independence in the nucleon-nucleon system.
Stochastic integration of the Bethe-Salpeter equation for two bound fermions
International Nuclear Information System (INIS)
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.)
The connection of two-particle relativistic quantum mechanics with the Bethe-Salpeter equation
International Nuclear Information System (INIS)
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
Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit
Frederico, T; Viviani, M
2015-01-01
For the first time, the inhomogeneous Bethe-Salpeter Equation for an interacting system, composed by two massive scalars exchanging a massive scalar, is numerically investigated in ladder approximation, directly in Minkowski space, by using an approach based on the Nakanishi integral representation. In this paper, the limiting case of zero-energy states is considered, extending the approach successfully applied to bound states presented in Phys. Rev. D 89, (2014) 016010, where the Nakanishi integral representation has been exploited for solving the homogeneous Bethe-Salpeter Equation. The numerical values of scattering lengths, evaluated by using two different integral equations that stem within the Nakanishi framework, are compared with the analogous quantities recently obtained, within a totally different framework. Moreover, relevant functions, like the Nakanishi weight functions and the distorted part of the zero-energy Light-front wave functions are also presented. Interestingly, a highly non trivial iss...
Light composite Higgs boson from the normalized Bethe-Salpeter equation
Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil); Natale, A. A.; da Silva, P. S. Rodrigues
2009-01-01
Scalar composite boson masses have been computed in QCD and Technicolor theories with the help of the homogeneous Bethe-Salpeter equation (BSE), resulting in a scalar mass that is twice the dynamically generated fermion or technifermion mass ($m_{dyn}$). We show that in the case of walking (or quasi-conformal) technicolor theories, where the $m_{dyn}$ behavior with the momenta may be quite different from the one predicted by the standard operator product expansion, this result is incomplete a...
Gluon bound state and asymptotic freedom derived from the Bethe--Salpeter equation
Fukamachi, Hitoshi; Nishino, Shogo; Shinohara, Toru
2016-01-01
In this paper we study the two-body bound states for gluons and ghosts in a massive Yang-Mills theory which is obtained by generalizing the ordinary massless Yang-Mills theory in a manifestly Lorentz covariant gauge. First, we give a systematic derivation of the coupled Bethe-Salpeter equations for gluons and ghosts by using the Cornwall-Jackiw-Tomboulis effective action of the composite operators within the framework of the path integral quantization. Then, we obtain the numerical solutions for the Bethe-Salpeter amplitude representing the simultaneous bound states of gluons and ghosts by solving the homogeneous Bethe-Salpeter equation in the ladder approximation. We study how the inclusion of ghosts affects the two-gluon bound states in the cases of the standing and running gauge coupling constant. Moreover, we show explicitly that the approximate solutions obtained for the gluon-gluon amplitude are consistent with the ultraviolet asymptotic freedom signaled by the negative $\\beta$ function.
Symmetry preserving truncations of the gap and Bethe-Salpeter equations
Binosi, Daniele; Chang, Lei; Papavassiliou, Joannis; Qin, Si-Xue; Roberts, Craig D.
2016-05-01
Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one- and two-body problems, which must be preserved in any veracious treatment of mesons as bound states. In this connection, one may view the dressed gluon-quark vertex, Γμa , as fundamental. We use a novel representation of Γμa , in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, K , that is symmetry consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalize on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of H -diagrams in K , which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of Γμa in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladderlike truncation; and, moreover, adding any number of similarly dressed crossed-box diagrams cannot improve the situation.
Symmetry preserving truncations of the gap and Bethe-Salpeter equations
Energy Technology Data Exchange (ETDEWEB)
Binosi, Daniele; Chang, Lei; Papavassiliou, Joannis; Qin, Si-Xue; Roberts, Craig D.
2016-05-01
Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one-and two-body problems, which must be preserved in any veracious treatment of mesons as bound states. In this connection, one may view the dressed gluon-quark vertex, Gamma(alpha)(mu), as fundamental. We use a novel representation of Gamma(alpha)(mu), in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, K, that is symmetry consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalize on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of H-diagrams in K, which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of Gamma(alpha)(mu) in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladderlike truncation; and, moreover, adding any number of similarly dressed crossed-box diagrams cannot improve the situation.
Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
de Paula, W; Salmè, G; Viviani, M
2016-01-01
Actual solutions of the Bethe-Salpeter equation for a two-fermion bound system are becoming available directly in Minkowski space, by virtue of a novel technique, based on the so-called Nakanishi integral representation of the Bethe-Salpeter amplitude and improved by expressing the relevant momenta through light-front components, i.e. $k^\\pm=k^0 \\pm k^3$. We solve a crucial problem that widens the applicability of the method to real situations by providing an analytically exact treatment of the singularities plaguing the two-fermion problem in Minkowski space, irrespective of the complexity of the irreducible Bethe-Salpeter kernel. This paves the way for feasible numerical investigations of relativistic composite systems, with any spin degrees of freedom. We present a thorough comparison with existing numerical results, evaluated in both Minkowski and Euclidean space, fully corroborating our analytical treatment, as well as fresh light-front amplitudes illustrating the potentiality of non perturbative calcula...
On string solutions of Bethe equations in N=4 supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
The Bethe equations, arising in description of the spectrum of the dilatation operator for the su(2) sector of the N=4 supersymmetric Yang-Mills theory, are considered in the anti-ferromagnetic regime. These equations are deformation of those for the Heisenberg XXX magnet. It is proven that in the thermodynamic limit roots of the deformed equations group into strings. It is proven that the corresponding Yang's action is convex, which implies uniqueness of solution for centers of the strings. The state formed of strings of length (2n+1) is considered and the density of their distribution is found. It is shown that the energy of such a state decreases as n grows. It is observed that non-analyticity of the left hand side of the Bethe equations leads to an additional contribution to the density and energy of strings of even length. Whence it is concluded that the structure of the anti-ferromagnetic vacuum is determined by the behaviour of exponential corrections to string solutions in the thermodynamic limit and possibly involves strings of length 2. (orig.)
Norm of Bethe Wave Function as a Determinant
Korepin, Vladimir E
2009-01-01
This is a historical note. Bethe Ansatz solvable models are considered, for example XXZ Heisenberg anti-ferromagnet and Bose gas with delta interaction. Periodic boundary conditions lead to Bethe equation. The square of the norm of Bethe wave function is equal to a determinant of linearized system of Bethe equations (determinant of matrix of second derivatives of Yang action). The proof was first published in Communications in Mathematical Physics, vol 86, page 391 in l982. Also domain wall boundary conditions for 6 vertex model were discovered in the same paper [see Appendix D]. These play an important role for algebraic combinatorics: alternating sign matrices, domino tiling and plane partition. Many publications are devoted to six vertex model with domain wall boundary conditions.
Exact treatment of the Pauli exclusion operator in the nuclear matter Bethe-Goldstone equation
International Nuclear Information System (INIS)
We solve the Bethe-Goldstone equation in nuclear matter for the scattering of a nucleon of a few hundred MeV. The angular momentum coupling caused by the nonspherical part of the Pauli blocking operator is treated exactly. It is found that standard approximation of angle averaging the Pauli operator is quite accurate for bulk properties of the reaction matrix even at energies as high as 300 MeV. Our result justifies one of the common approximations previously untested in the microscopic calculation of the optical model potential
Abe, Yuya
2016-01-01
We investigate a simple model using the numerical simulation in the complex Langevin equation (CLE) and the analytical approximation with the Gaussian Ansatz. We find that the Gaussian Ansatz captures the essential and even quantitative features of the CLE results quite well including unwanted behavior in the unstable region where the CLE converges to a wrong answer. The Gaussian Ansatz is therefore useful for looking into this convergence problem and we find that the exact answer in the unstable region is nicely reproduced by another solution that is naively excluded from the stability condition. We consider the Gaussian probability distributions corresponding to multiple solutions along the Lefschetz thimble to discuss the stability and the locality. Our results suggest a prescription to improve the convergence of the CLE simulation to the exact answer.
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.
Ground State Mass Spectrum for Scalar Diquarks with Bethe-Salpeter Equation
Institute of Scientific and Technical Information of China (English)
WANG Zhi-Gang; WAN Shao-Long; YANG Wei-Min
2007-01-01
In this article,we study the structures of the pseudoscalar mesons π,K and the scalar diquarks Ua,Da,Sa in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential.The u,d,s quarks have small current masses,and the renormalization is very large,the mass poles in the timelike region are absent which implements confinement naturally.The Bethe-Salpeter wavefunctions of the pseudoscalar mesons π,K,and the scalar diquarks Ua,Da,Sa have the same type (Gaussian type) momentum dependence,center around zero momentum and extend to the energy scale about q2 = 1 GeV2,which happens to be the energy scale for the chiral symmetry breaking,the strong interactions in the infrared region result in bound (or quasi-bound) states.The numerical results for the masses and decay constants of the π and K mesons can reproduce the experimental values,and the ground state masses of the scalar diquarks Ua,Da,Sa are consistent with the existing theoretical calculations.We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diquarks.
Many-body-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation
Lindgren, I.; Salomonson, S.; Hedendahl, D.
2005-03-01
The connection between many-body perturbation theory (MBPT) and quantum electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based on the recently developed covariant-evolution-operator method for QED calculations (I. Lindgren, S. Salomonson, and B. Asen. Phys. Rep. 389, 161 (2004)), which is quite similar in structure to MBPT. At the same time, this procedure is closely related to the S-matrix and Green's-function formalisms and can therefore serve as a bridge connecting various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schrodinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. This is a multi-state equation that has the same relation to the single-state BS equation as the standard Bloch equation has to the ordinary Schrodinger equation. It can be used to generate a perturbation expansion compatible with the BS equation even in the case of a quasi-degenerate model space.
Intriguin solutions of Bethe-Salpeter equation for radially excited pseudoscalar charmonia
Sauli, Vladimir
2012-01-01
When generalizing recent various quantum mechanical models of heavy quarkonia to Quantum Filed theoretical approach based on Bethe-Salpeter equation one is faced to the solutions that do not exist in nonrelativistic limit. Mainly, there is unexpected doubling of the spectrum when comparing to the experimentally known spectrum as well as the ones obtained from the solution of the Schroedinger equation. These additional states are not apriory unphysical as both of them have the same symmetry. Our study strongly suggests that these solutions appear due to the sensitivity of BSE to the details of the analytical form of the constituents quark and antiquark propagators, more specifically they are consequence of using unconfining free propagators. To show this explicitly we develop and describe the efficient method of the numerical solution for quarkonium BSE and numerically solve it for the case of pseudoscalar charmonia. For the bare propagators of constituents we are able to find BSE solution for arbitrarily high...
Symmetry preserving truncations of the gap and Bethe-Salpeter equations
Binosi, Daniele; Papavassiliou, Joannis; Qin, Si-Xue; Roberts, Craig D
2016-01-01
Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one- and two-body problems, which must be preserved in any veracious treatment of mesons as bound-states. In this connection, one may view the dressed gluon-quark vertex, $\\Gamma_\\mu^a$, as fundamental. We use a novel representation of $\\Gamma_\\mu^a$, in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, $K$, that is symmetry-consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalise on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of $H$-diagrams in $K$, which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of $\\Gamma_\\mu^a$ in a Bethe-Salpeter kernel nor expressed as a member of the class...
Bethe-Salpeter equation for non-self conjugate mesons in a power-law potential
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
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.)
Gadjiev, S A
2001-01-01
Scattering amplitude of fermions and bosons in the ladder approximation at high energies is investigated. For the imaginary part of the scattering amplitude the set of Bethe-Salpeter type integral equations is constructed. Solutions of this set in the Regge asymptotic form are found. The impact of mass parameters on the behavior of the amplitude at high energies is studied.
Solving the inhomogeneous Bethe-Salpeter equation in Minkowski space: the zero-energy limit
Frederico, Tobias; Salmè, Giovanni; Viviani, Michele
2015-08-01
The inhomogeneous Bethe-Salpeter equation for an interacting system, composed of two massive scalars exchanging a massive scalar, is numerically investigated in the ladder approximation directly in Minkowski space, by using for the first time in the continuum an approach based on the Nakanishi integral representation. In this paper, the limiting case of zero-energy states is considered, thus extending an approach that has already been successfully applied to bound states. The numerical values of scattering lengths, are calculated for several values of the Yukawa coupling constant, by using two different integral equations that stem from the Nakanishi framework. Those low-energy observables are compared with (1) the analogous quantities recently obtained in literature, within a totally different framework, and (2) the non-relativistic evaluations, to illustrate the relevance of a nonperturbative, genuine field theoretical treatment in Minkowski space, even in the low-energy regime. Moreover, dynamical functions, like the Nakanishi weight functions and the distorted part of the zero-energy light-front wave functions are also presented. Interestingly, a highly non-trivial issue related to the abrupt change in the width of the support of the Nakanishi weight function, when the zero-energy limit is approached, is elucidated, ensuring a sound basis to the forthcoming evaluation of phase shifts.
Solving the inhomogeneous Bethe-Salpeter equation in Minkowski space: the zero-energy limit
Energy Technology Data Exchange (ETDEWEB)
Frederico, Tobias [Instituto Tecnologico de Aeronautica, DCTA, Dept. de Fisica, Sao Paulo (Brazil); Salme, Giovanni [Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Roma (Italy); Viviani, Michele [Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Pisa (Italy)
2015-08-15
The inhomogeneous Bethe-Salpeter equation for an interacting system, composed of two massive scalars exchanging a massive scalar, is numerically investigated in the ladder approximation directly in Minkowski space, by using for the first time in the continuum an approach based on the Nakanishi integral representation. In this paper, the limiting case of zero-energy states is considered, thus extending an approach that has already been successfully applied to bound states. The numerical values of scattering lengths, are calculated for several values of the Yukawa coupling constant, by using two different integral equations that stem from the Nakanishi framework. Those low-energy observables are compared with (1) the analogous quantities recently obtained in literature, within a totally different framework, and (2) the non-relativistic evaluations, to illustrate the relevance of a nonperturbative, genuine field theoretical treatment in Minkowski space, even in the low-energy regime. Moreover, dynamical functions, like the Nakanishi weight functions and the distorted part of the zero-energy light-front wave functions are also presented. Interestingly, a highly non-trivial issue related to the abrupt change in the width of the support of the Nakanishi weight function, when the zero-energy limit is approached, is elucidated, ensuring a sound basis to the forthcoming evaluation of phase shifts. (orig.)
International Nuclear Information System (INIS)
Radiative decay widths are calculated for the radiative decay processes observed experimentally in the charmonium system. The model uses a Bethe-Salpeter equation with a static kernel and harmonic oscillator potentials to model the c-anti c system. Each decay width is calculated for 21 different choices of the c-quark mass. The potential used was a linear combination of a vector coupled and a scalar coupled harmonic oscillator potential. The quark mass and the scalar to vector coupling ratio were determined by trying to fit simultaneously the psi'(3685) - psi(3095) mass difference, the psi(3095) → e+ + e-decay width and the 3P/sub J/ mass splittings. A single choice of the quark mass and scalar to vector coupling ratio could not simultaneously fit all these constraints. The best fit to these constraints occurred when the quark mass was 5.5 and the scalar to vector coupling ratio parameter was -0.16. The decay width calculations are shown graphically for values of the quark mass from 0.00 to 16 GeV. The decay widths were calculated two different ways: (1) using the matrix elements of the quark momentum; (2) using the matrix elements of the quark position. Most of the published calculations use method (2). The widths computed by methods (1) and (2) are quite different for all masses and all transitions implying that the usual method (2) give incorrect results, and the fits with experimental data are fortuitous
Non-regular eigenstate of the XXX model as some limit of the Bethe state
International Nuclear Information System (INIS)
For the one-dimensional XXX model under the periodic boundary conditions, we discuss two types of eigenvectors, regular eigenvectors which have finite-valued rapidities satisfying the Bethe ansatz equations and non-regular eigenvectors which are descendants of some regular eigenvectors under the action of the SU(2) spin-lowering operator. It has been pointed out by many authors that the non-regular eigenvectors should correspond to the Bethe ansatz wavefunctions which have multiple infinite rapidities. However, it has not been explicitly shown whether such a delicate limiting procedure is possible. In this paper, we discuss it explicitly at the level of wavefunctions: we prove that any non-regular eigenvector of the XXX model is derived from the Bethe ansatz wavefunctions through some limit of infinite rapidities. We formulate the regularization also in terms of the algebraic Bethe ansatz method. As an application of infinite rapidity, we discuss the period of the spectral flow under the twisted periodic boundary conditions. (author)
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived newly from QCD in the case where the quark and the antiquark are of different flavors. The technique of the derivation is the usage of the irreducible decomposition of the Green's functions involved in the Bethe-Salpeter equation satisfied by the quark-antiquark four-point Green's function. The interaction kernel derived is given a closed and explicit expression which shows a specific structure of the kernel since the kernel is represented in terms of the quark, antiquark and gluon propagators and some kinds of quark, antiquark and/or gluon three, four, five and six-point vertices. Therefore,the expression of the kernel is not only convenient for perturbative calculations, but also suitable for nonperturbative investigations.
Multi-Regge limit of the n-gluon bubble ansatz
Energy Technology Data Exchange (ETDEWEB)
Bartels, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Schomerus, V.; Sprenger, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-07-15
We investigate n-gluon scattering amplitudes in the multi-Regge region of N=4 supersymmetric Yang-Mills theory at strong coupling. Through a careful analysis of the thermodynamic bubble ansatz (TBA) for surfaces in AdS{sub 5} with n-g(lu)on boundary conditions we demonstrate that the multi-Regge limit probes the large volume regime of the TBA. In reaching the multi-Regge regime we encounter wall-crossing in the TBA for all n>6. Our results imply that there exists an auxiliary system of algebraic Bethe ansatz equations which encode valuable information on the analytical structure of amplitudes at strong coupling.
Osano, Bob
2016-01-01
We present an ansatz for the relationship between magnetic flux density and fluid vorticity evolution equations. We also suggest that the magnetic flux density evolution equations be compared to the evolution equation for an effective vorticity ($\\omega_{eff}$), which bears a power law relation to the ordinary vorticity.
Bethe vectors for XXX-spin chain
International Nuclear Information System (INIS)
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
Bethe vectors for XXX-spin chain
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.
Bethe vectors of GL(3)-invariant integrable models
International Nuclear Information System (INIS)
We study GL(3)-invariant integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the Bethe vectors and the actions of the generators of the Yangian Y(gl3) on the Bethe vectors are considered. These actions are relevant for the calculation of correlation functions and form factors of local operators of the underlying quantum models. (paper)
Hadronic Observables from Dyson-Schwinger and Bethe-Salpeter equations
Sanchis-Alepuz, Helios
2015-01-01
In these proceedings we present a mini-review on the topic of the Dyson-Schwinger/Bethe-Salpeter approach to the study of relativistic bound-states in physics. In particular, we present a self-contained discussion of their derivation, as well as their truncation such that important symmetries are maintained.
On the history of a stochastic ansatz for solving the transport equation
International Nuclear Information System (INIS)
A very useful approximate tool for understanding the role of random material properties on solutions of the transport equation is described and its historical derivation given. The development of this stochastic tool, from its introduction by Randall, to its use in describing current problems involving dichotomic or pseudo-dichotomic Markov processes is discussed.
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...
Mass of Y(3940) in Bethe-Salpeter equation for quarks
Energy Technology Data Exchange (ETDEWEB)
Chen, Xiaozhao [Shandong University of Science and Technology, Department of Foundational Courses, Taian (China); Lue, Xiaofu [Sichuan University, Department of Physics, Chengdu (China); The Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); CCAST (World Laboratory), Beijing (China)
2015-03-01
The general form of the Bethe-Salpeter wave functions for the bound states composed of two vector fields of arbitrary spin and definite parity is corrected. Using the revised general formalism, we investigate the observed Y(3940) state, which is considered as a molecule state consisting of D{sup *0} anti D{sup *0}. Though the attractive potential between D{sup *0} and anti D{sup *0} including one light meson (σ, π, ω, ρ) exchange is considered, we find that in our approach the contribution from one-π exchange is equal to zero and consider SU(3) symmetry breaking. The obtained mass of Y(3940) is consistent with the experimental value. (orig.)
International Nuclear Information System (INIS)
In this article, we investigate the structures of the pseudoscalar mesons (π, K, D, Ds, B and Bs) in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential (infrared modified flat bottom potential). The Schwinger-Dyson functions for the u, d and s quarks are greatly renormalized at small momentum region and the curves are steep at about q2=1 GeV2 which indicates an explicitly dynamical symmetry breaking. The Euclidean time Fourier transformed quark propagators have no mass poles in the time-like region which naturally implements confinement. As for the c and b quarks, the current masses are very large, the renormalization are more tender, however, mass poles in the time-like region are also absent. The Bethe-Salpeter wavefunctions for those mesons have the same type (Gaussian type) momentum dependence and center around small momentum which indicate that the bound states exist in the infrared region. The decay constants for those pseudoscalar mesons are compatible with the values of experimental extractions and theoretical calculations, such as lattice simulations and QCD sum rules
Gamma Matrix Expansion of the Bethe-Salpeter Equation for Nucleon-Nucleon System
Kinpara, Susumu
2016-01-01
For the coefficients of the amplitude a set of simultaneous equations is derived in momentum space. By the auxiliary conditions they are equivalent to nonrelativistic equations and suitable for the investigation of two-nucleon system.
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In this paper the general structure of leptonic decay constants of vector mesons is evaluated in the framework of Bethe-Salpeter Equation under Covariant Instantaneous Ansatz (CIA) with a modified structure of the Hqq-bar vertex function Γ which is generalized to include Dirac covariants other than the leading Dirac covariant γμ within its structure. The numerical values of fv in this CIA framework are calculated. (author)
Gaind, Vaibhav
Fluorescence resonance energy transfer (FRET) has found many applications in in vitro imaging as an indicator of molecular activity. However, till now, in vivo FRET imaging has been restricted to near-surface multiphoton microscopy. Optical diffusion tomography (ODT) is an emerging tool for deep tissue imaging. In this work, FRET was incorporated in an ODT framework, thereby allowing FRET to be applied in deep tissue imaging. Using simulations and tissue phantom and small animal imaging experiments, the possibility of imaging molecular activity on the nanometer scale using macroscopic measurements is demonstrated. The diffusion equation model is limited to regions of high scatter and low absorption. The Bethe-Salpeter equation has been used extensively to explain various scattering phenomena and is more fundamental than the Boltzmann transport equation. In this work, the Bethe-Salpeter equation has been investigated for modeling photon transport in the non-diffusive regime.
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We realize an extended version of the trigonometric Cherednik algebra as affine Dunkl operators involving Heaviside functions. We use the quadratic Casimir element of the extended trigonometric Cherednik algebra to define an explicit nonstationary Schrödinger equation with delta-potential. We use coordinate Bethe ansatz methods to construct solutions of the nonstationary Schrödinger equation in terms of generalized Bethe wave functions. It is shown that the generalized Bethe wave functions satisfy affine difference Knizhnik-Zamolodchikov equations as functions of the momenta. The relation to the vector valued root system analogs of the quantum Bose gas on the circle with delta-function interactions is indicated.
Meson states from the Bethe-Salpeter equation: successes and challenges
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Full text: Dyson-Schwinger equations provide a nonperturbative continuum approach to QCD. The infinite coupled system of integral equations is truncated in a symmetry preserving manner to allow for both proof of exact results as well as sophisticated model calculations to illustrate these results and to perform qualitative as well as quantitative studies of hadronic observables. Over the past years a lot of investigations have used the so-called rainbow-ladder truncation. I will report the successes and ongoing progress within this truncation and demonstrate the need for a 'step beyond' with the help of examples taken from meson physics. (author)
Bruneval, Fabien; Hamed, Samia M.; Neaton, Jeffrey B.
2015-01-01
The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green's function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased, and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for ...
On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
Borsato, Riccardo; Sfondrini, Alessandro; Stefanski, Bogdan; Torrielli, Alessandro
2016-01-01
Integrability is believed to underlie the AdS3/CFT2 correspondence with sixteen supercharges. We elucidate the role of massless modes within this integrable framework. Firstly, we find the dressing factors that enter the massless and mixed-mass worldsheet S matrix. Secondly, we derive a set of all-loop Bethe Equations for the closed strings, determine their symmetries and weak-coupling limit. Thirdly, we investigate the underlying Yangian symmetry in the massless sector and show that it fits into the general framework of Yangian integrability. In addition, we compare our S matrix in the near-relativistic limit with recent perturbative worldsheet calculations of Sundin and Wulff.
The method of spherical harmonics as an ansatz for the solution of non-linear Boltzmann equations
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A new coordinate-free representation of the differential scattering probability function of the binary self-collision leads to a scattering kernel which is particularly appropriate for the expansion in Legendre polynomials. Thus, the non-linear transport equation can be treated using the spherical harmonics method. Assuming the scattering in the centre-of-mass system to be isotropic, the non-linear moment equations of the particle distribution function are derived. (orig.)
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A series of simple stopping power (SP) formulas, modified from the relativistic Bethe equation, is presented that is based on the concepts of target effective atomic number and mean excitation energy (MEE). The analytical model function is constructed to approximate experimental or calculated SPs at low electron energies and tend asymptotically to the relativistic Bethe function at high energies. The energy dependencies of our effective values, in contrast with theoretical approaches, are defined empirically by parametrization with tuning parameters. A least-squares fitting routine based on the Levenberg–Marquardt algorithm was developed. We utilize the material parameters and numerical calculations of SPs from optical data using the full Penn-algorithm. Our formula is thought to be applicable for energies above 60 eV. Our simulations of SPs for 41 elemental solids are found to be in good agreement with published numerical results. The flexibility of a general empirical formula is shown. Shortened formulas were developed that are applicable for particular energy ranges, and effective MEEs are proposed that differ from previously recommended values. The presented formulas may be used for analytical calculation of SPs over a broad projectile energy region
Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner's Classification
Aghaei, S.; Chenaghlou, A.
2013-09-01
In this paper quasi-exact solvability (QES) of Dirac equation with some scalar potentials based on sl(2) Lie algebra is studied. According to the quasi-exact solvability theory, we construct the configuration of the classes II, IV, V, and X potentials in the Turbiner's classification such that the Dirac equation with scalar potential is quasi-exactly solved and the Bethe ansatz equations are derived in order to obtain the energy eigenvalues and eigenfunctions.
Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner's Classification
International Nuclear Information System (INIS)
In this paper quasi-exact solvability (QES) of Dirac equation with some scalar potentials based on sl(2) Lie algebra is studied. According to the quasi-exact solvability theory, we construct the configuration of the classes II, IV, V, and X potentials in the Turbiner's classification such that the Dirac equation with scalar potential is quasi-exactly solved and the Bethe ansatz equations are derived in order to obtain the energy eigenvalues and eigenfunctions. (general)
Bethe Vectors of Quantum Integrable Models with GL(3 Trigonometric R-Matrix
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Samuel Belliard
2013-10-01
Full Text Available We study quantum integrable models with GL(3 trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz.Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the quantum affine algebra $U_q(widehat{mathfrak{gl}}_3$ onto intersections of different types of Borel subalgebras, we prove that the set of the nested Bethe vectors is closed under the action of the elements of the monodromymatrix.
Multireference Coupled Cluster Ansatz
Jeziorski, Bogumil
2010-01-01
Abstract The origin of the multireference coupled cluster Ansatz for the wave function and the wave operator, discovered in Quantum Theory Project in 1981, is presented from the historical perspective. Various methods of obtaining the cluster amplitudes - both state universal and state selective are critically reviewed and further prospects of using the multireference coupled cluster Ansatz in electronic structure theory are briefly discussed.
π- and K-meson Bethe-Salpeter amplitudes
International Nuclear Information System (INIS)
Independent of assumptions about the form of the quark-quark scattering kernel K, we derive the explicit relation between the flavor-nonsinglet pseudoscalar-meson Bethe-Salpeter amplitude ΓH and the dressed-quark propagator in the chiral limit. In addition to a term proportional to γ5, ΓH necessarily contains qualitatively and quantitatively important terms proportional to γ5γ·P and γ5γ·kk·P, where P is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by ΓH, whose residue is the leptonic decay constant for the bound state. The pseudoscalar vertex also contains such a bound state pole and, in the chiral limit, the residue of this pole is related to the vacuum quark condensate. The axial-vector Ward-Takahashi identity relates these pole residues, with the Gell-Mann endash Oakes endash Renner relation a corollary of this identity. The dominant ultraviolet asymptotic behavior of the scalar functions in the meson Bethe-Salpeter amplitude is fully determined by the behavior of the chiral limit quark mass function, and is characteristic of the QCD renormalization group. The rainbow-ladder Ansatz for K, with a simple model for the dressed-quark-quark interaction, is used to illustrate and elucidate these general results. The model preserves the one-loop renormalization group structure of QCD. The numerical studies also provide a means of exploring procedures for solving the Bethe-Salpeter equation without a three-dimensional reduction. copyright 1997 The American Physical Society
Algebraization of difference eigenvalue equations related to $U_q(sl_2)$
Wiegmann, P. B.; Zabrodin, A. V.
1995-01-01
A class of second order difference (discrete) operators with a partial algebraization of the spectrum is introduced. The eigenfuncions of the algebraized part of the spectrum are polinomials (discrete polinomials). Such difference operators can be constructed by means of $U_q(sl_2)$, the quantum deformation of the $sl_2$ algebra. The roots of polinomials determine the spectrum and obey the Bethe Ansatz equations. A particular case of difference equations for $q$-hypergeometric and Askey-Wilso...
Kp and Toda Tau Functions in Bethe Ansatz
Takasaki, Kanehisa
2011-10-01
Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model with DWBC, the finite XXZ chain of spin 1/2, the phase model on a finite chain, etc.) is reviewed. Some additional information on this issue is also presented.
KP and Toda tau functions in Bethe ansatz
Takasaki, Kanehisa
2010-01-01
Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model with DWBC, the finite XXZ chain of spin 1/2, the phase model on a finite chain, etc.) is reviewed. Some additional information on this issue is also presented.
Quasi-exactly solvable Fokker-Planck equations
Ho, Choon-Lin; Sasaki, Ryu
2007-01-01
We consider exact and quasi-exact solvability of the one-dimensional Fokker-Planck equation based on the connection between the Fokker-Planck equation and the Schr\\"odinger equation. A unified consideration of these two types of solvability is given from the viewpoint of prepotential together with Bethe ansatz equations. Quasi-exactly solvable Fokker-Planck equations related to the $sl(2)$-based systems in Turbiner's classification are listed. We also present one $sl(2)$-based example which i...
Hutsalyuk, A; Pakuliak, S Z; Ragoucy, E; Slavnov, N A
2016-01-01
We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing $\\mathfrak{gl}(2|1)$ symmetry. Using explicit formulas of the monodromy matrix entries multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with $\\mathfrak{gl}(1|1)$ symmetry.
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Gomes, Adriano Doff Sotta [Universidade Tecnologica Federal do Parana (UTFPR), Pato Branco, PR (Brazil)
2011-07-01
Full text: Scalar composite boson masses have been computed in QCD and Technicolor theories with the help of the homogeneous Bethe-Salpeter equation (BSE), resulting in a scalar mass that is twice the dynamically generated fermion or technifermion mass (m{sub dyn}). In the A. Doff, A. A. Natale and P. S. Rodrigues da Silva, Phys. Rev. D 80, 055005 (2009) we study the effect of the normalization condition on the determination of scalar boson masses in dynamically broken gauge theories and verify that the normalization condition does not modify the value of the scalar boson mass when its wave function has the asymptotic behavior exactly as predicted by the OPE. However in walking (or quasi-conformal) gauge theories the asymptotic behavior of fermionic self-energies and the wave function of scalar bound states are dominated by higher order interactions and are characterized by a much harder decrease with the momentum, therefore, in this case, we show that the normalization condition of the BSE do constrain the scalar masses. In this work we apply some results obtained in the cited reference to the model described in A. Doff, Phys. Rev. D 81, 117702 (2010), in particular we compute the Higgs boson masses generated in the model assuming the effects of mixing in the wave function of scalar bound states due to the U(1){sub x} interaction of U' and D' techniquarks. (author)
International Nuclear Information System (INIS)
The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green’s function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for neutral electronic excitations of organic molecules exist. Here, we study the performance of the BSE for the 28 small molecules in Thiel’s widely used time-dependent density functional theory benchmark set [Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. We observe that the BSE produces results that depend critically on the mean-field starting point employed in the perturbative approach. We find that this starting point dependence is mainly introduced through the quasiparticle energies obtained at the intermediate GW step and that with a judicious choice of starting mean-field, singlet excitation energies obtained from BSE are in excellent quantitative agreement with higher-level wavefunction methods. The quality of the triplet excitations is slightly less satisfactory
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...
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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 Ds and D*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.
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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.
Bethe subalgebras in affine Birman–Murakami–Wenzl algebras and flat connections for q-KZ equations
Isaev, A. P.; Kirillov, A. N.; Tarasov, V. O.
2016-05-01
Commutative sets of Jucys–Murphy elements for affine braid groups of {A}(1),{B}(1),{C}(1),{D}(1) types were defined. Construction of R-matrix representations of the affine braid group of type {C}(1) and its distinguished commutative subgroup generated by the {C}(1)-type Jucys–Murphy elements are given. We describe a general method to produce flat connections for the two-boundary quantum Knizhnik–Zamolodchikov equations as necessary conditions for Sklyanin's type transfer matrix associated with the two-boundary multicomponent Zamolodchikov algebra to be invariant under the action of the {C}(1)-type Jucys–Murphy elements. We specify our general construction to the case of the Birman–Murakami–Wenzl algebras (BMW algebras for short). As an application we suggest a baxterization of the Dunkl–Cherednik elements {Y}\\prime {{s}} in the double affine Hecke algebra of type A. Dedicated to Professor Rodney Baxter on the occasion of his 75th Birthday.
Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
Babichenko, Andrei; Sax, Olof Ohlsson
2014-01-01
We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantization of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.
Bethe vectors of quantum integrable models based on Uq( gl-hat N)
International Nuclear Information System (INIS)
We study quantum Uq( gl-hat N) integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by certain morphisms of the positive Borel subalgebra in Uq( gl-hat N) into analogous subalgebra in Uq−1( gl-hat N). (paper)
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We proposed the algorithm for umerical solving a boundary value problem for two-quark bound states described by the Salpeter equation with potential V0r2-αs/r which is coupled integro-differential equations depending on physical parameters m0 and αs. In this algorithm an iteration scheme of the continuous analogy of Newton's method, with corresponding choice of the iteration parameter, is realized. It is shown that using the continuation over parameter (m0, αs) method allows one to extend considerably a region of convergence of the iteration method. The solutions of the Salpeter equation for set of parameters m0 and αs are obtained, which reproduce the results are available (when m0=αs=0). 17 refs.; 1 fig.; 2 tabs
CEval-Ansatz zur Wirkungsevaluation / Stockmann'scher Ansatz
Silvestrini, Stefan; Reade, Nicolà
2008-01-01
Der im Rahmen zahlreicher Evaluationsstudien erprobte Ansatz zur Wirkungsevaluation von Projekten und Programmen wurde von Reinhard Stockmann am Centrum für Evaluation (CEval) entwickelt. Der Ansatz, der hier in seiner Grundstruktur vorgestellt wird, ist so gestaltet, dass er flexibel an verschiedenartige Themenfelder sowie an jeweilige organisatorische oder institutionelle Rahmenbedingungen angepasst werden kann. Aufgrund seiner Flexibilität eignet sich der Stockmann'sche Ansatz zur Wirkungs...
On the central quadric ansatz: integrable models and Painleve reductions
Ferapontov, E V; Zhang, A
2012-01-01
It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called central quadric ansatz). It was demonstrated that generic solutions of this type are described by Painleve equations PIII and PII, respectively. The aim of our paper is threefold: -- Based on the method of hydrodynamic reductions, we classify integrable models possessing the central quadric ansatz. This leads to the five canonical forms (including BF and dKP). -- Applying the central quadric ansatz to each of the five canonical forms, we obtain all Painleve equations PI - PVI, with PVI corresponding to the generic case of our classification. -- We argue that solutions coming from the central quadric ansatz constitute a subclass of two-phase solutions provided by the method of hydrodynamic reductions.
Quantisation of Kadomtsev-Petviashvili equation
Kozlowski, Karol K; Torrielli, Alessandro
2016-01-01
A quantisation of the KP equation on a cylinder is proposed that is equivalent to an infinite system of non-relativistic one-dimensional bosons carrying masses $m=1,2,\\ldots$ The Hamiltonian is Galilei-invariant and includes the split $\\Psi^\\dagger_{m_1}\\Psi^\\dagger_{m_2}\\Psi_{m_1+m_2}$ and merge $\\Psi^\\dagger_{m_1+m_2}\\Psi_{m_1}\\Psi_{m_2}$ terms for all combinations of particles with masses $m_1$, $m_2$ and $m_1+m_2$, with a special choice of coupling constants. The Bethe eigenfunctions for the model are constructed. The consistency of the coordinate Bethe Ansatz, and therefore, the quantum integrability of the model is verified up to the mass $M=8$ sector.
Exact Polynomial Solutions of Schrödinger Equation with Various Hyperbolic Potentials
International Nuclear Information System (INIS)
The Schrödinger equation with hyperbolic potential V(x) = −V0sinh2q(x/d)/cosh6(x/d) (q = 0,1,2,3) is studied by transforming it into the confluent Heun equation. We obtain general symmetric and antisymmetric polynomial solutions of the Schrödinger equation in a unified form via the Functional Bethe ansatz method. Furthermore, we discuss the characteristic of wavefunction of bound state with varying potential strengths. Particularly, the number of wavefunction's nodes decreases with the increase of potential strengths, and the particle tends to the bottom of the potential well correspondingly. (general)
Gottfried, Kurt
2005-01-01
"There are a handful of people who soar, whose accompalishments are so off-scale as to nearly defy belief. Hans Bethe (2 July 1906 - 6 March 2005) was of that caliber. As just one measure of his stature, imagine the task of copying his published opus by hand, for that is how he wrote most of it" (2 pages)
An Improved Harmonic Map Ansatz
Ioannidou, T A; Zakrzewski, W J; Ioannidou, Theodora; Kleihaus, Burkhard; Zakrzewski, Wojtek
2004-01-01
The rational map ansatz of Houghton et al is generalised by allowing the profile function, usually a function of $r$, to depend also on $z$ and $\\bar{z}$. It is shown that, within this ansatz, the energies of the lowest B=2,3,4 field configurations of the SU(2) Skyrme model are closer to the corresponding values of the true solutions of the model than those obtained within the original rational map ansatz. In particular, we present plots of the profile functions which do exhibit their dependence on $|z|^2$.
Zhang, L; Weng, M -H
2016-01-01
The matrix element of the weak transition {\\Lambda}_b\\rightarrow{\\Lambda}_c can be expressed in terms of six form factors. {\\Lambda}_Q(Q = b;c) can be regarded as composed of a heavy quark Q(Q = b;c) and a diquark which is made up of the remaining two light quarks. In this picture, we express these six form factors in terms of Bethe-Salpeter wave functions to second order in the 1/m_Q expansion. With the kernel containing both the scalar confinement and the one-gluon-exchange terms we calculate the form factors and the decay widths of the semileptonic decay {\\Lambda}_b\\rightarrow{\\Lambda}_clv as well as nonleptonic decays {\\Lambda}_b\\rightarrow{\\Lambda}_cP(V) numerically. We also add QCD corrections since they are comparable with 1/m_Q corrections.
An improved harmonic map ansatz
Energy Technology Data Exchange (ETDEWEB)
Ioannidou, Theodora [Maths Division, School of Technology, University of Thessaloniki, Thessaloniki 54124 (Greece)]. E-mail: ti3@auth.gr; Kleihaus, Burkhard [Institut fuer Physik, Universitaet Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany)]. E-mail: kleihaus@theorie.physik.uni-oldenburg.de; Zakrzewski, Wojtek [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom)]. E-mail: w.j.zakrzewski@durham.ac.uk
2004-09-16
The rational map ansatz of Houghton et al. [Nucl. Phys. B 510 (1998) 507] is generalised by allowing the profile function, usually a function of r, to depend also on z and z-bar . It is shown that, within this ansatz, the energies of the lowest B=2,3,4 field configurations of the SU(2) Skyrme model are closer to the corresponding values of the true solutions of the model than those obtained within the original rational map ansatz. In particular, we present plots of the profile functions which do exhibit their dependence on z and z-bar .The obvious generalisation of the ansatz to higher SU(N) models involving the introduction of more projectors is briefly mentioned.
An improved harmonic map ansatz
International Nuclear Information System (INIS)
The rational map ansatz of Houghton et al. [Nucl. Phys. B 510 (1998) 507] is generalised by allowing the profile function, usually a function of r, to depend also on z and z-bar . It is shown that, within this ansatz, the energies of the lowest B=2,3,4 field configurations of the SU(2) Skyrme model are closer to the corresponding values of the true solutions of the model than those obtained within the original rational map ansatz. In particular, we present plots of the profile functions which do exhibit their dependence on z and z-bar .The obvious generalisation of the ansatz to higher SU(N) models involving the introduction of more projectors is briefly mentioned
Hedgehog ansatz and its generalization for self-gravitating Skyrmions
Canfora, Fabrizio
2013-01-01
The hedgehog ansatz for spherically symmetric spacetimes in self-gravitating nonlinear sigma models and Skyrme models is revisited and its generalization for non-spherically symmetric spacetimes is proposed. The key idea behind our construction is that, even if the matter fields depend on the Killing coordinates in a non-trivial way, still the corresponding energy-momentum tensor can be compatible with spacetime symmetries. Our generalized hedgehog ansatz reduces the Skyrme equations to coupled differential equations for two scalar fields together with several constraint equations between them. Some particular field configurations satisfying those constraints are presented in several physically important spacetimes including stationary and axisymmetric spacetimes. Incidentally, a new exact solution is obtained under the standard hedgehog ansatz, which represents a global monopole inside a black hole with the Skyrme effect.
Hedgehog ansatz and its generalization for self-gravitating Skyrmions
Canfora, Fabrizio; Maeda, Hideki
2013-04-01
The hedgehog ansatz for spherically symmetric spacetimes in self-gravitating nonlinear sigma models and Skyrme models is revisited and its generalization for nonspherically symmetric spacetimes is proposed. The key idea behind our construction is that, even if the matter fields depend on the Killing coordinates in a nontrivial way, the corresponding energy-momentum tensor can still be compatible with spacetime symmetries. Our generalized hedgehog ansatz reduces the Skyrme equations to coupled differential equations for two scalar fields together with several constraint equations between them. Some particular field configurations satisfying those constraints are presented in several physically important spacetimes, including stationary and axisymmetric spacetimes. Incidentally, new exact solutions are obtained under the standard hedgehog ansatz, one of which represents a global monopole inside a black hole with the Skyrme effect.
Obituary: Hans Albrecht Bethe, 1906-2005
Wijers, Ralph
2007-12-01
now call the "Bethe Ansatz." Soon after his acceptance of an assistant professorship at Tübingen in 1932, he had to flee Hitler's Germany because his mother was Jewish. Bethe went to the Bragg Institute in Manchester, England, where he worked again with Peierls. In 1934, Cornell University unexpectedly offered him a position as part of R. Clifton Gibbs's expansion of the physics department; he accepted and stayed there for the rest of his life. Right from the start, Bethe enjoyed America and its atmosphere very much. His first activity there was to write the "Bethe Bible": three articles in Reviews of Modern Physics to educate his colleagues in theoretical nuclear physics. Then he did the work that astrophysicists will still appreciate him most for, and which brought him the 1967 Nobel Prize. Having worked with George Gamow's student Charles Critchfield (at Gamow's suggestion) on the proton-proton chain for nuclear fusion in the Sun (published in 1938), Bethe was initially a bit discouraged with Arthur Eddington's estimates of the Solar core temperature; their calculations did not agree well with the observed solar luminosity. However, at the Washington conference in 1937, he heard of Strömgren's new estimates of the solar interior, which brought his and Critchfield's theory into much better agreement with the data. Fairly soon after the meeting, Bethe also worked out the process whereby more massive stars must accomplish hydrogen fusion, in what we now call the CNO cycle. Curiously, Bethe held up its publication briefly in order to compete for a prize for the best unpublished paper on energy production in stars. He did win, and used the money in part to bring his mother to the United States; eventually, the paper appeared in Physics Review in 1939, and founded a whole branch of astrophysics. The war brought Bethe to the Manhattan project, of which he became one of the intellectual leaders. He ploughed through problems theoretical and practical by attacking them
Coordinate Bethe ANSÄTZE for Non-Diagonal Boundaries
Ragoucy, Eric
2013-11-01
Bethe ansatz goes back to 1931, when H. Bethe invented it to solve some one-dimensional models, such as XXX spin chain, proposed by W. Heisenberg in 1928. Although it is a very powerful method to compute eigenvalues and eigenvectors of the corresponding Hamiltonian, it can be applied only for very specific boundary conditions: periodic boundary ones, and so-called open-diagonal boundary ones. After reviewing this method, we will present a generalization of it that applies also to open-triangular boundary conditions. This short note presents only the basic ideas of the technique, and does not attend to give a general overview of the subject. Interested readers should refer to the original papers and references therein.
Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion
International Nuclear Information System (INIS)
The boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in http://dx.doi.org/10.1007/JHEP08(2012)134http://dx.doi.org/10.1007/JHEP10(2013)135 to describe the cusp anomalous dimension contain imaginary chemical potentials and singular boundary fugacities, which make its systematic expansion problematic. We propose an alternative formulation based on real chemical potentials and additional source terms. We expand our equations to double wrapping order and find complete agreement with the direct two-loop gauge theory computation of the cusp anomalous dimension
Bernstein, Jeremy
2012-10-01
In 1937, two years after he moved to the US to escape Nazi persecution, the physicist Hans Bethe sent a letter to his mother in Germany. In it, he wrote, "I think I am about the leading theoretician in America. [Eugene] Wigner is certainly better and [Robert] Oppenheimer and [Edward] Teller probably just as good. But I do more and talk more and that counts too."
The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing
International Nuclear Information System (INIS)
A connection is made between the exact eigen states of the BCS Hamiltonian and the predictions made by the Tamm-Dancoff Approximation. This connection is made by means of a parametrised algebra, which gives the exact quasi-spin algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the other. Using this algebra to construct the Bethe Ansatz solution of the BCS Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An example is discussed in depth.
Combined Exp-Function Ansatz Method and Applications
Directory of Open Access Journals (Sweden)
Gui Mu
2013-01-01
Full Text Available Our aim is to present a combined Exp-function ansatz method. This method replaces the traditional assumptions of multisolitons by a combination of the hyperbolic functions and triangle functions in Hirota bilinear forms of nonlinear evolution equation. Using this method, we can obtain many new type analytical solutions of various nonlinear evolution equations including multisoliton solutions as well as breath-like solitons solutions. These solutions will exhibit interesting dynamic diversity.
Ising spin glass on Bethe-like lattices
International Nuclear Information System (INIS)
Ising spin glass on Bethe-like lattices is studied focusing on the replica symmetry breaking near the spin glass transition temperature. To see the frustration effects of small loops, spin glass order parameter functions and the de Almeida-Thouless (AT) lines in small magnetic fields are obtained for the Bethe-like cactus lattices. As approximations for realistic short range models, they are compared with the results for the Bethe lattice without small loops to see the effects of the loops. Triangular, tetrahedral and square cactus lattices are studied. The slope of the spin glass order parameter function for a cactus lattice is smaller than the corresponding one for the Bethe lattice. The replica symmetry breaking region in fields for the cactus lattice is larger than that for the corresponding Bethe lattice except for the smallest number of connectivity of the loops in the triangular and tetrahedral cactus lattices. To obtain the results, an equation among quantities that are related to the spin glass order parameter is used. This equation is shown to be related to an equation derived within a cluster approximation without using replicas. (author)
Generalized Hill-Wheeler ansatz
Energy Technology Data Exchange (ETDEWEB)
Nunez, J.; Esebbag, C.; Martin, M.T.; Rebollo, L.; Plastino, A.
1984-09-01
The Hill-Wheeler ansatz for the total wave function, within the Generator Coordinate Method framework, is generalized by recourse to the theory of distributions. The ensuing approach allows one to obtain a basis that spans the collective subspace, without having to deal explicitly with the eigenvectors and eigenvalues of the overlap kernel. Applications to an exactly soluble model and anharmonic vibrations illustrate the present treatment. 37 refs.
Regge behaviour within the Bethe-Salpeter approach
Kubrak, Stanislav; Williams, Richard
2014-01-01
We present a calculation of the spectrum of light and heavy quark bound states in the rainbow-ladder truncation of Dyson-Schwinger/Bethe-Salpeter equations. By extending the formalism include the case of total angular momentum J=3, we are able to explore Regge trajectories and make prediction of tensor bound states for light and heavy quarkonia.
Parameter-free ansatz for inferring ground state wave functions of even potentials
Flego, S. P.; A. Plastino; Plastino, A.R.
2011-01-01
Schr\\"odinger's equation (SE) and the information-optimizing principle based on Fisher's information measure (FIM) are intimately linked, which entails the existence of a Legendre transform structure underlying the SE. In this comunication we show that the existence of such an structure allows, via the virial theorem, for the formulation of a parameter-free ground state's SE-ansatz for a rather large family of potentials. The parameter-free nature of the ansatz derives from the structural inf...
Pauli principle for one-dimensional bosons and the algebraic Bethe ansatz
International Nuclear Information System (INIS)
To construct the physical vacuum in completely integrable models of one-dimensional boson fields, it is essential that the momenta of all particles be distinct. A proof is present that they actually are distinct
International Nuclear Information System (INIS)
We consider quantum quenches in the so-called q-boson lattice model. We argue that the Generalized Eigenstate Thermalization Hypothesis holds in this model, therefore the Generalized Gibbs Ensemble (GGE) gives a valid description of the stationary states in the long time limit. For a special class of initial states (which are the pure Fock states in the local basis) we are able to provide the GGE predictions for the resulting root densities. We also give predictions for the long-time limit of certain local operators. In the q → ∞ limit the calculations simplify considerably, the wave functions are given by Schur polynomials and the overlaps with the initial states can be written as simple determinants. In two cases we prove rigorously that the GGE prediction for the root density is correct. Moreover, we calculate the exact time dependence of a physical observable (the one-site Emptiness Formation Probability) for the quench starting from the state with exactly one particle per site. In the long-time limit the GGE prediction is recovered. (paper)
Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States
Directory of Open Access Journals (Sweden)
Hermann Boos
2011-01-01
Full Text Available We generalize the results of [Comm. Math. Phys. 299 (2010, 825-866] (hidden Grassmann structure IV to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction. We establish an equivalence between a scaling limit of the partition function of the six-vertex model on a cylinder with quasi-local operators inserted and special boundary conditions, corresponding to particle-hole excitations, on the one hand, and certain three-point correlation functions of conformal field theory (CFT on the other hand. As in hidden Grassmann structure IV, the fermionic basis developed in previous papers and its conformal limit are used for a description of the quasi-local operators. In paper IV we claimed that in the conformal limit the fermionic creation operators generate a basis equivalent to the basis of the descendant states in the conformal field theory modulo integrals of motion suggested by A. Zamolodchikov (1987. Here we argue that, in order to completely determine the transformation between the above fermionic basis and the basis of descendants in the CFT, we need to involve excitations. On the side of the lattice model we use the excited-state TBA approach. We consider in detail the case of the descendant at level 8.
Newman-Janis Ansatz in conformastatic spacetimes
Gutiérrez-Piñeres, Antonio C
2016-01-01
The Newman-Janis Ansatz was used first to obtain the stationary Kerr metric from the static Schwarzschild metric. Many works have been devoted to investigate the physical significance of this Ansatz, but no definite answer has been given so far. We show that this Ansatz can be applied in general to conformastatic vacuum metrics, and leads to stationary generalizations which, however, do not preserve the conformal symmetry. We investigate also the particular case when the seed solution is given by the Schwarzschild spacetime and show that the resulting rotating configuration does not correspond to a vacuum solution, even in the limiting case of slow rotation. In fact, it describes in general a relativistic fluid with anisotropic pressure and heat flux. This implies that the Newman-Janis Ansatz strongly depends on the choice of representation for the seed solution. We interpret this result as as a further indication of its applicability limitations.
Exact solution of a new class of Hubbard-type models with open boundary conditions
International Nuclear Information System (INIS)
A new class of Hubbard-type models with open boundary conditions in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum, integrable boundary conditions and the corresponding Bethe ansatz equations are derived. (authors)
Hans Bethe and the Global Energy Problems
Ioffe, B. L.
2005-01-01
Bethe's view-point on the global energy problems is presented. Bethe claimed that the nuclear power is a necessity in future. Nuclear energetic must be based on breeder reactors. Bethe considered the non-proliferation of nuclear weapons as the main problem of long-range future of nuclear energetics. The solution of this problem he saw in heavy water moderated thermal breeders, using uranium-233, uranium-238 and thorium as a fuel.
Tetraquark bound states in a Bethe-Salpeter approach
Heupel, Walter; Eichmann, Gernot; Fischer, Christian S.
2012-01-01
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the o...
Convexifying the Bethe Free Energy
Meshi, Ofer; Globerson, Amir; Friedman, Nir
2012-01-01
The introduction of loopy belief propagation (LBP) revitalized the application of graphical models in many domains. Many recent works present improvements on the basic LBP algorithm in an attempt to overcome convergence and local optima problems. Notable among these are convexified free energy approximations that lead to inference procedures with provable convergence and quality properties. However, empirically LBP still outperforms most of its convex variants in a variety of settings, as we also demonstrate here. Motivated by this fact we seek convexified free energies that directly approximate the Bethe free energy. We show that the proposed approximations compare favorably with state-of-the art convex free energy approximations.
Bethe-Salpeter bound-state structure in Minkowski space
Gutierrez, C.; Gigante, V.; Frederico, T.; Salmè, G.; Viviani, M.; Tomio, Lauro
2016-08-01
The quantitative investigation of the scalar Bethe-Salpeter equation in Minkowski space, within the ladder-approximation framework, is extended to include the excited states. This study has been carried out for an interacting system composed by two massive bosons exchanging a massive scalar, by adopting (i) the Nakanishi integral representation of the Bethe-Salpeter amplitude, and (ii) the formally exact projection onto the null plane. Our analysis, on one hand, confirms the reliability of the method already applied to the ground state and, on the other one, extends the investigation from the valence distribution in momentum space to the corresponding quantity in the impact-parameter space, pointing out some relevant features, like (i) the equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and (ii) the leading exponential fall-off of the valence wave function in the impact-parameter space.
Bethe-Salpeter bound-state structure in Minkowski space
Gutierrez, C; Frederico, T; Salmè, G; Viviani, M; Tomio, Lauro
2016-01-01
The quantitative investigation of the scalar Bethe-Salpeter equation in Minkowski space, within the ladder-approximation framework, is extended to include the excited states. This study has been carried out for an interacting system composed by two massive bosons exchanging a massive scalar, by adopting (i) the Nakanishi integral representation of the Bethe-Salpeter amplitude, and (ii) the formally exact projection onto the null plane. Our analysis, on one hand, confirms the reliability of the method already applied to the ground state and, on the other one, extends the investigation from the valence distribution in momentum space to the corresponding quantity in the impact-parameter space, pointing out some relevant features, like (i) the equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and (ii) the leading exponential fall-off of the valence wave function in the impact-parameter space.
ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation
Ito, Katsushi
2016-01-01
We study the massive ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation. Based on the $\\psi$-system for the solutions of the associated linear problem, we obtain the Bethe ansatz equations. We also discuss the T-Q relations, the T-system and the Y-system, which are shown to be related to those of the $A_3/{\\bf Z}_2$ integrable system. We consider the case that the solution of the linear problem has a monodromy around the origin, which imposes nontrivial boundary conditions for the T-/Y-system. The high-temperature limit of the T- and Y-system and their monodromy dependence are studied numerically.
Parameter-free ansatz for inferring ground state wave functions of even convex potentials
International Nuclear Information System (INIS)
Schrödinger's equation (SE) and the information-optimizing principle based on Fisher's information measure are intimately linked (Frieden et al 1999 Phys. Rev. E 60 48), which entails the existence of a Legendre transform structure underlying the SE (Flego et al 2011 J. Math. Phys. 52 082103). In this paper, we show that the existence of such a structure allows, via the virial theorem, for the formulation of a parameter-free ground state's SE ansatz for a rather large family of potentials. The parameter-free nature of the ansatz derives from the structural information it incorporates through its Legendre properties. (paper)
Parameter-free ansatz for inferring ground state wave functions of even potentials
Flego, S P; Plastino, A R
2011-01-01
Schr\\"odinger's equation (SE) and the information-optimizing principle based on Fisher's information measure (FIM) are intimately linked, which entails the existence of a Legendre transform structure underlying the SE. In this comunication we show that the existence of such an structure allows, via the virial theorem, for the formulation of a parameter-free ground state's SE-ansatz for a rather large family of potentials. The parameter-free nature of the ansatz derives from the structural information it incorporates through its Legendre properties.
International Nuclear Information System (INIS)
The first part of this book is a literary portrait of the great natural scientist. The book was the result of a number of personal meetings, telephone interviews and letters exchanged, which began in 1977 and lasted two years. Bethes work comprises so many aspects of modern physics and astrophysics that only a fat encyclopedia could do him justice. The author hopes to convey at least an idea of the tremendous scope of this work. But the main theme in the article in 'The New Yorker' and in the resulting book is a discussion about energy. The importance of the energy problem is such that it completely penetrates science and politics. Thus, the third chapter is concerned with energy-political options, the catastrophe of and radioactivity after Chernobyl, and the development of concepts of reactor safety. (orig./HSCH)
Energy Technology Data Exchange (ETDEWEB)
Basso, Benjamin, E-mail: bbasso@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Rej, Adam, E-mail: arej@ias.edu [School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 (United States)
2014-02-15
Studying the scattering of excitations around a dynamical background has a long history in the context of integrable models. The Gubser–Klebanov–Polyakov string solution provides such a background for the string/gauge correspondence. Taking the conjectured all-loop asymptotic equations for the AdS{sub 4}/CFT{sub 3} correspondence as the starting point, we derive the S-matrix and a set of spectral equations for the lowest-lying excitations. We find that these equations resemble closely the analogous equations for AdS{sub 5}/CFT{sub 4}, which are also discussed in this paper. At large values of the coupling constant we show that they reproduce the Bethe equations proposed to describe the spectrum of the low-energy limit of the AdS{sub 4}×CP{sup 3} sigma model.
On the central quadric ansatz: integrable models and Painlevé reductions
Ferapontov, E. V.; Huard, B.; Zhang, A.
2012-05-01
It was observed by Tod (1995 Class. Quantum Grav.12 1535-47) and later by Dunajski and Tod (2002 Phys. Lett. A 303 253-64) that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called central quadric ansatz). It was demonstrated that generic solutions of this type are described by Painlevé equations PIII and PII, respectively. The aim of our paper is threefold: (1) Based on the method of hydrodynamic reductions, we classify integrable models possessing the central quadric ansatz. This leads to the five canonical forms (including BF and dKP). (2) Applying the central quadric ansatz to each of the five canonical forms, we obtain all Painlevé equations PI-PVI, with PVI corresponding to the generic case of our classification. (3) We argue that solutions coming from the central quadric ansatz constitute a subclass of two-phase solutions provided by the method of hydrodynamic reductions.
Zeilberger, Doron
2011-01-01
While it is trivial to multiply two C-finite sequences (just like integers), it is not quite so trivial to "factorize" them, or to decide whether they are "prime". The former is plain linear algebra, while the latter is heavy-duty non-linear algebra, getting hairy systems of algebraic equations that can be solved, in principle, using Gr\\"obner bases and the Buchberger algorithm, but, alas, sooner or later it becomes too hard even for the fastest and largest computers. The main technical novely of this article is a fast "algorithm" (it cheats and uses floating-point arithmetic, please don't tell anyone!) for deciding whether a given C-finite sequence can be written as a product of C-finite sequences of lower order. This article accompanies the Maple package Cfinite available from http://www.math.rutgers.edu/~zeilberg/tokhniot/Cfinite .
A generalized Hill-Wheeler ansatz
Nuñez, J.; Esebbag, C.; Martin, M. T.; Rebollo, L.; Plastino, A.
1984-06-01
The Hill-Wheeler ansatz for the total wave function, within the Generator Coordinate Method framework, is generalized by recourse to the theory of distributions. The ensuing approach allows one to obtain a basis that spans the collective subspace, without having to deal explicitly with the eigenvectors and eigenvalues of the overlap kernel. Applications to an exactly soluble model and anharmonic vibrations illustrate the present treatment.
A generalized Hill-Wheeler ansatz
International Nuclear Information System (INIS)
The Hill-Wheeler ansatz for the total wave function, within the Generator Coordinate Method framework, is generalized by recourse to the theory of distributions. The ensuing approach allows one to obtain a basis that spans the collective subspace, without having to deal explicitly with the eigenvectors and eigenvalues of the overlap kernel. Applications to an exactly soluble model and anharmonic vibrations illustrate the present treatment. (orig.)
Spectra of heavy mesons in the Bethe-Salpeter approach
Energy Technology Data Exchange (ETDEWEB)
Fischer, Christian S.; Kubrak, Stanislav; Williams, Richard [Justus-Liebig-Universitaet Giessen, Institut fuer Theoretische Physik, Giessen (Germany)
2015-01-01
We present a calculation of the spectrum of charmonia, bottomonia and B{sub c}-meson states with ''ordinary'' and exotic quantum numbers. We discuss the merits and limitations of a rainbow-ladder truncation of Dyson-Schwinger and Bethe-Salpeter equations and explore the effects of different shapes of the effective running coupling on ground and excited states in channels with quantum numbers J ≤ 3. We furthermore discuss the status of the X(3872) as a potential (excited) quark-antiquark state and give predictions for the masses of charmonia and bottomonia in the tensor channels with J= 2, 3. (orig.)
Direct Bethe-Salpeter solutions in Minkowski space
Carbonell, J
2016-01-01
We review a method to directly solve the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the many singularities which appear in the kernel and propagators. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange was computed for the first time. Using our Minkowski space solutions for the initial (bound) and final (scattering) states, we calculate elastic and transition (bound to scattering state) electromagnetic form factors. The conservation of the transition electromagnetic current J.q=0, verified numerically, confirms the validity of our solutions.
Tetra quark bound states in a Bethe-Salpeter approach
Energy Technology Data Exchange (ETDEWEB)
Heupel, Walter; Eichmann, Gernot [Institut fuer Theoretische Physik, Justus-Liebig-Universitaet Giessen, D-35392 Giessen (Germany); Fischer, Christian S., E-mail: christian.fischer@theo.physik.uni-giessen.de [Institut fuer Theoretische Physik, Justus-Liebig-Universitaet Giessen, D-35392 Giessen (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstr. 1, D-64291 Darmstadt (Germany)
2012-12-05
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion-pion constituents. Both results are in agreement with a meson molecule picture for the f{sub 0}(600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.
Tetraquark bound states in a Bethe-Salpeter approach
Heupel, Walter; Fischer, Christian S
2012-01-01
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion-pion constituents. Both results are in agreement with a meson molecule picture for the f_0(600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.
Tetraquark bound states in a Bethe-Salpeter approach
Heupel, Walter; Eichmann, Gernot; Fischer, Christian S.
2012-12-01
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion-pion constituents. Both results are in agreement with a meson molecule picture for the f0 (600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.
Tetra quark bound states in a Bethe-Salpeter approach
International Nuclear Information System (INIS)
We determine the mass of tetraquark bound states from a coupled system of covariant Bethe-Salpeter equations. Similar in spirit to the quark-diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark-gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion-pion constituents. Both results are in agreement with a meson molecule picture for the f0(600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.
Dhar, Abhishek; Sriram Shastry, B.
2000-09-01
We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1D for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. They are identified as generalized quantum Bloch wall states, and a simple physical picture is provided for the same.
Dhar, Abhishek; Shastry, B. Sriram
2000-01-01
We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1-d for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. These are identified as generalized quantum Bloch wall states, and a simple physical picture provided for the same.
Entanglement entropy in quantum many-particle systems and their simulation via ansatz states
Energy Technology Data Exchange (ETDEWEB)
Barthel, Thomas
2009-12-10
A main topic of this thesis is the development of efficient numerical methods for the simulation of strongly correlated quantum lattice models. For one-dimensional systems, the density-matrix renormalization-group (DMRG) is such a very successful method. The physical states of interest are approximated within a certain class of ansatz states. These ansatz states are designed in a way that the number of degrees of freedom are prevented from growing exponentially. They are the so-called matrix product states. The first part of the thesis, therefore, provides analytical and numerical analysis of the scaling of quantum nonlocality with the system size or time in different, physically relevant scenarios. For example, the scaling of Renyi entropies and their dependence on boundary conditions is derived within the 1+1-dimensional conformal field theory. Conjectures and analytical indications concerning the properties of entanglement entropy in critical fermionic and bosonic systems are confirmed numerically with high precision. For integrable models in the thermodynamic limit, general preconditions are derived under which subsystems converge to steady states. These steady states are non-thermal and retain information about the initial state. It is shown that the entanglement entropy in such steady states is extensive. For short times, the entanglement entropy grows typically linearly with time, causing an exponential increase in computation costs for the DMRG method. The second part of the thesis focuses on the development and improvement of the abovementioned numerical techniques. The time-dependent DMRG is complemented with an extrapolation technique for the evaluated observables. In this way, the problem of the entropy increase can be circumvented, allowing for a precise determination of spectral functions. The method is demonstrated using the example of the Heisenberg antiferromagnet and results are compared to Bethe-Ansatz data for T=0 and quantum Monte Carlo data
Entanglement entropy in quantum many-particle systems and their simulation via ansatz states
International Nuclear Information System (INIS)
A main topic of this thesis is the development of efficient numerical methods for the simulation of strongly correlated quantum lattice models. For one-dimensional systems, the density-matrix renormalization-group (DMRG) is such a very successful method. The physical states of interest are approximated within a certain class of ansatz states. These ansatz states are designed in a way that the number of degrees of freedom are prevented from growing exponentially. They are the so-called matrix product states. The first part of the thesis, therefore, provides analytical and numerical analysis of the scaling of quantum nonlocality with the system size or time in different, physically relevant scenarios. For example, the scaling of Renyi entropies and their dependence on boundary conditions is derived within the 1+1-dimensional conformal field theory. Conjectures and analytical indications concerning the properties of entanglement entropy in critical fermionic and bosonic systems are confirmed numerically with high precision. For integrable models in the thermodynamic limit, general preconditions are derived under which subsystems converge to steady states. These steady states are non-thermal and retain information about the initial state. It is shown that the entanglement entropy in such steady states is extensive. For short times, the entanglement entropy grows typically linearly with time, causing an exponential increase in computation costs for the DMRG method. The second part of the thesis focuses on the development and improvement of the abovementioned numerical techniques. The time-dependent DMRG is complemented with an extrapolation technique for the evaluated observables. In this way, the problem of the entropy increase can be circumvented, allowing for a precise determination of spectral functions. The method is demonstrated using the example of the Heisenberg antiferromagnet and results are compared to Bethe-Ansatz data for T=0 and quantum Monte Carlo data
On the new Continuous Matrix Product Ansatz
Chung, S. S.; Bauman, S.; Sun, Kuei; Bolech, C. J.
2016-03-01
The fertile new field of quantum information theory is inspiring new ways to study correlated quantum systems by providing fresh insights into the structure of their Hilbert spaces. One of the latest developments in this direction was the extension of the ubiquitous matrix-product-state constructions, epitomized by the density-matrix renormalization-group algorithm, to continuous space-time; so as to be able to describe low-dimensional field theories within a variational approach. Following the earlier success achieved for bosonic theories, we present the first implementation of a continuous matrix product state (cMPS) for spinfull non-relativistic fermions in 1D. We propose a construction of variational matrices with an efficient parametrization that respects the translational symmetry of the problem (without being overly constraining) and readily meets the regularity conditions that arise from removing the ultraviolet divergences in the kinetic energy. We tested the validity of our approach on an interacting spin-1/2 system with spin imbalance. We observe that the ansatz correctly predicts the ground-state magnetic properties for the attractive spin-1/2 Fermi gas, including a phase-oscillating pair correlation function in the partially polarized regime (the 1D correlate of the FFLO state). We shall also discuss how to generalize the cMPS ansatz to other situations.
Relativistic three-nucleon calculations within the Bethe-Salpeter approach
Bondarenko, S G; Yurev, S A
2015-01-01
The relativistic properties of the three-nucleon system are investigated using the Faddeev equations within the Bethe-Salpeter approach. The nucleon-nucleon interaction is chosen in a separable form. The Gauss quadrature method is used to calculate the integrals. The system of the integral equations are solving by iterations method. The binding energy and the partial-wave amplitudes (1S 0 and 3S 1) of the triton are found.
Relativistic Three-Nucleon Calculations within the Bethe-Salpeter Approach
Directory of Open Access Journals (Sweden)
Bondarenko S.G.
2016-01-01
Full Text Available The relativistic properties of the three-nucleon system are investigated using the Faddeev equations within the Bethe-Salpeter approach. The nucleon-nucleon interaction is chosen in a separable form. The Gauss quadrature method is used to calculate the integrals. The system of the integral equations is solved by an iterative method. The binding energy and the partial-wave amplitudes (1S0 and 3S1 of the triton are found.
Obituary: Hans Albrecht Bethe, 1906-2005
R. Wijers
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 superfluou
Quantum theory of nonlocal nonlinear Schrodinger equation
Vyas, Vivek M
2015-01-01
Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved by constructing another inner product over the vector space of the theory. The resultant theory is found to be identical to that of nonrelativistic bosons with delta function interaction potential, devoid of any nonlocality. The exact eigenstates are found using the Bethe ansatz technique.
G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra
International Nuclear Information System (INIS)
We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from the viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory
G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra
Energy Technology Data Exchange (ETDEWEB)
Okuda, Satoshi [Department of Physics, Rikkyo University,Toshima, Tokyo 171-8501 (Japan); Yoshida, Yutaka [High Energy Accelerator Research Organization (KEK),Tsukuba, Ibaraki 305-0801 (Japan)
2014-03-03
We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from the viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory.
G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra
Okuda, Satoshi
2013-01-01
We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from a viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory.
The Potts glass on the Bethe lattice
International Nuclear Information System (INIS)
It is considered the nearest-neighbor p-state random Potts model on a Cayley tree of infinite coordination. The problem is formulated as a discrete mapping whose fixed points correspond to solutions deep inside the tree. The introduction of an ansatz which allows for the breaking of the Potts symmetry leads to an instability of the spin glass fixed point for p > 4. (author)
Participatory management at Boston's Beth Israel Hospital.
Rabkin, M T; Avakian, L
1992-05-01
In the mid-1980s, the senior management of Boston's Beth Israel Hospital became concerned that continuous cost-cutting efforts could lower the quality of the hospital's services and the morale of its staff. This led them to investigate organizational approaches to "participatory management" to determine whether any of these might be of value to the hospital. They decided that an approach developed in the 1930s called the "Scanlon Plan" would be compatible with the workplace culture of Beth Israel, could help the hospital meet the ongoing problems of change, and could help the staff at all levels develop a sense that they owned the problems of quality, productivity, and efficiency, which would motivate them to address these problems constructively in the face of necessary budget constraints. This plan has two mechanisms to foster employees' positive participation: (1) a process to ensure that all members of the organization have the opportunity to improve productivity, primarily through an open suggestion system and a responsive committee structure, and (2) a means of providing equitable rewards for all members of the organization as productivity and quality improve. This essay describes in some detail the plan and why it was selected, explains how it was adapted, prepared for, and finally implemented in 1989, and reports its success, lessons learned, and future plans as of early 1992. The authors believe Beth Israel's experience with the Scanlon Plan is noteworthy as an example of a leading teaching hospital's taking a quality improvement program seriously and making it work. PMID:1575858
The Bethe-Brueckner-Goldstone expansion in nuclear and neutron matter
International Nuclear Information System (INIS)
The microscopic theory of nuclear matter is developed within the Bethe-Brueckner-Goldstone expansion. Starting from different realistic nucleon-nucleon interactions, the equation of state of symmetric nuclear matter and pure neutron matter is calculated up to three-hole level of approximation. The expansion shows to be convergent up to densities relevant for neutron stars studies. Within the same scheme, the nucleon strength function is calculated in the kinematical region pertinent to deep inelastic electron scattering. (author)
Instantaneous Bethe-Salpeter View of Goldstone-Type Pseudoscalar Mesons
Lucha, Wolfgang
2016-01-01
Describing the lightest pseudoscalar mesons as bound states of quark and antiquark within the framework of an instantaneous Bethe-Salpeter formalism constructed such as to retain (in contrast to Salpeter's equation) as much information on the relativistic effects provided by the full quark propagator as conceivable allows for a surprisingly simple implementation of their near masslessness mandatory for their interpretability as pseudo-Goldstone bosons related to the spontaneous breaking of the chiral symmetries of quantum chromodynamics.
Graph optimization problems on a Bethe lattice
de Oliveira, Mário J.
1989-01-01
The p-partitioning and p-coloring problems on a Bethe lattice of coordination number z are analyzed. It is shown that these two NP-complete optimization problems turn out to be equivalent to finding the ground-state energy of p-state Potts models with frustration. Numerical calculation of the cost function of both problems are carried out for several values of z and p. In the case of p=2 the results are identical to those obtained by Mézard and Parisi for the case of the bipartitioning problem. A numerical upper bound to the chromatic number is found for several values of z.
Excited TBA Equations II Massless Flow from Tricritical to Critical Ising Model
Pearce, P A; Ahn, C; Pearce, Paul A.; Chim, Leung; Ahn, Changrim
2003-01-01
We consider the massless tricritical Ising model M(4,5) perturbed by the thermal operator in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massless thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A_4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime IV. The resulting TBA equations describe the massless renormalization group flow from the tricritical to critical Ising model. As in the massive case of Part I, the excitations are completely classified in terms of (m,n) systems but the string content changes by one of three mechanisms along the flow. Using generalized q-Vandemonde identities, we show that this leads to a flow from tricritical to critical Ising characters. The excited TBA equations are solved numericall...
Zamolodchikov's tetrahedron equation and hidden structure of quantum groups
International Nuclear Information System (INIS)
The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not related to the size of the lattice, therefore the same solution of the tetrahedron equation defines different integrable models for different finite periodic cubic lattices. Obviously, any such three-dimensional model can be viewed as a two-dimensional integrable model on a square lattice, where the additional third dimension is treated as an internal degree of freedom. Therefore every solution of the tetrahedron equation provides an infinite sequence of integrable 2d models differing by the size of this 'hidden third dimension'. In this paper, we construct a new solution of the tetrahedron equation, which provides in this way the two-dimensional solvable models related to finite-dimensional highest weight representations for all quantum affine algebra Uq(sl-circumflex(n)), where the rank n coincides with the size of the hidden dimension. These models are related to an anisotropic deformation of the sl(n)-invariant Heisenberg magnets. They were extensively studied for a long time, but the hidden 3d structure was hitherto unknown. Our results lead to a remarkable exact 'rank-size' duality relation for the nested Bethe Ansatz solution for these models. Note also that the above solution of the tetrahedron equation arises in the quantization of the 'resonant three-wave scattering' model, which is a well-known integrable classical system in 2 + 1 dimensions
Continuous representations of scalar products of Bethe vectors
Galleas, W
2016-01-01
We present families of single determinantal representations of on-shell scalar products of Bethe vectors. Our families of representations are parameterized by a continuous complex variable which can be fixed at convenience. Here we consider Bethe vectors in two versions of the six-vertex model: the case with boundary twists and the case with open boundaries.
Overlaps of Partial Neel States and Bethe States
Foda, O
2015-01-01
Partial Neel states are generalizations of the ordinary Neel (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.
Obituary: Beth Brown (1969-2008)
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
Hopfions interaction from the viewpoint of the product ansatz
Acus, A; Shnir, Ya
2014-01-01
We discuss the relation between the solutions of the Skyrme model of lower degrees and the corresponding axially symmetric Hopfions which is given by the projection onto the coset space SU(2)/U(1). The interaction energy of the Hopfions is evaluated directly from the product ansatz. Our results show that if the separation between the constituents is not very small, the product ansatz can be considered as a relatively good approximation to the general pattern of the charge one Hopfions interaction both in repulsive and attractive channel.
Hopfions interaction from the viewpoint of the product ansatz
Energy Technology Data Exchange (ETDEWEB)
Acus, A.; Norvaišas, E. [Vilnius University, Institute of Theoretical Physics and Astronomy, Goštauto 12, Vilnius 01108 (Lithuania); Shnir, Ya. [BLTP, JINR, Dubna (Russian Federation); Institute of Physics, Carl von Ossietzky University, Oldenburg (Germany)
2014-06-02
We discuss the relation between the solutions of the Skyrme model of lower degrees and the corresponding axially symmetric Hopfions which is given by the projection onto the coset space SU(2)/U(1). The interaction energy of the Hopfions is evaluated directly from the product ansatz. Our results show that if the separation between the constituents is not very small, the product ansatz can be considered as a relatively good approximation to the general pattern of the charge 1 Hopfions interaction both in repulsive and attractive channels.
Note about lepton masses and mixings in two Ansatze
Jora, Renata; Shahid, M Naeem
2013-01-01
We consider two Ansatze for the neutrino masses and mixings in which the permutation symmetry is implemented in various orders. We discuss the possible see-saw mechanisms and the charged lepton masses for the two cases in the presence of a Higgs triplet and three Higgs doublets.
Agglomerative percolation on the Bethe lattice and the triangular cactus
Chae, Huiseung; Yook, Soon-Hyung; Kim, Yup
2013-08-01
Agglomerative percolation (AP) on the Bethe lattice and the triangular cactus is studied to establish the exact mean-field theory for AP. Using the self-consistent simulation method based on the exact self-consistent equations, the order parameter P∞ and the average cluster size S are measured. From the measured P∞ and S, the critical exponents βk and γk for k = 2 and 3 are evaluated. Here, βk and γk are the critical exponents for P∞ and S when the growth of clusters spontaneously breaks the Zk symmetry of the k-partite graph. The obtained values are β2 = 1.79(3), γ2 = 0.88(1), β3 = 1.35(5) and γ3 = 0.94(2). By comparing these exponents with those for ordinary percolation (β∞ = 1 and γ∞ = 1), we also find β∞ γ3 > γ2. These results quantitatively verify the conjecture that the AP model belongs to a new universality class if the Zk symmetry is broken spontaneously, and the new universality class depends on k.
Agglomerative percolation on the Bethe lattice and the triangular cactus
International Nuclear Information System (INIS)
Agglomerative percolation (AP) on the Bethe lattice and the triangular cactus is studied to establish the exact mean-field theory for AP. Using the self-consistent simulation method based on the exact self-consistent equations, the order parameter P∞ and the average cluster size S are measured. From the measured P∞ and S, the critical exponents βk and γk for k = 2 and 3 are evaluated. Here, βk and γk are the critical exponents for P∞ and S when the growth of clusters spontaneously breaks the Zk symmetry of the k-partite graph. The obtained values are β2 = 1.79(3), γ2 = 0.88(1), β3 = 1.35(5) and γ3 = 0.94(2). By comparing these exponents with those for ordinary percolation (β∞ = 1 and γ∞ = 1), we also find β∞ 3 2 and γ∞ > γ3 > γ2. These results quantitatively verify the conjecture that the AP model belongs to a new universality class if the Zk symmetry is broken spontaneously, and the new universality class depends on k. (paper)
Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields
Zhang, Xin; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
2013-01-01
The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are derived for the second eigenvalue problem associated with spin degrees of freedom. It is found that the second eigenvalue problem can be transformed to that of the transfer matrix of the inhomogeneous XXX spin chain, which allows us to obtain the spectrum of the Hamiltonian and the associated Bethe ansatz equations by the off-diagonal Bethe ansatz method.
Ruban, V P
2015-01-01
The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of Gaussian variational ansatz applied to the corresponding (1+2D) hyperbolic nonlinear Schr\\"odinger equation, a simplified Lagrangian system of differential equations is derived, which determines the evolution of coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description for the process of nonlinear spatio-temporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system is integrated in quadratures, which fact allows us to understand qualitative differences between the linear and nonlinear regimes of the focusing of wave packet. Comparison of the Gaussian model predictions with results of direct numerical simulation of fully nonlinear long-cres...
Modified Bethe-Weizsaecker mass formula for hypernuclei
International Nuclear Information System (INIS)
The Bethe-Weizsaecker mass formula originally designed to reproduce the gross features of nuclear binding energies for medium and heavy mass nuclei, fails for light nuclei especially away from the line of stability. To alleviate this problem a modified Bethe-Weizsaecker mass formula was suggested which explained the gross features of the binding energy versus neutron number curves of all the elements from Li to Bi
International Nuclear Information System (INIS)
Highlights: ► We develop a perturbation expansion for the Bardeen–Cooper–Schrieffer Hamiltonian. ► We show that deviations from mean-field results are underextensive for relevant operators for any order of the perturbation theory. ► We discuss the relation between the BCS wave function and the exact wave function, which can be found by using Richardson approach. -- Abstract: The Bogoliubov approach to superconductivity provides a strong mathematical support to the wave function ansatz proposed by Bardeen, Cooper and Schrieffer (BCS). Indeed, this ansatz — with all pairs condensed into the same state — corresponds to the ground state of the Bogoliubov Hamiltonian. Yet, this Hamiltonian only is part of the BCS Hamiltonian. As a result, the BCS ansatz definitely differs from the BCS Hamiltonian ground state. This can be directly shown either through a perturbative approach starting from the Bogoliubov Hamiltonian, or better by analytically solving the BCS Schrödinger equation along Richardson–Gaudin exact procedure. Still, the BCS ansatz leads not only to the correct extensive part of the ground state energy for an arbitrary number of pairs in the energy layer where the potential acts — as recently obtained by solving Richardson–Gaudin equations analytically — but also to a few other physical quantities such as the electron distribution, as here shown. The present work also considers arbitrary filling of the potential layer and evidences the existence of a super dilute and a super dense regime of pairs, with a gap different from the usual gap. These regimes constitute the lower and upper limits of density-induced BEC–BCS cross-over in Cooper pair systems
Nuclear forces the making of the physicist Hans Bethe
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...
Peculiarities in the Structure of Two-Particle States within the Bethe-Salpeter Approach
Dorkin, S. M.; Semikh, S. S.; Beyer, M.; Kaptari, L. P.
2006-01-01
The two-fermion bound system is an attractive subject of atomic and sub-atomic physics. Despite these systems are rather simple the study of two-particle bound states is challenging and still remains a source of progress in quantum theory. Here we present a new method of solving the Bethe Salpeter equations for the bound states of spinor particles by using the expansion of the vertex functions over the complete set of four-dimensional hyperspherical harmonics. Within this method the BS equati...
Physical properties of the pion in the covariant Bethe-Salpeter formalism
International Nuclear Information System (INIS)
Some problems concerned with normalization of wave functions, which are obtained from the general method for the Lorentz-covariant Bethe-Salpeter equation of the Goldstone boson developed in our previous work, are discussed in connection with the axial Ward-Takahashi identity. Physical properties of the pion, including the π0→γγ amplitude, are calculated in QCD-motivated models with the general method. Both the chiral limit and the effect of explicit chiral-symmetry breaking by the bare quark mass are considered. A quite good agreement with experimental data is obtained with these models
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.
The tensor analyzing power T20 in deuteron break-up reactions within the Bethe-Salpeter formalism
International Nuclear Information System (INIS)
The deuteron tensor analyzing power T20 in the deuteron break-up reaction Dp → pX is calculated within a relativistic approach based on the Bethe-Salpeter equation with a realistic meson-exchange potential. Our results on T20 and the cross section are compared with experimental data and non-relativistic calculations and with the outcome of a relativization procedure of the deuteron wave function. (orig.)
The embedded atom method ansatz: validation and violation
International Nuclear Information System (INIS)
The addition of the embedding energy term to pair interaction contribution has made the embedded atom method (EAM) potentials a simple and vastly superior alternative to popular classical pair potentials. EAM relies on the ansatz that the embedding energy is a function of a linear superposition of spherically averaged atomic electron densities. This ansatz is taken to be self-evident and inviolate. Using density functional theory (DFT) calculations of a model face-centered cubic (fcc) Cu system, we systematically investigate the validity of this foundational ansatz of EAM. We conclude that it (1) agrees well with DFT calculations along a path with changing coordination and symmetry, (2) captures the exponential decrease of the background electron density with respect to distance, (3) demonstrates transferability as seen by agreement of electron densities for other non-fcc structures with first nearest neighbor (NN) coordination ranging from 4 to 12 and (4) fails to explain the behavior of background electron density with respect to second NN distance and arrangements. This failure may be remedied by including a fraction of the second NN atomic electron density in the background electron density, including angular contributions to the density, or including electron density rearrangement. These insights likely make EAM approaches more broadly applicable, more predictive and perhaps unique, and in the process broadly impact atomistic modeling. A new EAM potential is presented that for the first time reproduces electron densities from DFT calculations as well as experimental properties of Cu in the potential fitting. (paper)
The Tamm-Dancoff Approximation as the Contraction Limit of the Richardson-Gaudin Equations
de Baerdemacker, S.
2013-03-01
A connection is made between the exact eigenstates of the level-independent Bardeen-Cooper-Schrieffer (BCS) Hamiltonian and its Tamm-Dancoff Approximation (TDA). This is done by means of a deformation of the quasi-spin algebra, which connects the Bethe Ansatz states with a unique multi-phonon mode of the TDA. The procedure is illustrated with a model describing neutron superluidity in 56Fe.
Exact solution of the XXX Gaudin model with generic open boundaries
Hao, Kun; Cao, Junpeng; Yang, Tao; Yang, Wen-Li
2015-03-01
The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated Gaudin operators have six free parameters which break the U(1) -symmetry. With the help of the off-diagonal Bethe ansatz, we successfully obtained the eigenvalues of these Gaudin operators and the corresponding Bethe ansatz equations.
Exact solution of the XXX Gaudin model with the generic open boundaries
Hao, Kun; Yang, Tao; Yang, Wen-Li
2014-01-01
The XXX Gaudin model with generic integrable boundaries specified by the most general non-diagonal K-matrices is studied by the off-diagonal Bethe ansatz method. The eigenvalues of the associated Gaudin operators and the corresponding Bethe ansatz equations are obtained.
The matrix product Ansatz for integrable U(1)N models in Lunin-Maldacena backgrounds
International Nuclear Information System (INIS)
We obtain through a Matrix Product Ansatz (MPA) the exact solution of the most general N-state spin chain with U(1)N symmetry and nearest neighbour interaction. In the case N = 6 this model contain as a special case the integrable SO(6) spin chain related to the one loop mixing matrix for anomalous dimensions in N =4 SYM, dual to type IIB string theory in the generalised Lunin-Maldacena backgrounds. This MPA is construct by a map between scalar fields and abstract operators that satisfy an appropriate associative algebra. We analyses the Yang-Baxter equation in the N = 3 sector and the consistence of the algebraic relations among the matrices defining the MPA and find a new class of exactly integrable model unknown up to now
Adiabatic electronic flux density: a Born-Oppenheimer Broken Symmetry ansatz
Pohl, Vincent
2016-01-01
The Born-Oppenheimer approximation leads to the counterintuitive result of a vanishing electronic flux density upon vibrational dynamics in the electronic ground state. To circumvent this long known issue, we propose using pairwise anti-symmetrically translated vibronic densities to generate a symmetric electronic density that can be forced to satisfy the continuity equation approximately. The so-called Born-Oppenheimer broken symmetry ansatz yields all components of the flux density simultaneously while requiring only knowledge about the nuclear quantum dynamics on the electronic adiabatic ground state potential energy surface. The underlying minimization procedure is transparent and computationally inexpensive, and the solution can be computed from the standard output of any quantum chemistry program. Taylor series expansion reveals that the implicit electron dynamics originates from non-adiabatic coupling to the explicit Born-Oppenheimer nuclear dynamics. The new approach is applied to the ${\\rm H}_2^+$ mo...
DKP equation under scalar and vector Cornell interactions
International Nuclear Information System (INIS)
Approximate analytical solutions of Duffin-Kemmer-Petiau (DKP) equation are obtained via the ansatz approach for scalar and vector interactions of Cornell type, and spectrum of the system is numerically reported
Selected Works Of Hans A Bethe (With Commentary)
International Nuclear Information System (INIS)
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
Constrained variational results for the new Bethe homework problem
International Nuclear Information System (INIS)
Bethe has proposed two model N-N interactions, one containing a central plus sigma1.sigma2 spin dependence and the other containing in addition a tensor force, to study the convergence of various many-body techniques for calculating the bulk properties of many fermion fluids. Following the success of using constrained variational calculations in describing the behaviour of the original Bethe homework problem involving a purely central interaction, results in neutron matter and nuclear matter for the new spin-dependent potentials, are here presented. (author)
Improved Numerical Generalization of Bethe- Weizsacker Mass Formula
Mavrodiev, Strachimir
2016-01-01
In this paper is presented explicit improved numerical generalization of Bethe-Weizsacker mass formulae which describes the values of measured 2654 nuclear mass in AME2012 nuclear database with accuracy less than 2.2 MeV, starting from the number of protons Z=1 and number of neutrons N=1. In the obtained generazation of the Bethe-Weizsacker formula the influence of magic numbers and boundaries of their influence between them is defined for nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers.
Gordon and Kerr-Schild ansatze in massive and bimetric gravity
Baccetti, Valentina; Visser, Matt
2012-01-01
We develop the "generalized Gordon ansatz" for the ghost-free versions of both massive and bimetric gravity, an ansatz which is general enough to include almost all spacetimes commonly considered to be physically interesting, and restricted enough to greatly simplify calculations. The ansatz allows explicit calculation of the matrix square root gamma = sqrt{g^{-1} f} appearing as a central feature of the ghost-free analysis. In particular, this ansatz automatically allows us to write the effective stress-energy tensor as that corresponding to a perfect fluid. A qualitatively similar "generalized Kerr-Schild ansatz" can also be easily considered, now leading to an effective stress-energy tensor that corresponds to a null fluid. Cosmological implications are considered, as are consequences for black hole physics. Finally we have a few words to say concerning the null energy condition in the framework provided by these ansatze.
Pionierin der Religionspsychologie: Marianne Beth (1890-1984)
J.A. Belzen
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 religio
International Nuclear Information System (INIS)
The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves
Some constant solutions to Zamolodchikov's tetrahedron equations
Hietarinta, Jarmo
1992-01-01
In this letter we present constant solutions to the tetrahedron equations proposed by Zamolodchikov. In general, from a given solution of the Yang-Baxter equation there are two ways to construct solutions to the tetrahedron equation. There are also other kinds of solutions. We present some two-dimensional solutions that were obtained by directly solving the equations using either an upper triangular or Zamolodchikov's ansatz.
Discontinuities of BFKL amplitudes and the BDS ansatz
Fadin, V. S.; Fiore, R.
2015-12-01
We perform an examination of discontinuities of multiple production amplitudes, which are required for further development of the BFKL approach. It turns out that the discontinuities of 2 → 2 + n amplitudes obtained in the BFKL approach contradict to the BDS ansatz for amplitudes with maximal helicity violation in N = 4 supersymmetric Yang-Mills theory with large number of colors starting with n = 2. Explicit expressions for the discontinuities of the 2 → 3 and 2 → 4 amplitudes in the invariant mass of pairs of produced gluons are obtained in the planar N = 4 SYM in the next-to-leading logarithmic approximation. These expressions can be used for checking the conjectured duality between the light-like Wilson loops and the MHV amplitudes.
Generalized Fukugita–Tanimoto–Yanagida neutrino mass Ansatz
International Nuclear Information System (INIS)
We generalize the Fukugita–Tanimoto–Yanagida Ansatz by allowing the masses of three heavy right-handed Majorana neutrinos, Mi (i = 1,2,3), to be partially non-degenerate and search for the parameter space which can be consistent with the current neutrino oscillation data, for three non-degenerate mass cases (A) M3 = M2 ≠ M1, (B) M2 = M1 ≠ M3 and (C) M1 = M3 ≠ M2. We also examine the effect of the deviation from the complete mass degeneracy in each case. Finally, we obtain the numerical constraints on three light neutrino masses, three neutrino mixing angles and three CP-violating phases, together with the predictions for the Jarlskog invariant of CP violation and the effective masses of the tritium beta decay and the neutrinoless double-beta decay. (author)
Maggio, Emanuele; Kresse, Georg
2016-06-01
The correlation energy of the homogeneous electron gas is evaluated by solving the Bethe-Salpeter equation (BSE) beyond the Tamm-Dancoff approximation for the electronic polarization propagator. The BSE is expected to improve on the random-phase approximation, owing to the inclusion of exchange diagrams. For instance, since the BSE reduces in second order to Møller-Plesset perturbation theory, it is self-interaction free in second order. Results for the correlation energy are compared with quantum Monte Carlo benchmarks and excellent agreement is observed. For low densities, however, we find imaginary eigenmodes in the polarization propagator. To avoid the occurrence of imaginary eigenmodes, an approximation to the BSE kernel is proposed that allows us to completely remove this issue in the low-electron-density region. We refer to this approximation as the random-phase approximation with screened exchange (RPAsX). We show that this approximation even slightly improves upon the standard BSE kernel.
Dotsenko, Victor
2012-01-01
The distribution function of the free energy fluctuations in one-dimensional directed polymers with free boundary conditions is derived by mapping the replicated problem to the N-particle quantum boson system with attractive interactions. It is shown that in the thermodynamic limit this function is described by the universal Tracy-Widom distribution of the Gaussian orthogonal ensemble.
Covariant Bethe-Salpeter wave functions for heavy hadrons
International Nuclear Information System (INIS)
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
On the Bethe approximation to the reactance matrix
International Nuclear Information System (INIS)
The Bethe approximation to the reactance matrix is considered for electron-neutral-atom collisions. Analytic expressions are given for the matrix elements. For the special case of electron-neutral-atom scattering the sum rules of Burgess are simplified. Particular consideration is given to the problem of calculating cross sections for dipole transitions. Partial cross sections are presented for all non-exact resonance dipole transitions between hydrogen atom states, with n, n' = 11, 31, 51, 71, 91. (author)
Multiplication factor in multiwire proportional chambers: a Bethe formulation
International Nuclear Information System (INIS)
This work presents a model describing the electronic gain for multiwire proportional chambers. An expression for the electronic multiplication is achieved through the ionization cross section of the filling gas by electron impact. The individual ionization process is considered as a transition into continuum and estimated by the Bethe formula. This model is compared to both experimental and semi-empirical previously reported data. ((orig.))
Bethe-Peierls approximation and the inverse Ising model
Nguyen, H. Chau; Berg, Johannes
2011-01-01
We apply the Bethe-Peierls approximation to the problem of the inverse Ising model and show how the linear response relation leads to a simple method to reconstruct couplings and fields of the Ising model. This reconstruction is exact on tree graphs, yet its computational expense is comparable to other mean-field methods. We compare the performance of this method to the independent-pair, naive mean- field, Thouless-Anderson-Palmer approximations, the Sessak-Monasson expansion, and susceptibil...
Theory of x-ray absorption: a Bethe-Salpeter approach
Shirley, Eric L.
2002-03-01
First-principles calculations of x-ray absorption spectra of solids is a well-established field. The best known and most used treatments are probably those based on real-space multiple-scattering theory. Such Green's Function approaches are particular useful for incorporating electron damping effects (self-energy effects) that broaden spectral features at high electron kinetic energy. Near-edge structure can also be treated, and it can also be treated in super-cell calculations. In this talk, I will present results obtained using an alternative, reciprocal-space approach based on solving the Bethe-Salpeter equation, which is related to the Bethe-Salpeter method used to treat valence excitation signatures in optical absorption spectra. This amounts to solving the coupling equations of motion for the electron-core hole pair that is produced by x-ray absorption. Mutual localization of the electron and core hole in real space is realized by permitting the electron to exist as a wave-packet of Bloch states peaked near the core hole, governed by the excitation process and ensuing electron core-hole attraction. Because this approach permits state-of-the-art electron band structure calculations to be used to evaluate the electron wave function, this approach is particularly well suited for detailed near-edge structure. In presenting the approach and results obtained, particular attention is focused on (1) the role of the electron-hole interaction, (2) the need to deal with core-hole screening accurately, (3) the evaluation of accurate transition matrix elements between core states and Bloch states, and (4) computational-time scaling issues. This work has been done in collaboration with J.A. Soininen, J.J. Rehr, E.K. Chang, and others. This work was supported in part by the U.S. Deparment of Energy (DOE) Grant DE-FG03-97ER45623 and facilitated by the DOE Computational Materials Science Network (CMSN).
Loopy Belief Propagation, Bethe Free Energy and Graph Zeta Function
Watanabe, Yusuke
2011-01-01
We propose a new approach to the theoretical analysis of Loopy Belief Propagation (LBP) and the Bethe free energy (BFE) by establishing a formula to connect LBP and BFE with a graph zeta function. The proposed approach is applicable to a wide class of models including multinomial and Gaussian types. The connection derives a number of new theoretical results on LBP and BFE. This paper focuses two of such topics. One is the analysis of the region where the Hessian of the Bethe free energy is positive definite, which derives the non-convexity of BFE for graphs with multiple cycles, and a condition of convexity on a restricted set. This analysis also gives a new condition for the uniqueness of the LBP fixed point. The other result is to clarify the relation between the local stability of a fixed point of LBP and local minima of the BFE, which implies, for example, that a locally stable fixed point of the Gaussian LBP is a local minimum of the Gaussian Bethe free energy.
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.
All-electron Bethe-Salpeter calculations for shallow-core x-ray absorption near-edge structures
Olovsson, W.; Tanaka, I.; Mizoguchi, T.; Puschnig, P.; Ambrosch-Draxl, C.
2009-01-01
X-ray absorption near-edge structure spectra are calculated by fully solving the electron/core-hole Bethe-Salpeter equation (BSE) in an all-electron framework. We study transitions from shallow core states, including the Mg L2,3 edge in MgO, the Li K edge in the Li halides LiF, LiCl, LiBr, and LiI, as well as Li2O. We illustrate the advantage of the many-body approach over a core-hole supercell calculation. Both schemes lead to strongly bound excitons, but the nonlocal treatment of the electr...
Kaltsas, Dimitrios A
2016-01-01
We derive exact solutions of the general linear form of the Grad-Shafranov (GS) equation, including incompressible equilbrium flow, using similarity reduction ansatzes motivated by the ansatz-based methods of group foliation and direct reduction. The linearity of the equilibrium equation allows linear combinations of solutions in order to obtain axisymmetric MHD equilibria with closed and nested magnetic surfaces which are favorable for the effective confinenment of laboratory plasmas. Employing the afforementioned ansatzes we also obtain analytical solutions for several non-linear forms of the GS equation.
Toward a standard model 2, via Kaluza ansatz 2
Batakis, Nikolaos A
2012-01-01
New results and perspectives precipitate from the (modified as) Kaluza ansatz 2 (KA2), whereby, instead of appending $n$ Planck-scale (${\\rm L_o}$) compact SL dimensions to ordinary 4D spacetime, one augments $n$ such dimensions by 3 large ones. By KA2, the fundamental role of gravity in the dynamics of vacuum geometry is being conceded to the remaining fundamental interactions. The ground state in KA2 is of the form $\\bar{\\cal M}^{n+4}=\\bar{\\cal C}^{n+1}\\times\\IR^3$, where the static (averaged-out over scales ${\\rm L}>>{\\rm L_o}$) $\\bar{\\cal C}^{n+1}$ carries {\\em effective torsion} as relic of the deeper vacuum dynamics at Planck scale. For the simplest non-trivial implementation of KA2, the Bianchi IX subclass of SU(2)-invariant ${\\cal B}^4_{\\rm IX}$ provides the $\\bar{\\cal C}^5=\\bar{\\cal B}^4_{\\rm M}\\times S^1$, with the $S^1$ coming from 'augmentability', a complement to compactification. The classical action involves (i) the gravitational and EW sectors in elegant {\\em hierarchy}, (ii) the {\\em higgsles...
A generalized local ansatz and its effect on halo bias
Shandera, Sarah; Huterer, Dragan
2010-01-01
Motivated by the properties of early universe scenarios that produce observationally large local non-Gaussianity, we perform N-body simulations with non-Gaussian initial conditions from a generalized local ansatz. The bispectra are schematically of the local shape, but with scale-dependent amplitude. We find that in such cases the size of the non-Gaussian correction to the bias of small and large mass objects depends on the amplitude of non-Gaussianity roughly on the scale of the object. In addition, some forms of the generalized bispectrum alter the scale dependence of the non-Gaussian term in the bias by a fractional power of k. These features may allow significant observational constraints on the particle physics origin of any observed local non-Gaussianity, distinguishing between scenarios where a single field or multiple fields contribute to the curvature fluctuations. While analytic predictions for the non-Gaussian bias agree qualitatively with the simulations, we find numerically a stronger observation...
LIVING LABS – Ein Ansatz für die Innovation klimaresilienter Infrastrukturen?
Schäfer, Ernst
2014-01-01
Die vorliegende Arbeit untersucht, inwiefern sich im Kontext des Klimawandels der Ansatz der Reallabore (Living Labs) für die Initiierung struktureller Veränderungen von Infrastruktursystemen hin zu resilienten Infrastrukturen eignet. Darüber hinaus wird eine erste Konzeptualisierung und Strukturierung des Ansatzes der Reallabore anhand ausgewählter internationaler Beispiele vorgenommen. Anhand einer Untersuchung des gegenwärtigen Forschungsstandes zu den Themenfeldern Klimawandel und Klimaan...
Mass Ansatze for the standard model fermions from a composite perspective
Fariborz, Amir H; Nasri, Salah
2016-01-01
We consider a composite model in which the standard model fermions are bound states of elementary spin $\\frac{1}{2}$ particles, the preons, situated in the conjugate product representation of the color group. In this framework we propose and analyze two mass Ansatze one for the leptons, the other one for the quarks, based on mass formulae of the Gell-Mann Okubo type. We find that these mass Ansatze can give an adequate description of the known standard model fermion masses.
Quantum $k$-core conduction on the Bethe lattice
Cao, L.; Schwarz, J. M.
2010-01-01
Classical and quantum conduction on a bond-diluted Bethe lattice is considered. The bond dilution is subject to the constraint that every occupied bond must have at least $k-1$ neighboring occupied bonds, i.e. $k$-core diluted. In the classical case, we find the onset of conduction for $k=2$ is continuous, while for $k=3$, the onset of conduction is discontinuous with the geometric random first-order phase transition driving the conduction transition. In the quantum case, treating each occupi...
Physics over easy Breakfasts with Beth and physics
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
Pressure exerted by a grafted polymer: Bethe lattice solution
Mynssem Brum, Rafael; Stilck, Jürgen F.
2015-01-01
We solve the problem of a chain, modeled as a self-avoiding walk (SAW), grafted to the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point. The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walks on regular lattices and gaussian walks. The adsorption transition, which is discontinuous, and its influence on the pressure are also studied.
$\\pi$ and K-meson Bethe-Salpeter Amplitudes
Maris, P
1997-01-01
Independent of assumptions about the form of the quark-quark scattering kernel, K, we derive the explicit relation between the flavour-nonsinglet pseudoscalar meson Bethe-Salpeter amplitude, Gamma_H, and the dressed-quark propagator in the chiral limit. In addition to a term proportional to gamma_5, Gamma_H necessarily contains qualitatively and quantitatively important terms proportional to gamma_5 gamma.P and gamma_5 gamma.k k.P, where P is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by Gamma_H, whose residue is the leptonic decay constant for the bound state. The pseudoscalar vertex also contains such a bound state pole and, in the chiral limit, the residue of this pole is related to the vacuum quark condensate. The axial-vector Ward-Takahashi identity relates these pole residues; with the Gell-Mann--Oakes--Renner relation a corollary of this identity. The dominant ultraviolet asymptotic behaviour of the scalar functions in the meson Bethe-Salpeter a...
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; Sauer, Stephan P. A.
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...
Spinning solitons of a modified nonlinear Schroedinger equation
International Nuclear Information System (INIS)
We study soliton solutions of a modified nonlinear Schroedinger (MNLS) equation. Using an ansatz for the time and azimuthal angle dependence previously considered in the studies of the spinning Q balls, we construct multinode solutions of the MNLS equation as well as spinning generalizations
Numerical Generalization of the Bethe-Weizs\\"{a}cker Mass Formula
Mavrodiev, S Cht
2016-01-01
Based on the AME2012 nuclear database and the semi-empirical mass formula of Bethe and von Weizs\\"{a}cker we formulated and solved the inverse problem for its numerical generalization in step by step way. The established parametrization describes the measured nuclear masses of 2564 isotopes with an accuracy better than 2.6 MeV, starting from the number of protons $Z=1$ and number of neutrons $N=1$. The set of parameters $\\{a_{i}\\}$, $i=1,\\dots, {N}_{\\rm{total}}$ of our fit represent the solution of an overdetermined system of algebraic equations, which represent equalities between the binding energy $E_{B}^{\\rm{Expt}}(A_{j},Z_{j})$ and its model $E_{B}^{\\rm{Th}}(A_{j},Z_{j},\\{a_{i}\\})$, where $j=1,\\dots,2564$. The solution of the overdetermined system of equations has been obtained with the help of the Aleksandrov's auto-regularization method of Gauss-Newton type for ill-posed problems (Dubna FORTRAN code REGN). The explicit form of unknown functions was discovered in a step-by-step way using the LCH procedur...
Sinky, Hussein Mohammed
The latest advances in radiation oncology emphasizes the importance of the theory of energy loss of charged particles through matter. Since the development of the Bethe-Bloch stopping power for heavy charged incident particles in 1930, many corrections have been proposed to improve this equation's theoretical approximation. The region of applicability of this formula, with respect to the velocity and the charge of the incident particle as well as the characteristics of the target, is restricted by the validity of the approximation adopted. One of the major unsolved problems is the relativistic treatment of the inner-shell electrons for medium and heavy target elements. The stopping power theory treats atomic electrons non-relativistically for these targets which put serious limitation on the theory because the basic sum rules on which the theory relies are not amenable to vigorous relativistic generalization as pointed out by Fano. To solve this problem we assume completeness by employing the Dirac Hamiltonian, and then present a semi-relativistic approach to order v 2/c2 following the Foldy-Wouthuysen-Transformation (FWT) to exclude the contributions from the negative-energy states. To establish this goal we developed a very elegant, practical, and accurate step-by-step procedure using Baker-Hausdroff Lemma to do the FWT to any desired order for any functions of coordinate or momentum operator, or to any entire functions of both coordinate and momentum operators. We applied this procedure to general function of position where the result is then applied to find the TRK and Bethe sum rules by using semirelativistic Hamiltonian. This procedure can be used to find any desired sum rule by doing more computation relations of the transformed Hamiltonian of the system with the transformed function of position. For example, Sk sum rule will require k times commutation relations to be calculated. The resulting Bethe sum rule relativistic correction is then used to find the
International Nuclear Information System (INIS)
In this work, we construct an alternative formulation to the traditional algebraic Bethe ansätze for quantum integrable models derived from a generalized rational Gaudin algebra realized in terms of a collection of spins 1/2 coupled to a single bosonic mode. The ensemble of resulting models which we call Dicke–Jaynes–Cummings–Gaudin models are particularly relevant for the description of light–matter interaction in the context of quantum optics. Having two distinct ways to write any eigenstate of these models we then combine them in order to write overlaps and form factors of local operators in terms of partition functions with domain wall boundary conditions. We also demonstrate that they can all be written in terms of determinants of matrices whose entries only depend on the eigenvalues of the conserved charges. Since these eigenvalues obey a much simpler set of quadratic Bethe equations, the resulting expressions could then offer important simplifications for the numerical treatment of these models. (paper)
A Weizsacker-Bethe type mass formula for hypernuclei
International Nuclear Information System (INIS)
Theoretical estimates of hypernuclear binding energies are generally much larger than the empirical value and the disagreement is rather marked for the binding energy of sub(Λ)5He. Here we try to explain the so-called over-binding problem by way of introducing a Weizsacker-Bethe type mass formula used for ordinary nuclei. Using the most recent data on binding energies of hypernuclei, parameters of the hypernuclear mass formula are estimated by fitting a least-square curve as is the usual practice in nuclear physics. Theoretical predictions for hypernuclear binding energies are then made by using the formula as obtained above and results compared with experimental values. Agreement with experiment is found to be rather good and in particular the result obtained for sub(Λ)5He, although slightly larger than the observed value, has shown significant improvement over earlier estimates. (author)
Potts models with invisible states on general Bethe lattices
International Nuclear Information System (INIS)
The number of so-called invisible states which need to be added to the q-state Potts model to transmute its phase transition from continuous to first order has attracted recent attention. In the q = 2 case, a Bragg–Williams (mean-field) approach necessitates four such invisible states while a 3-regular random graph formalism requires seventeen. In both of these cases, the changeover from second- to first-order behaviour induced by the invisible states is identified through the tricritical point of an equivalent Blume–Emery–Griffiths model. Here we investigate the generalized Potts model on a Bethe lattice with z neighbours. We show that, in the q = 2 case, invisible states are required to manifest the equivalent Blume–Emery–Griffiths tricriticality. When z = 3, the 3-regular random graph result is recovered, while z → ∞ delivers the Bragg–Williams (mean-field) result. (paper)
Self-avoiding walks on a bilayer Bethe lattice
International Nuclear Information System (INIS)
We propose and study a model of polymer chains in a bilayer. Each chain is confined in one of the layers and polymer bonds on first neighbor edges in different layers interact. We also define and comment on results for a model with interactions between monomers on first neighbor sites of different layers. The thermodynamic properties of the model are studied in the grand-canonical formalism and both layers are considered to be Cayley trees. In the core region of the trees, which we call a bilayer Bethe lattice, we find a very rich phase diagram in the parameter space defined by the two activities of monomers and the Boltzmann factor associated with the interlayer interaction between bonds or monomers. In addition to critical and coexistence surfaces, there are tricritical, bicritical and critical endpoint lines, as well as higher order multicritical points. (paper)
Self-avoiding walks on a bilayer Bethe lattice
Serra, Pablo; Stilck, Jürgen F.
2014-04-01
We propose and study a model of polymer chains in a bilayer. Each chain is confined in one of the layers and polymer bonds on first neighbor edges in different layers interact. We also define and comment on results for a model with interactions between monomers on first neighbor sites of different layers. The thermodynamic properties of the model are studied in the grand-canonical formalism and both layers are considered to be Cayley trees. In the core region of the trees, which we call a bilayer Bethe lattice, we find a very rich phase diagram in the parameter space defined by the two activities of monomers and the Boltzmann factor associated with the interlayer interaction between bonds or monomers. In addition to critical and coexistence surfaces, there are tricritical, bicritical and critical endpoint lines, as well as higher order multicritical points.
Modified binary encounter Bethe model for electron-impact ionization
Guerra, M; Indelicato, P; Santos, J P
2013-01-01
Theoretical expressions for ionization cross sections by electron impact based on the binary encounter Bethe (BEB) model, valid from ionization threshold up to relativistic energies, are proposed. The new modified BEB (MBEB) and its relativistic counterpart (MRBEB) expressions are simpler than the BEB (nonrelativistic and relativistic) expressions because they require only one atomic parameter, namely the binding energy of the electrons to be ionized, and use only one scaling term for the ionization of all sub-shells. The new models are used to calculate the K-, L- and M-shell ionization cross sections by electron impact for several atoms with Z from 6 to 83. Comparisons with all, to the best of our knowledge, available experimental data show that this model is as good or better than other models, with less complexity.
Neutron and proton drip lines using the modified Bethe-Weizsacker mass formula
Basu, D N
2003-01-01
Proton and neutron separation energies have been calculated using the extended Bethe-Weizsacker mass formula. This modified Bethe-Weizsacker mass formula describes minutely the positions of all the old and the new magic numbers. It accounts for the disappearance of some traditional magic numbers for neutrons and provides extra stability for some new neutron numbers. The neutron and proton drip lines have been predicted using this extended Bethe-Weizsacker mass formula. The implications of the proton drip line on the astrophysical rp-process and of the neutron drip line on the astrophysical r-process have been discussed.
Hans A. Bethe Prize: Neutron Stars and Core-Collapse Supernovae
Lattimer, James
2015-04-01
Core-collapse supernovae lead to the formation of neutron stars, and both are sensitive to the dense matter equation of state. Hans Bethe first recognized that the matter in the collapsing core of a massive star has a relatively low entropy which prevents nuclear dissociation until nuclei merge near the nuclear saturation density. This recognition means that collapse continues until the core exceeds the saturation density. This prediction forms the foundation for modern simulations of supernovae. These supernovae sample matter up to about twice nuclear saturation density, but neutron stars are sensitive to the equation of state both near the saturation density and at several times higher densities. Two important recent developments are the discovery of two-solar mass neutron stars and refined experimental determinations of the behavior of the symmetry energy of nuclear matter near the saturation density. Combined with the assumption of causality, they imply that the radii of observed neutron stars are largely independent of their mass, and that this radius is in the range of 11 to 13 km. These theoretical results are not only consistent with expectations from theoretical studies of pure neutron matter, but also accumulated observations of both bursting and cooling neutron stars. In the near future, new pulsar timing data, which could lead to larger measured masses as well as measurements of moments of inertia, X-ray observations, such as from NICER, of bursting and other sources, and gravitational wave observations of neutron stars in merging compact binaries, will provide important new constraints on neutron stars and the dense matter equation of state. DOE DE-FG02-87ER-40317.
Generalized Hedgehog ansatz and Gribov copies in regions with non trivial topologies
Canfora, Fabrizio
2013-01-01
In this paper the arising of Gribov copies both in Landau and Coulomb gauges in regions with non-trivial topologies but flat metric, (such as closed tubes S1XD2, or RXT2) will be analyzed. Using a novel generalization of the hedgehog ansatz beyond spherical symmetry, analytic examples of Gribov copies of the vacuum will be constructed. Using such ansatz, we will also construct the elliptic Gribov pendulum. The requirement of absence of Gribov copies of the vacuum satisfying the strong boundary conditions implies geometrical constraints on the shapes and sizes of the regions with non-trivial topologies.
Generalized hedgehog ansatz and Gribov copies in regions with nontrivial topologies
Canfora, Fabrizio; Salgado-Rebolledo, Patricio
2013-02-01
In this paper the arising of Gribov copies both in Landau and Coulomb gauges in regions with nontrivial topologies but flat metric, (such as closed tubes S1×D2, or R×T2) will be analyzed. Using a novel generalization of the hedgehog ansatz beyond spherical symmetry, analytic examples of Gribov copies of the vacuum will be constructed. Using such ansatz, we will also construct the elliptic Gribov pendulum. The requirement of absence of Gribov copies of the vacuum satisfying the strong boundary conditions implies geometrical constraints on the shapes and sizes of the regions with nontrivial topologies.
Testing an Ansatz for the Leading Secular Loop Corrections from Quantum Gravity during Inflation
Basu, S
2016-01-01
It is widely believed that the leading secular loop corrections from quantum gravity can be subsumed into a coordinate redefinition. Hence the apparent infrared logarithm corrections to any quantity would be just the result of taking the expectation value of the tree order quantity at the transformed coordinates in the graviton vacuum. We term this the Transformation Ansatz and we compare its predictions against explicit one loop computations in Maxwell + Einstein and Dirac + Einstein on de Sitter background. In each case the ansatz fails.
Topological and non-topological soliton solutions to some time-fractional differential equations
Indian Academy of Sciences (India)
M Mirzazadeh
2015-07-01
This paper investigates, for the first time, the applicability and effectiveness of He’s semi-inverse variational principle method and the ansatz method on systems of nonlinear fractional partial differential equations. He’s semi-inverse variational principle method and the ansatz method are used to construct exact solutions of nonlinear fractional Klein–Gordon equation and generalized Hirota–Satsuma coupled KdV system. These equations have been widely applied in many branches of nonlinear sciences such as nonlinear optics, plasma physics, superconductivity and quantum mechanics. So, finding exact solutions of such equations are very helpful in the theoretical and numerical studies.
Energy Technology Data Exchange (ETDEWEB)
Modarres, M., E-mail: mmodares@ut.ac.ir [Physics Department, University of Tehran, North-Kargar Ave., 1439955961 Tehran (Iran, Islamic Republic of); Tafrihi, A.; Hatami, A. [Physics Department, University of Tehran, North-Kargar Ave., 1439955961 Tehran (Iran, Islamic Republic of)
2012-04-01
The neutron matter equation of states of the so-called Bethe homework problem (NMESB) is obtained using the (extended) lowest order constrained variational ((E) LOCV), the lowest order factorized Iwamoto-Yamada (LOF) and the Fermi (hypernetted) chain (FC (FHNC)) formalisms. The FC and the FHNC approximations are performed, using the LOCV or the ELOCV correlation function. It is shown that, if the normalization constraint is satisfied, then the NMESB results by using the LOCV, the ELOCV, the FC and the FHNC formalisms, will become close together and agree well with the corresponding FHNC calculations performed by Zabolitzky (Z) with the parameterized Krotscheck and Takahashi (KT) correlation function. It is also demonstrated that the LOF and the FC calculations, evaluated by employing a parameterized correlation function, are far from the above results, particularly at high densities. Finally, in order to test the convergence of LOF approximation, the two- and the three-body normalization factors are calculated and it is shown that in the LOF approximation, the truncation of cluster expansion after the first few leading terms is not reliable (which is well known as the Emery difficulty).
International Nuclear Information System (INIS)
The neutron matter equation of states of the so-called Bethe homework problem (NMESB) is obtained using the (extended) lowest order constrained variational ((E) LOCV), the lowest order factorized Iwamoto–Yamada (LOF) and the Fermi (hypernetted) chain (FC (FHNC)) formalisms. The FC and the FHNC approximations are performed, using the LOCV or the ELOCV correlation function. It is shown that, if the normalization constraint is satisfied, then the NMESB results by using the LOCV, the ELOCV, the FC and the FHNC formalisms, will become close together and agree well with the corresponding FHNC calculations performed by Zabolitzky (Z) with the parameterized Krotscheck and Takahashi (KT) correlation function. It is also demonstrated that the LOF and the FC calculations, evaluated by employing a parameterized correlation function, are far from the above results, particularly at high densities. Finally, in order to test the convergence of LOF approximation, the two- and the three-body normalization factors are calculated and it is shown that in the LOF approximation, the truncation of cluster expansion after the first few leading terms is not reliable (which is well known as the Emery difficulty).
Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
Gorbounov, V.; Rimányi, R.; Tarasov, V.; Varchenko, A.
2013-12-01
We interpret the equivariant cohomology algebra HGLn×C∗∗(T∗F;C) of the cotangent bundle of a partial flag variety F parametrizing chains of subspaces 0=F0⊂F1⊂⋯⊂FN=Cn, dimFi/F=λi, as the Yangian Bethe algebra B∞({1}/{D}Vλ-) of the g-weight subspace {1}/{D}Vλ- of a Y(g)-module {1}/{D}V-. Under this identification the dynamical connection of Tarasov and Varchenko (2002) [12] turns into the quantum connection of Braverman et al. (2010) [4] and Maulik and Okounkov (2012) [5]. As a result of this identification we describe the algebra of quantum multiplication on HGLn×C∗∗(T∗F;C) as the algebra of functions on fibers of a discrete Wronski map. In particular this gives generators and relations of that algebra. This identification also gives us hypergeometric solutions of the associated quantum differential equation. That fact manifests the Landau-Ginzburg mirror symmetry for the cotangent bundle of the flag variety.
Singular solitons and other solutions to a couple of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
Mustafa Inc; Esma Uluta(s); Anjan Biswas
2013-01-01
This paper addresses the extended (G′/G)-expansion method and applies it to a couple of nonlinear wave equations.These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation.This extended method reveals several solutions to these equations.Additionally,the singular soliton solutions are revealed,for these two equations,with the aid of the ansatz method.
Bethe algebra of Gaudin model, Calogero-Moser space and Cherednik algebra
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009-01-01
We identify the Bethe algebra of the Gaudin model associated to gl(N) acting on a suitable representation with the center of the rational Cherednik algebra and with the algebra of regular functions on the Calogero-Moser space.
Janus-Facedness of the Pion: Analytic Instantaneous Bethe-Salpeter Models
Lucha, Wolfgang
2016-01-01
Inversion enables the construction of interaction potentials underlying - under fortunate circumstances even analytic - instantaneous Bethe-Salpeter descriptions of all lightest pseudoscalar mesons as quark-antiquark bound states of Goldstone-boson nature.
Bethe vectors for models based on the super-Yangian $Y(\\mathfrak{gl}(m|n))$
Pakuliak, S Z; Slavnov, N A
2016-01-01
We study Bethe vectors of integrable models based on the super-Yangian $Y(\\mathfrak{gl}(m|n))$. Starting from the super-trace formula, we exhibit recursion relations for these vectors in the case of $Y(\\mathfrak{gl}(2|1))$ and $Y(\\mathfrak{gl}(1|2))$. These recursion relations allow to get explicit expressions for the Bethe vectors. Using an antimorphism of the super-Yangian $Y(\\mathfrak{gl}(m|n))$, we also construct a super-trace formula for dual Bethe vectors, and, for $Y(\\mathfrak{gl}(2|1))$ and $Y(\\mathfrak{gl}(1|2))$ super-Yangians, show recursion relations for them. Again, the latter allow us to get explicit expressions for dual Bethe vectors.
Algebraic solutions of an sl-boson system in the U(2l+1)↔O(2l+2) transitional region
International Nuclear Information System (INIS)
Exact eigen-energies and the corresponding wavefunctions of an interacting sl-boson system in a U(2l+1)↔O(2l+2) transitional region are obtained by using the Bethe ansatz within an infinite-dimensional Lie algebra. A numerical algorithm for solving the Bethe ansatz equations is introduced. As an example, spectra for the U(3)↔O(4) transitional region of the U(4) Vibron model are analysed. (author)
Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
International Nuclear Information System (INIS)
We describe a Bethe ansatz based method to derive, starting from a multiple integral representation, the long-distance asymptotic behavior at finite temperature of the density-density correlation function in the interacting onedimensional Bose gas. We compute the correlation lengths in terms of solutions of non-linear integral equations of the thermodynamic Bethe ansatz type. Finally, we establish a connection between the results obtained in our approach with the correlation lengths stemming from the quantum transfer matrix method. (orig.)
A Numerical Study of Entanglement Entropy of the Heisenberg Model on a Bethe Cluster
Friedman, Barry; Levine, Greg
2015-01-01
Numerical evidence is presented for a nearest neighbor Heisenberg spin model on a Bethe cluster, that by bisecting the cluster, the generalized Renyi entropy scales as the number of sites in the cluster. This disagrees with spin wave calculations and a naive application of the area law but agrees with previous results for non interacting fermions on the Bethe cluster. It seems this scaling is not an artifact of non interacting particles. As a consequence, the area law in greater then one dime...
A black hole solution of higher-dimensional Weyl-Yang-Kaluza-Klein theory by the Wu-Yang ansatz
Kuyrukcu, Halil
2016-01-01
We consider the Weyl-Yang gauge theory of gravitation in a $(4+3)$-dimensional curved space-time within the scenario of the non-Abelian Kaluza-Klein theory for the source and torsion-free limits. The explicit forms of the field equations containing a new spin current term and the energy-momentum tensors in the usual four dimensions are obtained by the well-known dimensional reduction procedure. In this limit, these field equations admit (anti)-dyon and magnetic (anti)-monopole solutions as well as a non-Einsteinian solution in the presence of a generalized Wu-Yang ansatz and some specific scalar potentials when the extra dimensions associated with the round and squashed three-sphere $S^{3}$ are, respectively, included. The (anti)-dyonic solution has similar properties to those of the Reissner-Nordstr\\"{o}m-de Sitter black holes of the Einstein-Yang-Mills system. The cosmological constant naturally appears in this approach, and that it associates with the constant dilaton field as well as the three-sphere radi...
A String-inspired Ansatz for Quark Masses and Mixing
Kobayashi, Tatsuo; Xing, Zhi-zhong
1996-01-01
We propose a simple but realistic pattern of quark mass matrices at the string scale, which can be derived from orbifold models of superstring theory with no use of gauge symmetries. This pattern is left-right symmetric and preserves the structural parallelism between up and down quark sectors. Its phenomenological consequences on flavor mixing and $CP$ violation are confronted with current experiments at the weak scale by use of the renormalization-group equations in the framework of the min...
M. K. Bahar; Yasuk, ; F.
2013-01-01
Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.
Energy Technology Data Exchange (ETDEWEB)
Slevin, K. (Service de Physique de l' Etat Condense, Centre d' Etudes de Saclay, 91 - Gif-sur-Yvette (France)); Pichard, J.L. (Service de Physique de l' Etat Condense, Centre d' Etudes de Saclay, 91 - Gif-sur-Yvette (France)); Muttalib, K.A. (Florida Univ., Gainesville, FL (United States). Dept. of Physics)
1993-06-01
The transmission of electrons through a disordered conductor is described by a transmission matrix t. In random matrix theory the joint probability distribution of the eigenvalues of t[dagger]t can be derived from a maximum entropy ansatz in which the mean eigenvalue density is given as a constraint. For a microscopic Anderson model, we examine the density for different shapes of the conductor (quasi-1d,2d,3d). For the high transmission modes the form of the density is independent of disorder, size and dimensionality. We derive expressions for the eigenvalue correlations implied by the maximum entropy ansatz and compare these with the actual correlations of the Anderson model spectrum. We find that the correlations are qualitatively correct in all dimensions. However, the ansatz does not reproduce the weak system shape dependence of the universal conductance fluctuations (UCF), giving always results close to the quasi-1d UCF-value. A careful study of the variances of different appropriate quantities indicates that the ansatz is quantitatively exact in quasi-1d over the whole spectrum of t.t[dagger], but correctly describes the correlations in higher dimensions on intervals which are larger in the bulk of the spectrum than near the edge. We show that eigenvalues near the edge of the spectrum, corresponding to high transmission or reflection, remain correlated to associated non isotopically distributed eigenvectors. (orig.).
International Nuclear Information System (INIS)
The transmission of electrons through a disordered conductor is described by a transmission matrix t. In random matrix theory the joint probability distribution of the eigenvalues of t†t can be derived from a maximum entropy ansatz in which the mean eigenvalue density is given as a constraint. For a microscopic Anderson model, we examine the density for different shapes of the conductor (quasi-1d,2d,3d). For the high transmission modes the form of the density is independent of disorder, size and dimensionality. We derive expressions for the eigenvalue correlations implied by the maximum entropy ansatz and compare these with the actual correlations of the Anderson model spectrum. We find that the correlations are qualitatively correct in all dimensions. However, the ansatz does not reproduce the weak system shape dependence of the universal conductance fluctuations (UCF), giving always results close to the quasi-1d UCF-value. A careful study of the variances of different appropriate quantities indicates that the ansatz is quantitatively exact in quasi-1d over the whole spectrum of t.t†, but correctly describes the correlations in higher dimensions on intervals which are larger in the bulk of the spectrum than near the edge. We show that eigenvalues near the edge of the spectrum, corresponding to high transmission or reflection, remain correlated to associated non isotopically distributed eigenvectors. (orig.)
Cartesian Kerr-Schild variation on the Newman-Janis ansatz
Nawarajan, Deloshan
2016-01-01
The Newman-Janis ansatz is a procedure (an "ansatz" or "trick") for obtaining the Kerr spacetime from the Schwarzschild spacetime. This 50 year old "trick" continues to generate heated discussion and debate even to this day. Most of the debate focusses on whether the Newman-Janis procedure can be upgraded to the status of an "algorithm", or if it is perhaps merely an inspired "ansatz", or possibly just a random "trick" of no deep physical significance. (That the Newman-Janis procedure very quickly led to the discovery of the Kerr-Newman spacetime is a point very much in its favour.) In the current article we will not answer these deeper questions, we shall instead present a much simpler alternative variation on the theme of the Newman-Janis ansatz that might be easier to work with. We shall present a 2-step version of the Newman-Janis trick that works directly with the Kerr-Schild "Cartesian" metric presentation of the Kerr spacetime. That is, we show how the original 4-step Newman--Janis procedure can, (usin...
The Rosner-Worah Type Quark Mass Matrix and Ansatz of Maximal CP Violation
Koide, Y
1993-01-01
A democratic form version of the Rosner-Worah quark mass matrix is discussed from a phenomenological point of view. It is pointed out that an ansatz of "maximal CP violation" can provide reasonable values of the Kobayashi-Maskawa mixings.
A precise definition of reduction of partial differential equations
Zhdanov, Renat Z.; Tsyfra, Ivan M.; Popovych, Roman O.
2002-01-01
We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential equations. As an illustration we give an example of non-classical reduction of the nonlinear wave equa...
The equation of state of a model Fermi liquid
International Nuclear Information System (INIS)
Variational calculations are performed for the equation of state of the so-called 'Homework' neutron liquid. Adopting the familiar Jastrow ansatz for the wave function the energy per particle is computed by means of a recently developed summation technique for Fermi systems. (Auth.)
Exact periodic solution in coupled nonlinear Schrodinger equations
Institute of Scientific and Technical Information of China (English)
Li Qi-Liang; Chen Jun-Lang; Sun Li-Li; Yu Shu-Yi; Qian Sheng
2007-01-01
The coupled nonlinear Schrodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.
Relativistic static fluid spheres with a linear equation of state
Ivanov, B. V.
2001-01-01
It is shown that almost all known solutions of the kind mentioned in the title are easily derived in a unified manner when a simple ansatz is imposed on the metric. The Whittaker solution is an exception, replaced by a new solution with the same equation of state.
Spinning Solitons of a Modified Non-Linear Schroedinger equation
Brihaye, Y; Zakrzewski, W J; Brihaye, Yves; Hartmann, Betti; Zakrzewski, Wojtek J.
2003-01-01
We study soliton solutions of a modified non-linear Schroedinger (MNLS) equation. Using an Ansatz for the time and azimuthal angle dependence previously considered in the studies of the spinning Q-balls, we construct multi-node solutions of MNLS as well as spinning generalisations.
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
Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation
Lindgren, Ingvar
2005-01-01
The connection between many-body theory (MBPT)--in perturbative and non-perturbative form--and quantum-electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based upon the recently developed covariant-evolution-operator method for QED calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a structure quite akin to that of many-body perturbation theory. At the same time this procedure is closely connected to the S-matrix and t...
International Nuclear Information System (INIS)
Two sets of nonlinear partial differential equations originating from two different physical situations have been combined and a new set of nonlinear partial differential equations has been formed wherefrom the previous two sets can be obtained as particular cases. One of the two sets of equations was obtained by Yang while discussing the condition of self-duality of SU(2) gauge fields on Euclidean four-dimensional space. The second one was reported by Charap for the chiral invariant model of pion dynamics under tangential parametrization. Using the same type of ansatz in each case De and Ray obtained physical solutions of the two sets of equations. Here exact solutions of the combined set of equations with particular values of the coupling constants have been obtained for a similar ansatz. These solutions too are physical in nature. (author)
Didaktischer Ansatz für das Blended Learning: Konzeption und Anwendung von Educational Patterns
Köhne, Sandra
2005-01-01
Die Dissertation ?Didaktischer Ansatz für das Blended Learning: Konzeption und Anwendung von Educational Patterns? beschreibt die Gestaltung von Blended Learning mittels Educational Patterns. Blended Learning stellt eine Kombination verschiedener Lehr-/ Lernformen mit und ohne Technikeinsatz dar. Typischerweise wird es als Kombination von Präsenz- und Onlineunterricht verstanden. Allerdings machen die Mischung zur sinnvollen Gestaltung des Unterrichts ebenso Medien, Sozial- und Übermittlungsf...
Testing an Ansatz for the Leading Secular Loop Corrections from Quantum Gravity during Inflation
Basu, S; Woodard, R. P.
2016-01-01
It is widely believed that the leading secular loop corrections from quantum gravity can be subsumed into a coordinate redefinition. Hence the apparent infrared logarithm corrections to any quantity would be just the result of taking the expectation value of the tree order quantity at the transformed coordinates in the graviton vacuum. We term this the Transformation Ansatz and we compare its predictions against explicit one loop computations in Maxwell + Einstein and Dirac + Einstein on de S...
Ein symbolischer Ansatz für finite Differenzenverfahren partieller Differentialgleichungen
Dingler, Christian
2010-01-01
Zusammenfassung. In dieser Arbeit werden Probleme der numerischen Lösung finiter Differenzenverfahren partieller Differentialgleichungen in einem algebraischen Ansatz behandelt. Es werden sowohl theoretische Ergebnisse präsentiert als auch die praktische Implementierung mithilfe der Systeme SINGULAR und QEPCAD vorgeführt. Dabei beziehen sich die algebraischen Methoden auf zwei unterschiedliche Aspekte bei finiten Differenzenverfahren: die Erzeugung von Schemata mithilfe von Gröbnerbasen und d...
Trajektorienbasierte Teleoperation von Straßenfahrzeugen auf Basis eines Shared-Control-Ansatzes
Gnatzig, Sebastian
2015-01-01
Die Arbeit stellt einen Teleoperations-Ansatz zum sicheren fahrerlosen Fahren von Straßenfahrzeuge im innerstädtischen Verkehr vor. Dazu erfolgt eine Funktionsteilung zwischen Mensch und Maschine mittels Shared Control, wobei der Operator Trajektorien plant, die das Fahrzeug automatisch abfährt. Gegenüber der klassischen direkten Teleoperation hat dies den Vorteil, dass die Steuerung robust gegen Kommunikationszeitverzögerungen ist und im Notfall das Fahrzeug automatisch sicher anhält. Thi...
Scaling of entanglement entropy in the (branching) multiscale entanglement renormalization ansatz
Evenbly, G.; Vidal, G.
2014-01-01
We investigate the scaling of entanglement entropy in both the multiscale entanglement renormalization ansatz (MERA) and in its generalization, the branching MERA. We provide analytical upper bounds for this scaling, which take the general form of a boundary law with various types of multiplicative corrections, including power-law corrections all the way to a bulk law. For several cases of interest, we also provide numerical results that indicate that these upper bounds are saturated to leadi...
Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
Evenbly, Glen; Vidal, Guifre
2013-01-01
We investigate the scaling of entanglement entropy in both the multi-scale entanglement renormalization ansatz (MERA) and in its generalization, the branching MERA. We provide analytical upper bounds for this scaling, which take the general form of a boundary law with various types of multiplicative corrections, including power-law corrections all the way to a bulk law. For several cases of interest, we also provide numerical results that indicate that these upper bounds are saturated to lead...
Topologically Twisted SUSY Gauge Theory, Gauge-Bethe Correspondence and Quantum Cohomology
Chung, Hee-Joong
2016-01-01
We calculate partition function and correlation functions in A-twisted 2d $\\mathcal{N}=(2,2)$ theories and topologically twisted 3d $\\mathcal{N}=2$ theories containing adjoint chiral multiplet with particular choices of $R$-charges and the magnetic fluxes for flavor symmetries. According to Gauge-Bethe correspondence, they correspond to Heisenberg XXX and XXZ spin chain models. We identify the partition function as the inverse of the norm of the Bethe eigenstates. Correlation functions are identified as the coefficients of the expectation value of Baxter $Q$-operators. In addition, we consider correlation functions of 2d $\\mathcal{N}=(2,2)^*$ theory and their relation to equivariant quantum cohomology and equivariant integration of cotangent bundle of Grassmann manifolds. Also, we study the ring relations of supersymmetric Wilson loops in 3d $\\mathcal{N}=2^*$ theory and Bethe subalgebra of XXZ spin chain model.
Modified Bethe formula for low-energy electron stopping power without fitting parameters
International Nuclear Information System (INIS)
We propose a modified Bethe formula for low-energy electron stopping power without fitting parameters for a wide range of elements and compounds. This formula maintains the generality of the Bethe formula and gives reasonable agreement in comparing the predicted stopping powers for 15 elements and 6 compounds with the experimental data and those calculated within dielectric theory including the exchange effect. Use of the stopping power obtained from this formula for hydrogen silsesquioxane in Monte Carlo simulation gives the energy deposition distribution in consistent with the experimental data. - Highlights: • We propose a modified Bethe formula for low-energy electron stopping power without fitting parameters. • Our formula is found based on the stopping power calculated by the dielectric theory including the exchange effect. • We calculate the energy deposition distribution of 3 keV electrons in 15 nm HSQ resist layer on Si substrate
Modeling dynamical electron scattering with Bethe potentials and the scattering matrix.
Wang, A; De Graef, M
2016-01-01
Bethe potentials were introduced by Bethe in 1928 as a first order perturbation approach to reducing the number of diffracted beams in dynamical electron scattering problems. The approach starts from the Bloch wave representation, and uses a threshold criterion to split the diffracted beams into two subsets, namely strong and weak beams. Since the use of Bloch wave based Bethe potentials for defect simulations is somewhat tedious, this paper applies the perturbation approach to the scattering matrix formalism, which is more readily adaptable for defect image simulations. The size of the dynamical matrix, and hence the computation time, can be reduced significantly. A threshold criterion for the separation of scattered beams into strong and weak sets is introduced. A general guideline in setting the threshold for strong or weak beam selection is discussed along with several parameters that may influence the threshold values, such as atomic number, accelerating voltage, structure complexity, incident beam tilt and temperature. PMID:26433091
The Barkas-Effect Correction to Bethe-Bloch Stopping Power
Porter, L. E.
A brief history of the discovery of the Barkas-effect correction to the Bethe-Bloch stopping power formula is presented, followed by a recounting of the initial theoretical calculations prepared as a quantitative explanation. A current version of the modified Bethe-Bloch formula is described in detail. An overview of the current capability to assess the validity of several existing formalisms for calculating the Barkas-effect correction term is provided, in the course of which discussion of numerous sources of uncertainty ensues. Finally, an opinion on the significance of this departure from Bethe-Bloch theory is offered, along with a presentation of a few recent developments and of some areas for focus in future exploration in the field of the stopping power of matter for charged particles.
Haataja, Kim
2007-01-01
Die Autorin stellt den Ansatz des integrierten Sprach- und Fachlernens (CLIL), das „Content and Language Integrated Learning“ vor und diskutiert die Förderung des schulischen Mehrsprachenerwerbs in Europa. Während sie zunächst die Diskussion um die Sprachenerziehung innerhalb der europäischen Bildungspolitik kurz skizziert, stellt sie einige Profile des integrierten Sprach- und Fachlernens zusammenfassend vor. Des weiteren geht sie auf die Vorgeschichte dieses Ansatzes, die Terminologie um CL...
Ge, M. L.; et al.
1996-09-01
The Table of Contents for the full book PDF is as follows: * Preface * Part I: Satellite Meeting of STATPHYS-19 * Boundary Yang-Baxter in the RSOS/SOS Representation * Quantum Domains in Ferromagnetic Anisotropic Heisenberg Chains * The Generalized Chiral Clock Model and its Phase Diagram * Algebraic Solution of the Coincidence Problem for Crystals and Quasicrystals * Reflection Equations and Surface Critical Phenomena * Fully Packed Loop Models * Quantum Field Theories in terms of Group-Valued Local Fields: An Overview * C-Statiscal Transition Transforms of the Heisenberg Spin Chain and Braided Symmetry * U(1)-Invariant Local and Integrable Lattice Formulation of the Massive Thirring Model * Corner Transfer Matrices and Novel Polynomials * Rigorous and Numerical Results on Two-Dimensional Oriented Self-Avoiding Walks * The Price for Quantum Group Symmetry: Chiral Versus 2D WZNW Model * Integrable Zn-Chiral Potts Model : The Missing Rapidity-Momentum Relation * Dilute Algebras and Solvable Lattice Models * Falicov-Kimball Model: Ground States and Flux Phase Problem * Mutual Exclusion Statistics in the Exactly Solvable Model of the Mott Metal-Insulator Transition * Quantum Group and the Hofstadter Problem * Domain Walls in the Spin-S Quantum Ising Chain * Quantization of Nonultralocal Models - Generalization of the Theorem for the Multiple Coproduct * Multipoint Functions(Form-factors) of Quantum sine-Gordon Field with Boundary * Three-Dimensional Vertex Model * Probability of Phase Separation and Two Point Temperature Correlation Functions for the Bose Gas with Delta Interaction * On the Fundamental Invariant of the Hecke Algebra Hn(q) * Ternary Z3-Graded Algebras and New Gauge Theories * Thermodynamics of Integrable Quantum Chains : Free Energy and Correlation Lengths * Quantum Integrable Systems and Classical Discrete Nonlinear Dynamics * Quantum Jacobi-Trudi Formula and Analytic Bethe Ansatz * On Boundary Condition of Single Particle and the Spectrum of Many
New Rational Form Solutions to mKdV Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2005-01-01
In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.
Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
Indian Academy of Sciences (India)
Hitender Kumar; Anand Malik; Fakir Chand
2013-02-01
In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.
Construction of rogue wave and lump solutions for nonlinear evolution equations
Lü, Zhuosheng; Chen, Yinnan
2015-07-01
Based on symbolic computation and an ansatz, we present a constructive algorithm to seek rogue wave and lump solutions for nonlinear evolution equations. As illustrative examples, we consider the potential-YTSF equation and a variable coefficient KP equation, and obtain nonsingular rational solutions of the two equations. The solutions can be rogue wave or lump solutions under different parameter conditions. We also present graphic illustration of some special solutions which would help better understand the evolution of solution waves.
Analytical and numerical solutions of the Schrödinger–KdV equation
Indian Academy of Sciences (India)
Manel Labidi; Ghodrat Ebadi; Essaid Zerrad; Anjan Biswas
2012-01-01
The Schrödinger–KdV equation with power-law nonlinearity is studied in this paper. The solitary wave ansatz method is used to carry out the integration of the equation and obtain one-soliton solution. The ′/ method is also used to integrate this equation. Subsequently, the variational iteration method and homotopy perturbation method are also applied to solve this equation. The numerical simulations are also given.
ODE/IM correspondence and modified affine Toda field equations
Ito, Katsushi
2014-01-01
We study the two-dimensional affine Toda field equations for affine Lie algebra $\\hat{\\mathfrak{g}}$ modified by a conformal transformation and the associated linear equations. In the conformal limit, the associated linear problem reduces to a (pseudo-)differential equation. For classical affine Lie algebra $\\hat{\\mathfrak{g}}$, we obtain a (pseudo-)differential equation corresponding to the Bethe equations for the Langlands dual of the Lie algebra $\\mathfrak{g}$, which were found by Dorey et al. in study of the ODE/IM correspondence.
Indian Academy of Sciences (India)
Ahmet Bekir; Özkan Güner
2013-08-01
In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sech$^{p}$ and tanh$^{p}$ functions, we obtain exact analytical bright and dark soliton solutions for the considered model. These solutions may be useful and desirable for explaining some nonlinear physical phenomena in genuinely nonlinear dynamical systems.
International Nuclear Information System (INIS)
The Born-Hartree-Bethe approximation for the calculation of total (elastic + inelastic) integral cross section for high-energy electron-atom and electron-molecule scattering containing no free parameter is formulated. Corresponding results are obtained for He, Ne, Ar, Kr, Xe, H2 and N2 and compared with experimental data.
Dynamical polaron Ansatz: A theoretical tool for the ultrastrong-coupling regime of circuit QED
Díaz-Camacho, Guillermo; Bermudez, Alejandro; García-Ripoll, Juan José
2016-04-01
In this work we develop a semianalytical variational Ansatz to study the properties of few-photon excitations interacting with a collection of quantum emitters in regimes that go beyond the rotating-wave approximation. This method can be used to approximate both the static and dynamical properties of a superconducting qubit in an open transmission line, including the spontaneous emission spectrum and the resonances in scattering experiments. The approximations are quantitatively accurate for rather strong couplings, as shown by a direct comparison to matrix-product-state numerical methods, and provide also a good qualitative description for stronger couplings well beyond the Markovian regime.
Miyaji, Masamichi; Numasawa, Tokiro; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento
2015-10-23
We present how the surface-state correspondence, conjectured by Miyaji and Takayanagi, works in the setup of AdS(3)/CFT(2) by generalizing the formulation of a continuous multiscale entanglement renormalization group ansatz. The boundary states in conformal field theories play a crucial role in our formulation and the bulk diffeomorphism is naturally taken into account. We give an identification of bulk local operators which reproduces correct scalar field solutions on AdS(3) and bulk scalar propagators. We also calculate the information metric for a locally excited state and show that it reproduces the time slice of AdS(3). PMID:26551098
The Matrix Product Ansatz for integrable U(1)^N models in Lunin-Maldacena backgrounds
Lazo, Matheus Jatkoske
2008-01-01
We obtain through a Matrix Product Ansatz (MPA) the exact solution of the most general $N$-state spin chain with $U(1)^N$ symmetry and nearest neighbour interaction. In the case N=6 this model contain as a special case the integrable SO(6) spin chain related to the one loop mixing matrix for anomalous dimensions in ${\\cal N} = 4$ SYM, dual to type $IIB$ string theory in the generalised Lunin-Maldacena backgrounds. This MPA is construct by a map between scalar fields and abstract operators tha...
The generalized Kadanoff-Baym ansatz. Computing nonlinear response properties of finite systems
Balzer, K.; Hermanns, S.; Bonitz, M.
2013-03-01
For a minimal Hubbard-type system at different interaction strengths U, we investigate the density-response for an excitation beyond the linear regime using the generalized Kadanoff-Baym ansatz (GKBA) and the second Born (2B) approximation. We find strong correlation features in the response spectra and establish the connection to an involved double excitation process. By comparing approximate and exact Green's function results, we also observe an anomalous U-dependence of the energy of this double excitation in 2B+GKBA. This is in accordance with earlier findings [K. Balzer et al., EPL 98, 67002 (2012)] on double excitations in quantum wells.
Sierig, Jakob
2003-01-01
In dieser Arbeit wurde untersucht, ob sich Bodengasmessungen als Ansatz für eine Explorationsmethode auf oberflächennah lagerndes Steinsalz eignen. Die Untersuchungen basieren auf der Annahme, dass Steinsalz als Barriere auf nach oben strömendes CO2 geogener Herkunft wirkt und sich aus diesem Grund die Grenze des Salzlagers durch ein erhöhtes Kohlensäure-Vorkommen in der Bodenluft an der Erdoberfläche bemerkbar macht. Als Untersuchungsgebiet wurde das 12 km2 große Gelände über dem Salzbergwer...
The generalized Kadanoff-Baym ansatz. Computing nonlinear response properties of finite systems
International Nuclear Information System (INIS)
For a minimal Hubbard-type system at different interaction strengths U, we investigate the density-response for an excitation beyond the linear regime using the generalized Kadanoff-Baym ansatz (GKBA) and the second Born (2B) approximation. We find strong correlation features in the response spectra and establish the connection to an involved double excitation process. By comparing approximate and exact Green's function results, we also observe an anomalous U-dependence of the energy of this double excitation in 2B+GKBA. This is in accordance with earlier findings [K. Balzer et al., EPL 98, 67002 (2012)] on double excitations in quantum wells.
Mit Licht schreiben: ein ikonografisch-ikonologischer Ansatz zu Flüchtlingsfotografien
Lenette, Caroline
2016-01-01
Flüchtlingsfotografien werden oft genutzt, um die tiefe Verunsicherung und Not der Betroffenen zu vermitteln und so Aufmerksamkeit und Empathie anzuregen. Kritische Perspektiven zu fotografischer Repräsentation können hier zu einem nuancenreicheren Verständnis der Alltagserfahrungen von Flüchtlingen über die Zeit beitragen. In diesem Artikel beschreibe ich einen ikonografisch-ikonologischen Ansatz zur Analyse von vier Fotografien zu Situationen, die zwischen 20 bis 35 Jahren zurückliegen. Auf...
International Nuclear Information System (INIS)
The improved tanh function method [Chaos, Solitons and Fractals 2005;24:257] is further improved by constructing new ansatz solution of the considered equation. As its application, the (2 + 1)-dimensional Konopelchenko-Dubrovsky equations are considered and abundant new exact non-travelling wave solutions are obtained
Wu, Shuang-Qing
2015-01-01
In a previous paper [S.Q. Wu, Phys. Rev. D 83 (2011) 121502(R)], a new kind of metric ansatz has been found to fairly describe all already-known black hole solutions in the ungauged Kaluza-Klein (KK) supergravity theories. That metric ansatz is of somewhat a little resemblance to the famous Kerr-Schild (KS) form, but it is different from the KS one in two distinct aspects. That is, apart form a global conformal factor, the metric ansatz can be written as a vacuum background spacetime plus a "perturbation" modification term, the latter of which is associated with a timelike geodesic vector field rather than a null geodesic congruence in the usual KS ansatz. In this paper, we shall study this novel metric ansatz in details, aiming at achieving some inspirations to the construction of rotating charged AdS black holes with multiple charges in other gauged supergravity theories. In order to investigate the metric properties of the general KK-AdS solutions, in this paper we devise a new effective method, dubbed as ...
Web-based description of the space radiation environment using the Bethe-Bloch model
Cazzola, Emanuele; Calders, Stijn; Lapenta, Giovanni
2016-01-01
Space weather is a rapidly growing area of research not only in scientific and engineering applications but also in physics education and in the interest of the public. We focus especially on space radiation and its impact on space exploration. The topic is highly interdisciplinary, bringing together fundamental concepts of nuclear physics with aspects of radiation protection and space science. We give a new approach to presenting the topic by developing a web-based application that combines some of the fundamental concepts from these two fields into a single tool that can be used in the context of advanced secondary or undergraduate university education. We present DREADCode, an outreach or teaching tool to rapidly assess the current conditions of the radiation field in space. DREADCode uses the available data feeds from a number of ongoing space missions (ACE, GOES-13, GOES-15) to produce a first order approximation of the radiation dose an astronaut would receive during a mission of exploration in deep space (i.e. far from the Earth’s shielding magnetic field and from the radiation belts). DREADCode is based on an easy-to-use GUI interface available online from the European Space Weather Portal (www.spaceweather.eu/dreadcode). The core of the radiation transport computation to produce the radiation dose from the observed fluence of radiation observed by the spacecraft fleet considered is based on a relatively simple approximation: the Bethe-Bloch equation. DREADCode also assumes a simplified geometry and material configuration for the shields used to compute the dose. The approach is approximate and sacrifices some important physics on the altar of rapid execution time, which allows a real-time operation scenario. There is no intention here to produce an operational tool for use in space science and engineering. Rather, we present an educational tool at undergraduate level that uses modern web-based and programming methods to learn some of the most important
de Melo, Pedro Miguel M. C.; Marini, Andrea
2016-04-01
We present a full ab initio description of the coupled out-of-equilibrium dynamics of photons, phonons, and electrons. In the present approach, the quantized nature of the electromagnetic field as well as of the nuclear oscillations is fully taken into account. The result is a set of integrodifferential equations, written on the Keldysh contour, for the Green's functions of electrons, phonons, and photons where the different kinds of interactions are merged together. We then concentrate on the electronic dynamics in order to reduce the problem to a computationally feasible approach. By using the generalized Baym-Kadanoff ansatz and the completed collision approximation, we introduce a series of efficient but controllable approximations. In this way, we reduce all equations to a set of decoupled equations for the density matrix that describe all kinds of static and dynamical correlations. The final result is a coherent, general, and inclusive scheme to calculate several physical quantities: carrier dynamics, transient photoabsorption, and light emission, all of which include, at the same time, electron-electron, electron-phonon, and electron-photon interactions. We further discuss how all these observables can be easily calculated within the present scheme using a fully atomistic ab initio approach.
Zen, Andrea; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo
2014-01-01
Diradical molecules are essential species involved in many organic and inorganic chemical reactions. The computational study of their electronic structure is often challenging, because a reliable description of the correlation, and in particular of the static one, requires multi-reference techniques. The Jastrow correlated Antisymmetrized Geminal Power (JAGP) is a compact and efficient wave function ansatz, based on the valence-bond representation, which can be used within Quantum Monte Carlo (QMC) approaches. The AGP part can be rewritten in terms of molecular orbitals, obtaining a multi-determinant expansion with zero-seniority number. In the present work we demonstrate the capability of the JAGP ansatz to correctly describe the electronic structure of two diradical prototypes: the orthogonally twisted ethylene, C2H4, and the methylene, CH2, representing respectively a homosymmetric and heterosymmetric system. On the other hand, we show that the simple ansatz of a Jastrow correlated Single Determinant (JSD)...
Puschnig, Peter; Ambrosch-Draxl, Claudia
2007-03-01
The solution of the Bethe-Salpeter equation (BSE) has turned out to be the method of choice for the ab-initio calculation of optical properties of semiconductors and insulators which is capable of correctly accounting for excitonic effects. Commonly, however, the coupling between the resonant and anti-resonant excitations is neglected, referred to as the Tamm-Dancoff approximation (TDA). This is well justified in many cases, in particular, for the working horses of theoretical solid state physics, such as bulk Si and GaAs. Here, we report on a first-principles investigation of the optical properties of organic semiconductors which are highly anisotropic systems. We find that the TDA no longer holds in such low-dimensional systems, where the exciton binding energies are no longer small compared to the band gaps. Going beyond the TDA leads to an increase of the exciton binding energy in the order of several tenths of an eV thereby considerably improving the agreement with experiment.
Transformations for the variable coefficient Ginzburg Landau equation with symbolic computation
Institute of Scientific and Technical Information of China (English)
LIU Jian-guo; LI Ye-zhou
2006-01-01
This article is devoted to seek the solutions of the variable coefficient Ginzburg-Landau (vcGL) equation. With the help of symbolic computation and a direct ans(a)tz, four transformations, reduction of the vcGL equation to the standard and cylindrical nonlinear Schr(o)dinger equation, which have been found as variety of analytic solutions were obtained. Substituting these solutions into those transformations, the corresponding analytic solutions for the vcGL were obtained.
Higher order asymptotics for the Hirota equation via Deift–Zhou higher order theory
Energy Technology Data Exchange (ETDEWEB)
Huang, Lin, E-mail: huangl12@fudan.edu.cn [School of Mathematical Sciences, Fudan University, Shanghai 200433 (China); Xu, Jian, E-mail: jianxu02@gmail.com [College of Science, University of Shanghai for Science and Technology, Shanghai 200093 (China); Fan, En-gui, E-mail: faneg@fudan.edu.cn [School of Mathematical Sciences, Fudan University, Shanghai 200433 (China)
2015-01-02
In this paper, the Deift–Zhou higher order asymptotic theory is used to further establish the full asymptotic expansion for the solution of the Hirota equation to all order, as t→∞. The method is rigorous and does not rely on an a priori ansatz for the form of the solution. - Highlights: • Give RHP for Hirota equation. • Systemically apply Deift–Zhou theory. • Give full asymptotics for Hirota equation.
Accuracy of the Bethe approximation for hyperparameter estimation in probabilistic image processing
International Nuclear Information System (INIS)
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
A new integral representation for the scalar products of Bethe states for the XXX spin chain
Kazama, Yoichi; Komatsu, Shota; Nishimura, Takuya
2013-09-01
Based on the method of separation of variables due to Sklyanin, we construct a new integral representation for the scalar products of the Bethe states for the SU(2) XXX spin 1/2 chain obeying the periodic boundary condition. Due to the compactness of the symmetry group, a twist matrix must be introduced at the boundary in order to extract the separated variables properly. Then by deriving the integration measure and the spectrum of the separated variables, we express the inner product of an on-shell and an off-shell Bethe states in terms of a multiple contour integral involving a product of Baxter wave functions. Its form is reminiscent of the integral over the eigenvalues of a matrix model and is expected to be useful in studying the semi-classical limit of the product.
A new integral representation for the scalar products of Bethe states for the XXX spin chain
Kazama, Yoichi; Nishimura, Takuya
2013-01-01
Based on the method of separation of variables due to Sklyanin, we construct a new integral representation for the scalar products of the Bethe states for the SU(2) XXX spin 1/2 chain obeying the periodic boundary condition. Due to the compactness of the symmetry group, a twist matrix must be introduced at the boundary in order to extract the separated variables properly. Then by deriving the integration measure and the spectrum of the separated variables, we express the inner product of an on-shell and an off-shell Bethe states in terms of a multiple contour integral involving a product of Baxter wave functions. Its form is reminiscent of the integral over the eigenvalues of a matrix model and is expected to be useful in studying the semi-classical limit of the product.
Calculation of the relativistic Bethe logarithm in the two-center problem
Korobov, Vladimir I; Karr, Jean-Philippe
2013-01-01
We present a variational approach to evaluate relativistic corrections of order \\alpha^2 to the Bethe logarithm for the ground electronic state of the Coulomb two center problem. That allows to estimate the radiative contribution at m\\alpha^7 order in molecular-like three-body systems such as hydrogen molecular ions H_2^+ and HD^+, or antiprotonic helium atoms. While we get 10 significant digits for the nonrelativistic Bethe logarithm, calculation of the relativistic corrections is much more involved especially for small values of bond length R. We were able to achieve a level of 3-4 significant digits starting from R=0.2 bohr, that will allow to reach 10^{-10} relative uncertainty on transition frequencies.
International Nuclear Information System (INIS)
For the XXX Heisenberg spin-1/2 finite chain with integrable open boundary, the scalar products and the norm of Bethe eigenstates are computed directly in the F-basis. The results are represented as determinants of usual functions of the parameters of the model. The Gaudin formula for the square of the norm of the Bethe wave functions is proved for the case of integrable open boundary condition
International Nuclear Information System (INIS)
Spin and pseudospin symmetries of Dirac equation are solved under scalar and vector generalized isotonic oscillators and Cornell potential as a tensor interaction for arbitrary quantum number via the analytical ansatz approach. The spectrum of the system is numerically reported for typical values of the potential parameters
New Families of Nontravelling Wave Solutions to Two (3+1)-Dimensional Equations
International Nuclear Information System (INIS)
In this paper, two (3+1)-dimensional equations are investigated. Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types of exact solutions including some arbitrary functions. When these arbitrary functions are taken as some special functions, these solutions possess abundant structures. These solutions contain soliton-like solutions and rational solutions.
Stability estimate for the relativistic Schrödinger equation with time-dependent vector potentials
International Nuclear Information System (INIS)
We consider the relativistic Schrödinger equation with a time dependent vector and scalar potential on a bounded cylindrical domain. Using a geometric optics ansatz we establish a logarithmic stability estimate for the recovery of vector and scalar potentials. (paper)
Bondarenko, S G; Rogochaya, E P
2011-01-01
The electrodisintegration of the deuteron is considered within a relativistic model of nucleon-nucleon interaction based on the Bethe-Salpeter approach with a separable interaction kernel. The exclusive cross section is calculated within the impulse approximation under various kinematic conditions. Final state interactions between the outgoing nucleons are taken into account. The comparison of nonrelativistic and relativistic calculations is presented. Partial-wave states of the neutron-proton pair with total angular momentum $J=0,1$ are considered.
Electronic structure of disordered binary alloys with short range correlation in Bethe lattice
International Nuclear Information System (INIS)
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)
A Generalized Uhlenbeck and Beth Formula for the Third Cluster Coefficient
Larsen, Sigurd Yves; Amaya-Tapia, Alejandro
2016-01-01
Relatively recently (A. Amaya-Tapia, S. Y. Larsen and M. Lassaut. Ann. Phys., vol. 306 (2011) 406), we presented a formula for the evaluation of the third Bose fugacity coefficient - leading to the third virial coefficient - in terms of three-body eigenphase shifts, for particles subject to repulsive forces. An analytical calculation for a 1-dim. model, for which the result is known, confirmed the validity of this approach. We now extend the formalism to particles with attractive forces, and therefore must allow for the possibility that the particles have bound states. We thus obtain a true generalization of the famous formula of Uhlenbeck and Beth (G.E. Uhlenbeck and E. Beth. Physica, vol. 3 (1936) 729; E. Beth and G.E. Uhlenbeck. ibid, vol.4 (1937) 915) (and of Gropper (L. Gropper. Phys. Rev. vol. 50 (1936) 963; ibid vol. 51 (1937) 1108)) for the second virial. We illustrate our formalism by a calculation, in an adiabatic approximation, of the third cluster in one dimension, using McGuire's model as in our ...
Towards a model of pion generalized parton distributions from Dyson-Schwinger equations
Energy Technology Data Exchange (ETDEWEB)
Moutarde, H. [CEA, Centre de Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette (France)
2015-04-10
We compute the pion quark Generalized Parton Distribution H{sup q} and Double Distributions F{sup q} and G{sup q} in a coupled Bethe-Salpeter and Dyson-Schwinger approach. We use simple algebraic expressions inspired by the numerical resolution of Dyson-Schwinger and Bethe-Salpeter equations. We explicitly check the support and polynomiality properties, and the behavior under charge conjugation or time invariance of our model. We derive analytic expressions for the pion Double Distributions and Generalized Parton Distribution at vanishing pion momentum transfer at a low scale. Our model compares very well to experimental pion form factor or parton distribution function data.
Self-Similar Solutions of Three-Dimensional Navier-Stokes Equation
International Nuclear Information System (INIS)
In this article we will present pure three dimensional analytic solutions for the Navier-Stokes and the continuity equations in Cartesian coordinates. The key idea is the three-dimensional generalization of the well-known self-similar Ansatz of Barenblatt. A geometrical interpretation of the Ansatz is given also. The results are the Rummer functions or strongly related. Our final formula is compared with other results obtained from group theoretical approaches. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Infrared conductivity of cuprates using Yang-Rice-Zhang ansatz: Review of our recent investigations
International Nuclear Information System (INIS)
A review of our recent investigations related to the ac transport properties in the psedogapped state of cuprate high temperature superconductors is presented. For our theoretical calculations we use a phenomenological Green’s function proposed by Yang, Rice and Zhang (YRZ). This is based upon the renormalized mean-field theory of the Hubbard model and takes into account the strong electron-electron interaction present in Cuprates. The pseudogap is also taken into account through a proposed self energy. We have tested the form of the Green’s function by computing ac conductivity of cuprates and then compared with experimental results. We found agreement between theory and experiment in reproducing the doping evolution of ac conductivity but there is a problem with absolute magnitudes and their frequency dependence. This shows a partial success of the YRZ ansatz. The ways to rectify it are suggested and worked out
Füllsack, Manfred
1999-01-01
Als Teil einer breiter angelegten Untersuchungsreihe zur Habermas/Luhmann-Debatte untersucht der folgende Aufsatz einen Vorwurf Luhmanns und einiger seiner Anhänger, nach dem die diskurstheoretische Konzeption von Jürgen Habermas von überkommenen "quasi-metaphysischen" Prämissen, genauer von einem substanztheoretischen Ansatz ausgehe, und schon deswegen nicht mehr zeitgemäß sei.
Permutation-type solutions to the Yang-Baxter and other n-simplex equations
Hietarinta, Jarmo
1997-01-01
We study permutation type solutions to n-simplex equations, that is, solutions whose R matrix can be written as a product of delta- functions depending linearly on the indices. With this ansatz the D^{n(n+1)} equations of the n-simplex equation reduce to an [n(n+1)/2+1]x[n(n+1)/2+1] matrix equation over Z_D. We have completely analyzed the 2-, 3- and 4-simplex equations in the generic D case. The solutions show interesting patterns that seem to continue to still higher simplex equations.
Electromagnetic Currents and the Blankenbecler-Sugar Equation
Coester, F
1993-01-01
The effective electromagnetic current density for a two-nucleon system that is described by the Blankenbecler-Sugar equation is derived. In addition to the single nucleon currents there are exchange currents of two different origins. The first is the exchange current that is required to compensate for the violation of the continuity equation in the impulse approximation. The second is an exchange current, which arises in the quasipotential reduction from the Bethe-Salpeter equation, and which represents effects of suppressed degrees of freedom. Explicit general expressions are given for both of these exchange currents. The results are applicable to both elastic and inelastic processes.
Electromagnetic currents and the Blankenbecler-Sugar equation
International Nuclear Information System (INIS)
The effective electromagnetic current density for a two-nucleon system that is described by the Blankenbecler-Sugar equation is derived. In addition to the single nucleon currents there are exchange currents of two different origins. The first is the exchange current that is required to compensate for the violation of the continuity equation in the impulse approximation. The second is an exchange current, which arises in the quasipotential reduction from the Bethe-Salpeter equation and which represents effects of suppressed degrees of freedom. Explicit general expressions are given for both of these exchange currents. The results are applicable to both elastic and inelastic processes. 26 refs
Martirosyan, Arax; Saakian, David B.
2012-01-01
We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the Chemical Master Equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of Van Kampen method from HJE approach using a special ansatz. Using the Van Kampen method, we...
International Nuclear Information System (INIS)
The improved tanh function method [Commun. Theor. Phys. (Beijing, China) 43 (2005) 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the (2+1)-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.
An alternative S-matrix for N = 6 Chern-Simons theory?
International Nuclear Information System (INIS)
We have recently proposed an S-matrix for the planar limit of the N = 6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena which leads to the all-loop Bethe ansatz equations conjectured by Gromov and Vieira. An unusual feature of this proposal is that the scattering of A and B particles is reflectionless. We consider here an alternative S-matrix, for which A-B scattering is not reflectionless. We argue that this S-matrix does not lead to the Bethe ansatz equations which are consistent with perturbative computations.
A unified description for nuclear equation of state and fragmentation in heavy ion collisions
Pan, Jicai; Gupta, Subal Das
1995-01-01
We propose a model that provides a unified description of nuclear equation of state and fragmentations. The equation of state is evaluated in Bragg-Williams as well as in Bethe-Peierls approximations and compared with that in the mean field theory with Skyrme interactions. The model shows a liquid-gas type phase transition. The nuclear fragment distributions are studied for different densities at finite temperatures. Power law behavior for fragments is observed at critical point. The study of...
Darboux Transformation and Variable Separation Approach: the Nizhnik-Novikov-Veselov Equation
Institute of Scientific and Technical Information of China (English)
胡恒春; 楼森岳; 刘青平
2003-01-01
Darboux transformation (DT) is developed to systematically find variable separation solutions for the NizhnikNovikov-Veselov equation. Starting from a seed solution with some arbitrary functions, the one-step DT yields the variable separable solutions, which can be obtained from the truncated Painleve analysis, and the two-step DT leads to some new variable separable solutions, which are the generalization of the known results obtained by using a guess ansatz to solve the generalized trilinear equation.
Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential
Energy Technology Data Exchange (ETDEWEB)
Iacob, Felix, E-mail: felix@physics.uvt.ro [West University of Timişoara, V. Pârvan 4, Timişoara 300223 (Romania); Lute, Marina, E-mail: marina.lute@upt.ro [Politehnica University of Timişoara, Traian Lalescu 2, Timişoara 300223 (Romania)
2015-12-15
We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.
Singular and non-topological soliton solutions for nonlinear fractional differential equations
Institute of Scientific and Technical Information of China (English)
Ozkan Guner
2015-01-01
In this article, the fractional derivatives are described in the modified Riemann–Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations (FDEs) based on a fractional complex transform and apply it to solve nonlinear space–time fractional equations. As a result, the non-topological as well as the singular soliton solutions are obtained. This method can be suitable and more powerful for solving other kinds of nonlinear fractional FDEs arising in mathematical physics.
Free energy calculations, enhanced by a Gaussian ansatz, for the "chemical work" distribution.
Boulougouris, Georgios C
2014-05-15
The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the "chemical work" of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the "irreversible" work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible "chemical work" minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the "chemical work," accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the "chemical work." For a more general free energy perturbation scheme that the Gaussian ansatz may not be
Thermodynamics of 1D N-Component Bariev Model Under Open Boundary Conditions
Institute of Scientific and Technical Information of China (English)
WANG Chun; KE San-Min; YUE Rui-Hong
2006-01-01
The thermodynamic Bethe ansatz equations and free energy for 1D N-component Bariev model under open boundary conditions are derived based on the string hypothesis for both, a repulsive and an attractive interaction.These equations are discussed in some limiting cases, such as the ground state, weak and strong couplings.
The electronic structure of the F-center in alkali-halides-The Bethe cluster - lattice
International Nuclear Information System (INIS)
The electronic structure of the F-center in alkali-halides with the NaCl structure has been studied using the Bethe Cluster lattice method. The central cluster has been taken as constituted by the vacancy and the nearest- and second-neighbors to it, respectively cations and anions. The optical transitions have been calculated and compared to experimental data on the location of the peak of the F-absorption band. The agreement obtained indicates that this method may be used to study properties of this defect in alkali halides. (Author)
Femininity, Childhood and the Non-Making of a Sporting Celebrity: The Beth Tweddle Case
Cohen, R. L.
2013-01-01
Gymnastics is regularly classified as a feminine-appropriate sport, embodying grace and elegance. Furthermore, it is the Olympic sport which has regularly produced female sporting celebrities. Beth Tweddle is the most successful British gymnast of all time and the first to achieve international success, culminating in a medal at London 2012, yet she has received relatively little media coverage and few corporate endorsements. Employing a â€˜negative caseâ€™ methodology, this athleteâ€™s relat...
Probabilistic image processing by means of the Bethe approximation for the Q-Ising model
International Nuclear Information System (INIS)
The framework of Bayesian image restoration for multi-valued images by means of the Q-Ising model with nearest-neighbour interactions is presented. Hyperparameters in the probabilistic model are determined so as to maximize the marginal likelihood. A practical algorithm is described for multi-valued image restoration based on the Bethe approximation. The algorithm corresponds to loopy belief propagation in artificial intelligence. We conclude that, in real world grey-level images, the Q-Ising model can give us good results
Ein Frankfurter Physiker, der die Welt veränderte : Hans Albrecht Bethes bewegtes Leben
Schmidt-Böcking, Horst (Prof. Dr.)
2008-01-01
Der Nobelpreisträger Hans Albrecht Bethe war einer der ganz großen Physiker des 20. Jahrhunderts. Er gilt als einer der Väter der modernen Quantenphysik. In seiner Bedeutung für die Entwicklung der modernen Physik kommt er selbst Werner Heisenberg oder Max Planck sehr nahe. Er ist in Frankfurt aufgewachsen, hat hier das Goethe-Gymnasium besucht und an der Universität Frankfurt studiert. 1933 musste er emigrieren, da seine Mutter jüdischen Glaubens war. In seiner Heimatstadt Frankfurt ist er b...
Exclusive electrodisintegration of the deuteron in the Bethe-Salpeter approach
International Nuclear Information System (INIS)
An exclusive process of the deuteron electrodisintegration is analyzed in the framework of the Bethe-Salpeter formalism with a phenomenological Graz II rank-three separable interaction. The approximations made are the neglect of final-state interaction, two-body exchange currents, negative-energy components of the bound-state vertex function and the scattering T matrix. The comparison of the relativistic calculations of the exclusive cross section in the laboratory system with the experimental data is presented within different kinematic conditions
On the electrodisintegration of the deuteron in the Bethe-Salpeter formalism
Bondarenko, S G; Goy, A A; Rogochaya, E P
2006-01-01
The (ed -> enp) process in the frame of the Bethe-Salpeter approach with a separable kernel of the Nucleon-Nucleon (NN) interaction was considered. This conception keeps the covariance of description of the process. Special attention was devoted to a contribution of the D-states of the deuteron in the cross section of the electrodisintegration. It was shown that the spectator particle (neutron) plays an important role. The factorization of a cross section of this reaction in the impulse approximation was checked by analytical and numerical calculations.
Inner products of Bethe states as partial domain wall partition functions
Kostov, Ivan
2012-01-01
We study the inner product of Bethe states in the inhomogeneous periodic XXX spin-1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an on-shell M-magnon state with a generic M-magnon state is given by the same expression as the inner product of a 2M-magnon state with a vacuum descendent. The second inner product is proportional to the partition function of the six-vertex model on a rectangular Lx2M grid, with partial domain-wall boundary conditions.
Introduction to the Statistical Physics of Integrable Many-body Systems
Šamaj, Ladislav Å.; Bajnok, Zoltán
2013-05-01
Preface; Part I. Spinless Bose and Fermi Gases: 1. Particles with nearest-neighbour interactions: Bethe ansatz and the ground state; 2. Bethe ansatz: zero-temperature thermodynamics and excitations; 3. Bethe ansatz: finite-temperature thermodynamics; 4. Particles with inverse-square interactions; Part II. Quantum Inverse Scattering Method: 5. QISM: Yang-Baxter equation; 6. QISM: transfer matrix and its diagonalization; 7. QISM: treatment of boundary conditions; 8. Nested Bethe ansatz for spin-1/2 fermions with delta interactions; 9. Thermodynamics of spin-1/2 fermions with delta interactions; Part III. Quantum Spin Chains: 10. Quantum Ising chain in a transverse field; 11. XXZ Heisenberg chain: Bethe ansatz and the ground state; 12. XXZ Heisenberg chain: ground state in the presence of magnetic field; 13. XXZ Heisenberg chain: excited states; 14. XXX Heisenberg chain: thermodynamics with strings; 15. XXZ Heisenberg chain: thermodynamics without strings; 16. XYZ Heisenberg chain; 17. Integrable isotropic chains with arbitrary spin; Part IV. Strongly Correlated Electrons: 18. Hubbard model; 19. Kondo effect; 20. Luttinger many-fermion model; 21. Integrable BCS superconductors; Part V. Sine-Gordon Model: 22. Classical sine-Gordon theory; 23. Conformal quantization; 24. Lagrangian quantization; 25. Bootstrap quantization; 26. UV-IR relation; 27. Exact finite volume description from XXZ; 28. Two-dimensional Coulomb gas; Appendix A. Spin and spin operators on chain; Appendix B. Elliptic functions; References; Index.
First-Principles Theory of Momentum Dependent Local Ansatz Approach to Correlated Electron System
Chandra, Sumal; Kakehashi, Yoshiro
2016-06-01
We have extended the momentum-dependent local-ansatz (MLA) wavefunction method to the first-principles version using the tight-binding LDA+U Hamiltonian for the description of correlated electrons in the real system. The MLA reduces to the Rayleigh-Schrödinger perturbation theory in the weak correlation limit, and describes quantitatively the ground state and related low-energy excitations in solids. The theory has been applied to the paramagnetic Fe. The role of electron correlations on the energy, charge fluctuations, amplitude of local moment, momentum distribution functions, as well as the mass enhancement factor in Fe has been examined as a function of Coulomb interaction strength. It is shown that the inter-orbital charge-charge correlations between d electrons make a significant contribution to the correlation energy and charge fluctuations, while the intra-orbital and inter-orbital spin-spin correlations make a dominant contribution to the amplitude of local moment and the mass enhancement in Fe. Calculated partial mass enhancements are found to be 1.01, 1.01, and 3.33 for s, p, and d electrons, respectively. The averaged mass enhancement 1.65 is shown to be consistent with the experimental data as well as the recent results of theoretical calculations.
Antiferromagnetism in three-band Hubbard model: Local-ansatz approach
International Nuclear Information System (INIS)
The ground state of the three-band Hubbard Hamiltonian for CuO2 planes of high-Tc superconductors is investigated. Correlations between holes are included by a local-ansatz approach which starts from the Hartree-Fock approximation and emphasizes the local character of hole correlations. It is found that the hole distribution within CuO2 planes and the region of stability of an antiferromagnetic (AF) ground state are significantly modified by hole correlations. At the filling of one hole per CuO2 unit, and for realistic parameters, the ground state exhibits an AF long-range order. Taking into account the effect of quantum fluctuations, the magnetic moment amounts to 0.47μB which agrees very well with the experimental value for La2CuO4. The order parameter decreases with doping and disappears for the doping of 0.06 hole per unit cell. It is found that the nearest-neighbor oxygen hopping destabilizes AF ground state which proves the importance of this parameter for quantitative analysis. A favorable comparison between the present results and those obtained within variational Monte Carlo, as well as within the Gutzwiller approximation for a similar model, is presented
Antiferromagnetism in three-band Hubbard model: Local-ansatz approach
Energy Technology Data Exchange (ETDEWEB)
Dutka, J.; Oles, A.M. (Institute of Physics, Jagellonian University, Reymonta 4, PL-30-059 Krakow, Poland (PL))
1991-03-01
The ground state of the three-band Hubbard Hamiltonian for CuO{sub 2} planes of high-{ital T}{sub {ital c}} superconductors is investigated. Correlations between holes are included by a local-ansatz approach which starts from the Hartree-Fock approximation and emphasizes the local character of hole correlations. It is found that the hole distribution within CuO{sub 2} planes and the region of stability of an antiferromagnetic (AF) ground state are significantly modified by hole correlations. At the filling of one hole per CuO{sub 2} unit, and for realistic parameters, the ground state exhibits an AF long-range order. Taking into account the effect of quantum fluctuations, the magnetic moment amounts to 0.47{mu}{sub {ital B}} which agrees very well with the experimental value for La{sub 2}CuO{sub 4}. The order parameter decreases with doping and disappears for the doping of 0.06 hole per unit cell. It is found that the nearest-neighbor oxygen hopping destabilizes AF ground state which proves the importance of this parameter for quantitative analysis. A favorable comparison between the present results and those obtained within variational Monte Carlo, as well as within the Gutzwiller approximation for a similar model, is presented.
Ferreira, P. Castelo
2009-01-01
It is suggested a metric ansatz to describe local matter in an expanding universe, hence interpolating between the Schwarzschild metric at small spatial scales and the FLRW metric at large spatial scales. This is acomplished maintaining space-time free of singularities except for the Schwarzschild mass pole at the origin as opposed to metrics already considered in the literature with the same purpose, namely the McVittie metric. The modified Newton law is analyzed and the static orbit solutio...
Munshi, Dipak; Coles, Peter; Melott, Adrian L.
1999-01-01
We develop a diagrammatic technique to represent the multi-point cumulative probability density function (CPDF) of mass fluctuations in terms of the statistical properties of individual collapsed objects and relate this to other statistical descriptors such as cumulants, cumulant correlators and factorial moments. We use this approach to establish key scaling relations describing various measurable statistical quantities if clustering follows a simple general scaling ansatz, as expected in hi...
Resurgent transseries $\\&$ Dyson-Schwinger equations
Klaczynski, Lutz
2016-01-01
We employ resurgent transseries as algebraic tools to investigate two self-consistent Dyson-Schwinger equations, one in Yukawa theory and one in quantum electrodynamics. After a brief but pedagogical review, we derive fixed point equations for the associated anomalous dimensions and insert a moderately generic log-free transseries ansatz to study the possible strictures imposed. While proceeding in various stages, we develop an algebraic method to keep track of the transseries' coefficients. We explore what conditions must be violated in order to stay clear of fixed point theorems to eschew a unique solution, if so desired, as we explain. An interesting find is that the flow of data between the different sectors of the transseries shows a pattern typical of resurgence, ie the phenomenon that the perturbative sector of the transseries talks to the nonperturbative ones in a one-way fashion. However, our ansatz is not exotic enough as it leads to trivial solutions with vanishing nonperturbative sectors, even whe...
N=4 mechanics, WDVV equations and roots
International Nuclear Information System (INIS)
N = 4 superconformal multi-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial differential equations linear in U and generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation for F. Putting U≡0 yields a class of models (with zero central charge) which are encoded by the finite Coxeter root systems. We extend these WDVV solutions F in two ways: the An system is deformed n-parametrically to the edge set of a general orthocentric n-simplex, and the BCF-type systems form one-parameter families. A classification strategy is proposed. A nonzero central charge requires turning on U in a given F background, which we show is outside the reach of the standard root-system ansatz for indecomposable systems of more than three particles. In the three-body case, however, this ansatz can be generalized to establish a series of nontrivial models based on the dihedral groups I2(p), which are permutation symmetric if 3 divides p. We explicitly present their full prepotentials.
Efficient on-the-fly interpolation technique for Bethe-Salpeter calculations of optical spectra
Gillet, Yannick; Giantomassi, Matteo; Gonze, Xavier
2016-06-01
The Bethe-Salpeter formalism represents the most accurate method available nowadays for computing neutral excitation energies and optical spectra of crystalline systems from first principles. Bethe-Salpeter calculations yield very good agreement with experiment but are notoriously difficult to converge with respect to the sampling of the electronic wavevectors. Well-converged spectra therefore require significant computational and memory resources, even by today's standards. These bottlenecks hinder the investigation of systems of great technological interest. They are also barriers to the study of derived quantities like piezoreflectance, thermoreflectance or resonant Raman intensities. We present a new methodology that decreases the workload needed to reach a given accuracy. It is based on a double-grid on-the-fly interpolation within the Brillouin zone, combined with the Lanczos algorithm. It achieves significant speed-up and reduction of memory requirements. The technique is benchmarked in terms of accuracy on silicon, gallium arsenide and lithium fluoride. The scaling of the performance of the method as a function of the Brillouin Zone point density is much better than a conventional implementation. We also compare our method with other similar techniques proposed in the literature.
Semi-classical analysis of the inner product of Bethe states
Bettelheim, Eldad
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 subleading 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...
Matveev, V. I.; Makarov, D. N.
2011-09-01
A simple method including nonperturbative shell corrections has been developed for calculating energy losses on complex atoms. The energy losses of fast highly charged ions on neon, argon, krypton, and xenon atoms have been calculated and compared with experimental data. It has been shown that the inclusion of the non-perturbative shell corrections noticeably improves agreement with experimental data as compared to calculations by the Bethe-Bloch formula with the standard corrections. This undoubtedly helps to reduce the number of fitting parameters in various modifications of the Bethe-Bloch formula, which are usually determined semiempirically.
International Nuclear Information System (INIS)
Assessment of research records of Boron Neutron Capture Therapy was conducted at Brookhaven National Laboratory and Beth Israel Deaconess Medical Center using the Code of Federal Regulations, FDA Regulations and Good Clinical Practice Guidelines. Clinical data were collected FR-om subjects' research charts, and differences in conduct of studies at both centers were examined. Records maintained at Brookhaven National Laboratory were not in compliance with regulatory standards. Beth Israel's records followed federal regulations. Deficiencies discovered at both sites are discussed in the reports
Electromagnetic interactions for the two-body spectator equations
Adam, J; Gross, F; Gross, Franz
1998-01-01
This paper presents a new non-associative algebra which is used to (i) show how the spectator (or Gross) two-body equations and electromagnetic currents can be formally derived from the Bethe-Salpeter equation and currents if both are treated to all orders, (ii) obtain explicit expressions for the Gross two-body electromagnetic currents valid to any order, and (iii) prove that the currents so derived are exactly gauge invariant when truncated consistently to any finite order. In addition to presenting these new results, this work complements and extends previous treatments based largely on the analysis of sums of Feynman diagrams.
General analytic methods for solving coupled transport equations: From cosmology to beyond
White, G. A.
2016-02-01
We propose a general method to analytically solve transport equations during a phase transition without making approximations based on the assumption that any transport coefficient is large. Using a cosmic phase transition in the minimal supersymmetric standard model as a pedagogical example, we derive the solutions to a set of 3 transport equations derived under the assumption of supergauge equilibrium and the diffusion approximation. The result is then rederived efficiently using a technique we present involving a parametrized ansatz which turns the process of deriving a solution into an almost elementary problem. We then show how both the derivation and the parametrized ansatz technique can be generalized to solve an arbitrary number of transport equations. Finally we derive a perturbative series that relaxes the usual approximation that inactivates vacuum-expectation-value dependent relaxation and C P -violating source terms at the bubble wall and through the symmetric phase. Our analytical methods are able to reproduce a numerical calculation in the literature.
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I.; Wang, Chunguang
2014-01-01
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.
Boundary energy of the open XXX chain with a non-diagonal boundary term
International Nuclear Information System (INIS)
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. (fast track communications)
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I
2013-01-01
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.
Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
Li, Guang-Liang; Hao, Kun; Yang, Wen-Li; Shi, Kangjie
2016-01-01
The nested off-diagonal Bethe Ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T-Q relations and Bethe Ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the $SU_q(n)$ algebra.
Eigenvectors and scalar products for long range interacting spin chains II: the finite size effects
Serban, D
2013-01-01
In this note, we study the eigenvectors and the scalar products the integrable long-range deformation of a XXX spin chain which is solved exactly by algebraic Bethe ansatz, and it coincides in the bulk with the Inozemtsev spin chain. At the closing point it contains a defect which effectively removes the wrapping interactions. Here we concentrate on determining the defect term for the first non-trivial order in perturbation in the deformation parameter and how it affects the Bethe ansatz equations. Our study is motivated by the relation with the dilatation operator of the N = 4 gauge theory in the su(2) sector.
Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
Li, Guang-Liang; Cao, Junpeng; Hao, Kun; Wen, Fakai; Yang, Wen-Li; Shi, Kangjie
2016-09-01
The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the SUq (3)R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T-Q relations and Bethe ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the SUq (n) algebra.
Accurate calculation of the x-ray absorption spectrum of water via the GW/Bethe-Salpeter equation
Gilmore, Keith; Vinson, John; Kas, Josh; Vila, Fernando; Rehr, John
2014-03-01
We calculate x-ray absorption spectra (XAS) of water within the OCEAN code, which combines plane-wave, pseudopotential electronic structure, PAW transition elements, GW self-energy corrections, and the NIST BSE solver. Due to the computational demands of this approach, our initial XAS calculations were limited to 17 molecule super cells. This lead to unphysical, size dependent effects in the calculated spectra. To treat larger systems, we extended the OCEAN interface to support well-parallelized codes such as QuantumESPRESSO. We also implemented an efficient interpolation scheme of Shirley. We applied this large-scale GW/BSE approach to 64 molecule unit cell structures of water obtained from classical DFT/MD and PIMD simulations. In concurrence with previous work, we find the calculated spectrum both qualitatively and quantitatively reproduces the experimental features. The agreement implies that structures based on PIMD, which are similar to the traditional distorted tetrahedral view, are consistent with experimental observations. Supported by the DOE CMCSN through DOE award DE-SC0005180 (Princeton University) and in part by DOE Grant No. DE-FG03-97ER45623 (JJR) with computer support from NERSC.
On reduction and exact solutions of nonlinear many-dimensional Schroedinger equations
International Nuclear Information System (INIS)
With the help of the canonical decomposition of an arbitrary subalgebra of the orthogonal algebra AO(n) the rank n and n-1 maximal subalgebras of the extended isochronous Galileo algebra, the rank n maximal subalgebras of the generalized extended classical Galileo algebra AG(a,n) the extended special Galileo algebra AG(2,n) and the extended whole Galileo algebra AG(3,n) are described. By using the rank n subalgebras, ansatze reducing the many dimensional Schroedinger equations to ordinary differential equations is found. With the help of the reduced equation solutions exact solutions of the Schroedinger equation are considered
Nonlinear Kramers equation associated with nonextensive statistical mechanics.
Mendes, G A; Ribeiro, M S; Mendes, R S; Lenzi, E K; Nobre, F D
2015-05-01
Stationary and time-dependent solutions of a nonlinear Kramers equation, as well as its associated nonlinear Fokker-Planck equations, are investigated within the context of Tsallis nonextensive statistical mechanics. Since no general analytical time-dependent solutions are found for such a nonlinear Kramers equation, an ansatz is considered and the corresponding asymptotic behavior is studied and compared with those known for the standard linear Kramers equation. The H-theorem is analyzed for this equation and its connection with Tsallis entropy is investigated. An application is discussed, namely the motion of Hydra cells in two-dimensional cellular aggregates, for which previous measurements have verified q-Gaussian distributions for velocity components and superdiffusion. The present analysis is in quantitative agreement with these experimental results. PMID:26066118
Analysis of quantum spin models on hyperbolic lattices and Bethe lattice
Daniška, Michal; Gendiar, Andrej
2016-04-01
The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the tensor product variational formulation algorithm. The lattices are constructed by tessellation of congruent polygons with coordination number equal to four. The calculated ground-state energies of the XY and Heisenberg models and the phase transition magnetic field of the Ising model on the series of lattices are used to estimate the corresponding quantities of the respective models on the Bethe lattice. The hyperbolic lattice geometry induces mean-field-like behavior of the models. The ambition to obtain results on the non-Euclidean lattice geometries has been motivated by theoretical studies of the anti-de Sitter/conformal field theory correspondence.
Exact results for the spherical model with competing interactions on the Bethe lattice
Pimpinelli, Alberto; Cassi, Davide
1991-02-01
We extend to next-nearest-neighbor (NNN) interactions a technique which allows the exact solution of the spherical model of Berlin and Kac on a general discrete geometrical structure (a graph). We give the solution when the graph is a Bethe lattice. The model shows collinear (ferromagnetic or antiferromagnetic) long-range order at low temperature when NNN interactions favor the same order as nearest-neighbor ones, while it is disordered at any finite temperature when competition exceeds a critical value. For vanishing nearest-neighbor interaction the lattice decouples in two independent Cayley cacti; if the exchange on each sublattice is ferromagnetic, the model becomes ordered at a nonzero temperature, while antiferromagnetic exchange gives again disorder at any temperature.
Polymer models with competing collapse interactions on Husimi and Bethe lattices
Pretti, M.
2016-03-01
In the framework of Husimi and Bethe lattices, we investigate a generalized polymer model that incorporates as special cases different models previously studied in the literature, namely, the standard interacting self-avoiding walk, the interacting self-avoiding trail, and the vertex-interacting self-avoiding walk. These models are characterized by different microscopic interactions, giving rise, in the two-dimensional case, to collapse transitions of an apparently different nature. We expect that our results, even though of a mean-field type, could provide some useful information to elucidate the role of such different θ points in the polymer phase diagram. These issues are at the core of a long-standing unresolved debate.
On the extension of the Bethe-Weizsacker mass formula to light nuclei
Basu, D N
2004-01-01
Some general features of the Bethe-Weizsacker mass formula recently extended to light nuclei and some new shell closures have been explored. Though this formula improves fits to the properties of light nuclei and it does seem to work well in reproducing the irregularities in the magic numbers found in that region, yet it is not well tuned for predicting finer details. The mass predictions have also been found to be less accurate compared to those by the macroscopic-microscopic calculations. It is concluded that such semi-empirical mass formulae can not be a substitute for more fundamental mass formulae having its origin based upon the basic nucleon-nucleon effective interaction.
Analysis of quantum spin models on hyperbolic lattices and Bethe lattice
International Nuclear Information System (INIS)
The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the tensor product variational formulation algorithm. The lattices are constructed by tessellation of congruent polygons with coordination number equal to four. The calculated ground-state energies of the XY and Heisenberg models and the phase transition magnetic field of the Ising model on the series of lattices are used to estimate the corresponding quantities of the respective models on the Bethe lattice. The hyperbolic lattice geometry induces mean-field-like behavior of the models. The ambition to obtain results on the non-Euclidean lattice geometries has been motivated by theoretical studies of the anti-de Sitter/conformal field theory correspondence. (paper)
Network formed by movements of random walkers on a Bethe lattice
International Nuclear Information System (INIS)
We investigate a stochastic model of network formation where short-cut edges are assumed to be created between vertices in traces of random walkers. The network initially starts from a tree-like structure (Bethe lattice) with a finite number of shells, and develops into a complex network with many circuits generated by the movement of random walkers. We show that the resulting network has a power-law in the degree distribution with an exponent smaller than 2, and demonstrate the robustness against attacks on hubs in the networks. While scale-free networks without a degree correlation are usually vulnerable to attacks on its hubs, the robustness of the network connectivity in this model comes from a self-similar structure of the network. It is interesting that a simple stochastic process like random walks can cause various structures widely seen in real networks on tree-like graphs which play an important role in the graph theory
Born-Hartree-Bethe approximation in the theory of inelastic electron-molecule scattering
International Nuclear Information System (INIS)
We propose a new approximation in the theory of inelastic electron-atom and electron-molecule scattering. Taking into account the completeness property of atomic and molecular wavefunctions, considered in the Hartree approximation, and using Bethe's parametrization for electronic excitations during inelastic collisions via the mean excitation energy, we show that the calculation of the inelastic total integral cross-sections (TICS), in the framework of the first Born approximation, involves only the ground-state wavefunction. The final analytical formula obtained for the TICS, i.e. for the sum of elastic and inelastic ones, contains no adjusting parameters. Calculated TICS for electron scattering by light atoms and molecules (He, Ne, and H2) are in good agreement within the experimental data; results show asymptotic coincidence for heavier ones (Ar, Kr, Xe and N2).
How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application
Ren, Jingli; Zhang, Liying; Siegmund, Stefan
2016-03-01
Inhomogeneous percolation, for its closer relationship with real-life, can be more useful and reasonable than homogeneous percolation to illustrate the critical phenomena and dynamical behaviour of complex networks. However, due to its intricacy, the theoretical framework of inhomogeneous percolation is far from being complete and many challenging problems are still open. In this paper, we first investigate inhomogeneous site percolation on Bethe Lattices with two occupation probabilities, and then extend the result to percolation with m occupation probabilities. The critical behaviour of this inhomogeneous percolation is shown clearly by formulating the percolation probability with given occupation probability p, the critical occupation probability , and the average cluster size where p is subject to . Moreover, using the above theory, we discuss in detail the diffusion behaviour of an infectious disease (SARS) and present specific disease-control strategies in consideration of groups with different infection probabilities.
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
At the beginning of 16th century, mathematicians found it easy to solve equations of the first degree(linear equations, involving x) and of the second degree(quadratic equatiorts, involving x2). Equations of the third degree(cubic equations, involving x3)defeated them.
Directory of Open Access Journals (Sweden)
Kilic Bulent
2016-01-01
Full Text Available This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE with time dependent coefficients.
Dispersive shock waves in the Kadomtsev-Petviashvili and Two Dimensional Benjamin-Ono equations
Ablowitz, Mark J; Ma, Yi-Ping
2015-01-01
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using parabolic front initial data. Employing a front tracking type ansatz exactly reduces the study of DSWs in two space one time (2+1) dimensions to finding DSW solutions of (1+1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived in general and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with excellent agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with remarkable agreement. It i...
Directory of Open Access Journals (Sweden)
M. K. Bahar
2013-01-01
Full Text Available Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.
Correlators of the phase model
Bogolyubov, N N; Kitanine, N A
1996-01-01
We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the "darkness formation probability" are calculated in the thermodynamical limit. These results can be used to construct integrable equations for the correlation functions and to calculate there asymptotics.
On the scattering over the GKP vacuum
Fioravanti, Davide; Rossi, Marco
2013-01-01
By converting the Asymptotic Bethe Ansatz of ${\\cal N}=4$ SYM into non-linear integral equations, we find 2D scattering amplitudes of excitations on top of the GKP vacuum. We prove that this is a suitable and powerful set-up for the understanding and computation of the whole S-matrix.
Spectra in Conformal Field Theories from the Rogers Dilogarithm
Kuniba, A; Kuniba, Atsuo; Nakanishi, Tomoki
1992-01-01
We propose a system of functional relations having a universal form connected to the $U_q(X^{(1)}_r)$ Bethe ansatz equation. Based on the analysis of it, we conjecture a new sum formula for the Rogers dilogarithm function in terms of the scaling dimensions of the $X^{(1)}_r$ parafermion conformal field theory.
The sine-Gordon model revisited I
Energy Technology Data Exchange (ETDEWEB)
Niccoli, G.; Teschner, J.
2009-10-15
We study integrable lattice regularizations of the Sine-Gordon model with the help of the Separation of Variables method of Sklyanin and the Baxter Q-operators. This allows us to characterize the spectrum (eigenvalues and eigenstates) completely in terms of polynomial solutions of the Baxter equation with certain properties. This result is analogous to the completeness of the Bethe ansatz. (orig.)
Boundary Effects for One-Dimensional Bariev Model with Hard-Core Repulsion
Institute of Scientific and Technical Information of China (English)
LI Xiao-Jun; YUE Rui-Hong
2004-01-01
For the Bariey model for correlated hopping in one dimension under open boundary conditions, the Bethe ansatz equations are analyzed for both a repulsive and an attractive interaction in several limiting cases, i.e., the ground state, the weak and strong coupling limits. The contributions of the boundary fields to both the magnetic susceptibility and the specific heat are obtained.
Non-stationary probabilities for the asymmetric exclusion process on a ring
Indian Academy of Sciences (India)
V B Priezzhev
2005-06-01
A solution of the master equation for a system of interacting particles for finite time and particle density is presented. By using a new form of the Bethe ansatz, the totally asymmetric exclusion process on a ring is solved for arbitrary initial conditions and time intervals.
Classical and quantum dynamics of two-dimensional nonlinear field theories: a review
International Nuclear Information System (INIS)
Progress in understanding and solving a large class of two-dimensional nonlinear quantum field theories is reviewed. The discovery and development of the inverse scattering method for solving partial differential equations, and development of new perturbative methods are discussed. The generalized Bethe-ansatz method and its application to exactly diagonalize a fermionic problem are covered. 52 references
Dynamical systems theory for the Gardner equation.
Saha, Aparna; Talukdar, B; Chatterjee, Supriya
2014-02-01
The Gardner equation u(t) + auu(x) + bu(2)u(x)+μu(xxx) = 0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u(x,t) = φ(ξ), ξ = x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ϕ with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and μ. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013)]. PMID:25353592
Vinson, J.; Rehr, J. J.
2012-11-01
We present ab initio Bethe-Salpeter equation (BSE) calculations of the L2,3 edges of several insulating and metallic compounds containing Ca, V, Fe, Co, Ni, and Cu, spanning a range of 3d-electron occupations. Our approach includes the key ingredients of a unified treatment of both extended states and atomic multiplet effects, i.e., Bloch states, self-consistent crystal potentials, ground-state magnetism, GW self-energy corrections, spin-orbit terms, and Coulomb interactions between the L2 and L3 levels. The method is implemented in the ocean package, which uses plane-wave pseudopotential wave functions as a basis, a projector-augmented-wave construction for the transition matrix elements, and a resolvent formalism for the BSE calculation. The results are in near quantitative agreement with experiment, including both fine structure at the edges and the nonstatistical L3/L2 ratios observed for these systems. Approximations such as time-dependent density-functional theory are shown to be less accurate.
Quarter-BPS solutions in three-dimensional N=16 supergravity and the Liouville equation
Moutsopoulos, George
2016-01-01
We show how by assuming at least 8 real timelike supersymmetries in the maximally supersymmetric three-dimensional ungauged supergravity and a further simplifying Ansatz, we are naturally led to a pair of Liouville field equations. We also show that there are no solutions that preserve only 6 real timelike supersymmetries. The solution relies on the classification of complex spinors of Spin(8) to which the problem quickly reduces.
Reduction of the Poincare gauge field equations by means of a duality rotation
International Nuclear Information System (INIS)
A rather general procedure is developed in order to reduce the two field equations of the Poincare gauge theory of gravity by a modified ansatz for the curvature tensor involving double duality. In the case of quasi-linear Lagrangians of the Yang-Mills type it is shown that non-trivial torsion solutions with duality properties necessarily ''live'' on an Einstein space as metrical background. (author)
SU(N)-QCD2 meson equation in next-to-leading order
International Nuclear Information System (INIS)
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)
Mapping of the classical kinetic balance equations onto the Pauli equation
Pesci, Adriana I.; Goldstein, Raymond E.; Uys, Hermann
2005-01-01
Here we find a mapping onto the Pauli equation of the first two balance equations derived from the classical Boltzmann equation. The essence of this mapping, which we previously used to obtain the particular case of the Sturm-Liouville operator known as Schrödinger's equation, consists of applying a Fourier transform to the momentum coordinate of the distribution function. This procedure introduces a natural parameter η with units of angular momentum. The main difference between the two cases is the conditions imposed on the probability distribution function, a difference most clearly understood at the level of the hydrodynamic equations generated in the first steps of the mapping. The case leading to the Sturm-Liouville operator corresponds to an irrotational flow, while here the ansatz leading to the Pauli equation corresponds to a fluid with non-zero vorticity. In the context of fluid dynamics, the magnitude of the angular momentum associated with the vorticity is η/2. To perform the mapping we follow the standard technique common in hydrodynamic problems, namely writing the Lagrangian for the Euler equations with the corresponding constraints expressed in terms of the Clebsch variables.
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We consider the problem of correlated percolation on a Husimi cactus, which allows finite loops of size l, to investigate the effects of loop formation on percolation properties. In particular, we calculate how the percolation threshold and the percolation probability depend on l and the loop activity n. We calculate the contribution and its dependence on l and n from finite and infinite clusters to all densities. We show that macroscopic loops are formed immediately after percolation, and we calculate their density dependence on l and n. We compare the results on Husimi cactus with those on a Bethe lattice. We finally establish that the Husimi cactus turns into a Bethe lattice as l→∞. (author)
Sciarappa, Antonio
2016-01-01
Bethe/Gauge correspondence as it is usually stated is ill-defined in five dimensions and needs a "non-perturbative" completion; a related problem also appears in three dimensions. It has been suggested that this problem, probably due to incompleteness of Omega background regularization in odd dimension, may be solved if we consider gauge theory on compact $S^5$ and $S^3$ geometries. We will develop this idea further by giving a full Bethe/Gauge correspondence dictionary on $S^5$ and $S^3$ focussing mainly on the eigenfunctions of (open and closed) relativistic 2-particle Toda chain and its quantized spectral curve: these are most properly written in terms of non-perturbatively completed NS open topological strings. A key ingredient is Faddeev's modular double structure which is naturally implemented by the $S^5$ and $S^3$ geometries.
International Nuclear Information System (INIS)
The analytic method used in the evaluation of this type of supper-prompt critical core disruptive accident (CDA) in fast reactor was originally developed by Bethe and Tait in 1956, and had been modified by many authors since then. It is still of value today, because of its simplicity and relative ease to extend for improvements. It is particularly useful tp perform various parametric studies for better understanding of core disassembly process of LMFRs as well as to estimate upper-limit values of the energy release resulting from a power excursion. Moreover, the method would provide an essential experience and Knowledge base on the analysis of the hypothetical core disruptive accidents(HCDAs) in KALIMER. This report describes the concept and mathematical formations of the modified Bethe-Tait methods, and some salient results and insights that had come out of their use for the hypothetical supper-prompt critical accidents in fast reactors. (author)
A remark on an ansatz by M.W. Evans and the so-called Einstein-Cartan-Evans unified field theory
Hehl, F W
2006-01-01
M.W.Evans tried to relate the electromagnetic field strength to the torsion of a Riemann-Cartan spacetime. We show that this ansatz is untenable for at least two reasons: (i) Geometry: Torsion is related to the (external) translation group and cannot be linked to an internal group, like the U(1) group of electrodynamics. (ii) Electrodynamics: The electromagnetic field strength as a 2-form carries 6 independent components, whereas Evans' electromagnetic construct F^\\a is a vector-valued 2-form with 24 independent components. This doesn't match. One of these reasons is already enough to disprove the ansatz of Evans.
Maksimova A.A.
2016-01-01
The article presents the analysis carried out by Ph. D. Beth Ann Beschorner (University of Iowa, USA) which concerns the training program for parents aimed at teaching them how to arrange the Dialogic reading with their childrenand and which makes it possible to conclude that due to the experience and direct contact with the written language in preschool age the idea of literacy was being formed. The article compares the empirical data obtained independently in different areas of scientific k...
String equation from field equation
Gurovich, V T
1996-01-01
It is shown that the string equation can be obtain from field equations. Such work is performed to scalar field. The equation obtained in nonrelativistic limit describes the nonlinear string. Such string has the effective elasticity connencted with the local string curvature. Some examples of the movement such nonlinear elastic string are considered.
Remark on the phase shift in the Kuzmak-Whitham ansatz
Dobrokhotov, S. Yu.; Minenkov, D. S.
2011-03-01
We consider one-phase ( formal) asymptotic solutions in the Kuzmak-Whitham form for the nonlinear Klein-Gordon equation and for the Korteweg-de Vries equation. In this case, the leading asymptotic expansion term has the form X( S( x, t)/ h+Φ( x, t), I( x, t), x, t) + O( h), where h ≪ 1 is a small parameter and the phase S}( x, t) and slowly changing parameters I( x, t) are to be found from the system of "averaged" Whitham equations. We obtain the equations for the phase shift Φ( x, t) by studying the second-order correction to the leading term. The corresponding procedure for finding the phase shift is then nonuniform with respect to the transition to a linear (and weakly nonlinear) case. Our observation, which essentially follows from papers by Haberman and collaborators, is that if we incorporate the phase shift Φ into the phase and adjust the parameter Ĩ by setting tilde S = S + hΦ+ O( h 2), Ĩ = I + hI 1 + O( h 2), then the functions tilde S ( x, t, h) and Ĩ( x, t, h) become solutions of the Cauchy problem for the same Whitham system but with modified initial conditions. These functions completely determine the leading asymptotic term, which is X( tilde S ( x, t, h)/ h, Ĩ( x, t, h), x, t) + O( h).
CCCP Algorithms to Minimize the Bethe free energy of 3-SAT Problem
Habibulla, Yusupjan
2014-01-01
The k-sat problem is a prototypical constraint satisfaction problem. There are many algorithms to study k-sat problem, BP algorithm is famous one of them. But BP algorithm does not converge when $\\alpha$(constraint density)is bigger than some threshold value. In this paper we use CCCP (Concave Convex Procedure) algorithm to study 3-sat problem and we get better results than BP algorithm that CCCP algorithm still converges when BP algorithm does not converge. Our work almost builds on recent results by Yuille \\cite{Yuille2002} who apply the CCCP algorithm to Bethe and Kikuchi free energies and obtained two algorithms on 2D and 3D spin glasses. Our implementation of CCCP algorithm on 3-sat problem is some different from his implementation and we have some different views about CCCP algorithm's some properties. Some difference of these maybe because of CCCP algorithm have different properties and implementation process on different problem and some others of these are related to the CCCP algorithm itself. Our wo...
Effects of the projectile electronic structure on Bethe-Bloch stopping parameters for Ag
Moussa, D.; Damache, S.; Ouichaoui, S.
2010-06-01
Energy losses of protons and alpha particles in silver have been accurately measured under the same experimental conditions over the velocity range E=(0.192-2.595) MeV/amu using the transmission method. Deduced S(E) stopping powers are compared to most accurate ones from the literature, to values generated by the SRIM-2008 computer code and to ICRU-49 compilation. They were analyzed in the framework of modified Bethe-Bloch theory for extracting Ag target mean excitation and ionization potential, I, and Barkas effect parameter, b. Values of ( 466±5) eV and 1.20±0.01 for these two parameters were inferred from the proton S(E) data while the alpha particle data yielded values of (438±4) eV and 1.38±0.01, respectively. The ( I, b) stopping parameters thus exhibit opposite variations as the projectile charge increases, similarly as we have found previously for nickel [6]. This can be ascribed only to an effect of the projectile electronic structure at low velocities. The obtained results are discussed in comparison to previous ones reported in the literature.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Institute of Scientific and Technical Information of China (English)
陈勇; 闫振亚; 李彪; 张鸿庆
2003-01-01
In this paper, we make use of a new generalized ansatz in the homogeneous balance method, the well-known Riccati equation and the symbolic computation to study a generalized Hirota-Satsuma coupled KdV system and a coupled MKdV equation, respectively. As a result, numerous explicit exact solutions, comprising new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.
Munshi, D; Melott, A L; Munshi, Dipak; Coles, Peter; Melott, Adrian L.
1999-01-01
We develop a diagrammatic technique to represent the multi-point cumulative probability density function (CPDF) of mass fluctuations in terms of the statistical properties of individual collapsed objects and relate this to other statistical descriptors such as cumulants, cumulant correlators and factorial moments. We use this approach to establish key scaling relations describing various measurable statistical quantities if clustering follows a simple general scaling ansatz, as expected in hierarchical models. We test these detailed predictions against high-resolution numerical simulations. We show that, when appropriate variables are used, the count probability distribution function (CPDF) and void probability distribution function (VPF) shows clear scaling properties in the non-linear regime. Generalising the results to the two-point count probability distribution function (2CPDF), and the bivariate void probability function (2VPF) we find good match with numerical simulations. We explore the behaviour of t...
Cluster virial expansion for the equation of state of partially ionized hydrogen plasma.
Omarbakiyeva, Y A; Fortmann, C; Ramazanov, T S; Röpke, G
2010-08-01
We study the contribution of electron-atom interaction to the equation of state for partially ionized hydrogen plasma using the cluster-virial expansion. We use the Beth-Uhlenbeck approach to calculate the second virial coefficient for the electron-atom (bound cluster) pair from the corresponding scattering phase shifts and binding energies. Experimental scattering cross-sections as well as phase shifts calculated on the basis of different pseudopotential models are used as an input for the Beth-Uhlenbeck formula. By including Pauli blocking and screening in the phase shift calculation, we generalize the cluster-virial expansion in order to cover also near solid density plasmas. We present results for the electron-atom contribution to the virial expansion and the corresponding equation of state, i.e. pressure, composition, and chemical potential as a function of density and temperature. These results are compared with semiempirical approaches to the thermodynamics of partially ionized plasmas. Avoiding any ill-founded input quantities, the Beth-Uhlenbeck second virial coefficient for the electron-atom interaction represents a benchmark for other, semiempirical approaches. PMID:20866926
Weak and strong coupling limits of the Boltzmann equation in the relaxation-time approximation
Jaiswal, Amaresh; Redlich, Krzysztof
2016-01-01
We consider a momentum dependent relaxation time for the Boltzmann equation in the relaxation time approximation. We employ a power law parametrization for the momentum dependence of the relaxation time, and calculate the shear and bulk viscosity, as well as, the charge and heat conductivity. We show, that for the two popular parametrizations, referred to as the linear and quadratic ansatz, one can obtain transport coefficients which corresponds to the weak and strong coupling regimes, respectively. We also show that, for a system of massless particles with vanishing chemical potential, the off-equilibrium corrections to the phase-space distribution function calculated with the quadratic ansatz are identical with those of the Grad's 14-moment method.
Double scaling limit in random matrix models and a nonlinear hierarchy of differential equations
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We study the critical behaviour of a random Hermitian one-matrix model with nonsymmetric interaction at a critical point, in which the eigenvalue density function has a zero of degree 2m, m ≥ 1, inside a cut. We prove that in the generic case, m = 1, the model exhibits a third-order phase transition in temperature. We formulate an ansatz for the double scaling limit of recurrence coefficients, which is consistent with the quasiperiodic asymptotics of recurrence coefficients in the low temperature region, and from this ansatz we derive the Painleve II hierarchy of ordinary differential equations for the recurrence coefficients. In addition, we derive an integral kernel which governs the double scaling limit of correlation functions
A generalized Bethe-Weizsaecker mass formula for strange hadronic matter
International Nuclear Information System (INIS)
The Bethe-Weizsaecker nuclear mass formula is extended to strange hadronic matter composed of nucleons, lambdas and cascade hyperons. The generalized formula contains several volume and symmetry terms constrained by phenomenologically determined λ-nuclear, ξ-nuclear and λλ interaction parameters and by hyperon-hyperon (λλ, λξ, ξξ) interaction parameters suggested by One-Boson-Exchange models. We find that hypernuclei are generally unstable to λλ → ξN conversion. For strange hadronic matter, as function of the baryon number A, the line of strong-interaction stability, along which a large strangeness fraction |S|/A ∼ 0.5 - 1.1 and a low charge fraction q/A approx-lt 0.2 hold, and no fission occurs, is determined. The binding energy per baryon increases monotonically to its bulk limit, B/A → 38 MeV, |S|/A → 1.1 and q/A → 0 for the parameters adopted here assuming that the hyperon species saturate at densities similar to those of protons and neutrons in nuclei. Even in the extreme limit of vanishingly small hyperon-hyperon interaction strengths, strange hadronic matter with B/A → 15 MeV, |S|/A → 0.7 and q/A → 0 in the bulk limit should exist; the mass formula reproduces semi-quantitatively recent mean-field calculations which implicitly assumed weak hyperon-hyperon interactions
Simple polynomial approximation to modified Bethe formula low-energy electron stopping powers data
International Nuclear Information System (INIS)
A recently published detailed and exhaustive paper on cross-sections for ionisation induced by keV electrons clearly shows that electron phenomena occurring in parallel with X-ray processes may have been dramatically overlooked for many years, mainly when low atomic number species are involved since, in these cases, the fluorescence coefficient is smaller than the Auger yield. An immediate problem is encountered while attempting to tackle the issue. Accounting for electron phenomena requires the knowledge of the stopping power of electrons within, at least, a reasonably small error. Still, the Bethe formula for stopping powers is known to not be valid for electron energies below 30 keV, and its use leads to values far off experimental ones. Recently, a few authors have addressed this problem and both detailed tables of electron stopping powers for various atomic species and attempts to simplify the calculations, have emerged. Nevertheless, its implementation in software routines to efficiently calculate keV electron effects in materials quickly becomes a bit cumbersome. Following a procedure already used to establish efficient methods to calculate ionisation cross-sections by protons and alpha particles, it became clear that a simple polynomial approximation could be set, which allows retrieving the electronic stopping powers with errors of less than 20% for energies above 500 eV and less than 50% for energies between 50 eV and 500 eV. In this work, we present this approximation which, based on just six parameters, allows to recover electron stopping power values that are less than 20% different from recently published experimentally validated tabulated data
Tricomi, FG
2012-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and differential
Low-Temperature Thermodynamics of $A^{(2)}_2$ and su(3)-invariant Spin Chains
Mezincescu, L; Townsend, P K; Tsvelik, A M; Mezincescu, Luca; Nepomechie, Rafael I.
1993-01-01
We formulate the thermodynamic Bethe Ansatz (TBA) equations for the closed (periodic boundary conditions) $A^{(2)}_2$ quantum spin chain in an external magnetic field, in the (noncritical) regime where the anisotropy parameter $\\eta$ is real. In the limit $\\eta \\to 0$, we recover the TBA equations of the antiferromagnetic su(3)-invariant chain in the fundamental representation. We solve these equations for low temperature and small field, and calculate the specific heat and magnetic susceptibility.
Analytic thermodynamics and thermometry of Gaudin-Yang Fermi gases
Zhao, Erhai; Guan, Xi-Wen; Liu, W. Vincent; Batchelor, M. T.; Oshikawa, Masaki
2009-01-01
We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong...
Sarma, Amarendra K
2012-01-01
We report exact bright and dark soliton solution to the nonlinear evolution equation derived by Moses and Wise [Phys. Rev. Lett. 97, 073903, (2006)] for cascaded quadratic media beyond the slowly varying envelope approximations. The integrability aspects of the model are addressed. The traveling wave hypothesis as well as the ansatz method is employed to obtain an exact 1-soliton solution. Both bright and dark soliton solutions are obtained. The corresponding constraint conditions are obtained in order for the soliton solutions to exist.
Institute of Scientific and Technical Information of China (English)
CHENYong; LIBiao; ZHANGHong-Qing
2003-01-01
Based on the computerized symbolic system Mapte, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions' soliton-like solutions is presented by a new general ansatz. Making use of the method, we consider the (2+1)-dimensional breaking soliton equation, ut + buxxy + 4buvx+4buxv = O,uv=vx, and obtain rich new families of the exact solutions of the breaking sofiton equation, including then on-traveilin~ wave and constant function sofiton-like solutions, singular soliton-like solutions, and triangular function solutions.
Separable Kernel of Nucleon-Nucleon Interaction in the Bethe-Salpeter Approach for J=0,1
Bondarenko, S G; Hamamoto, N; Hosaka, Y; Manabe, Y; Toki, H
2003-01-01
The solution for the nucleon-nucleon T matrix in the framework of the covariant Bethe-Salpeter approach for a two spin-one-half particle system with a separable kernel of interaction is analyzed. The explicit analytical connection between parameters of the separable kernel and low energy scattering parameters, deuteron binding energy and phase shifts is established.Covariant separable kernels for positive-energy partial channels with total angular momentum J=0 (1S0+, 3P0+) and J=1 (3S1+-3D1+, 1P1+, 3P1+) are constructed by using obtained relations.
Hadron-hadron interactions from imaginary-time Nambu-Bethe-Salpeter wave function on the lattice
International Nuclear Information System (INIS)
Imaginary-time Nambu-Bethe-Salpeter (NBS) wave function is introduced to extend our previous approach for hadron-hadron interactions on the lattice. Scattering states of hadrons with different energies encoded in the NBS wave function are utilized to extract non-local hadron-hadron potential. “The ground state saturation”, which is commonly used in lattice QCD but is hard to be achieved for multi-baryons, is not required. We demonstrate that the present method works efficiently for the nucleon-nucleon interaction (the potential and the phase shift) in the 1S0 channel.
Hadron-hadron interactions from imaginary-time Nambu-Bethe-Salpeter wave function on the lattice
Energy Technology Data Exchange (ETDEWEB)
Ishii, Noriyoshi, E-mail: ishii@ribf.riken.jp [Kobe Branch, Center for Computational Sciences, University of Tsukuba, in RIKEN Advanced Institute for Computational Science (AICS), Portisland, Kobe 650-0047 (Japan); Aoki, Sinya [Graduate School of Pure and Applied Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571 (Japan); Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Doi, Takumi [Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 (Japan); Hatsuda, Tetsuo [Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 (Japan); Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan); Ikeda, Yoichi [Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551 (Japan); Inoue, Takashi [Nihon University, College of Bioresource Sciences, Fujisawa 252-0880 (Japan); Murano, Keiko [Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 (Japan); Nemura, Hidekatsu; Sasaki, Kenji [Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan)
2012-06-12
Imaginary-time Nambu-Bethe-Salpeter (NBS) wave function is introduced to extend our previous approach for hadron-hadron interactions on the lattice. Scattering states of hadrons with different energies encoded in the NBS wave function are utilized to extract non-local hadron-hadron potential. 'The ground state saturation', which is commonly used in lattice QCD but is hard to be achieved for multi-baryons, is not required. We demonstrate that the present method works efficiently for the nucleon-nucleon interaction (the potential and the phase shift) in the {sup 1}S{sub 0} channel.