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.
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...
N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
Ahn, Changrim
2008-01-01
We propose the exact S-matrix for the planar limit of the N=6 super Chern-Simons theory recently proposed by Aharony, Bergman, Jafferis, and Maldacena for the AdS_4/CFT_3 correspondence. Assuming SU(2|2) symmetry, factorizability and certain crossing-unitarity relations, we find the S-matrix including the dressing phase. We use this S-matrix to formulate the asymptotic Bethe ansatz. Our result for the Bethe-Yang equations and corresponding Bethe ansatz equations confirms the all-loop Bethe ansatz equations recently conjectured by Gromov and Vieira.
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
Directory of Open Access Journals (Sweden)
Katsushi Ito
2015-07-01
Full Text Available We study the linear problem associated with modified affine Toda field equation for the Langlands dual gˆ∨, where gˆ is an untwisted affine Lie algebra. The connection coefficients for the asymptotic solutions of the linear problem are found to correspond to the Q-functions for g-type quantum integrable models. The ψ-system for the solutions associated with the fundamental representations of g leads to Bethe ansatz equations associated with the affine Lie algebra gˆ. We also study the A2r(2 affine Toda field equation in massless limit in detail and find its Bethe ansatz equations as well as T–Q relations.
Algebraic Bethe ansatz for a singular solution
Nepomechie, Rafael I
2013-01-01
The Bethe equations for the spin-1/2 Heisenberg chain with N sites have a "two-string" solution i/2, -i/2 that is singular: both the corresponding energy and algebraic Bethe ansatz vector are divergent. We show that this solution must be carefully regularized in order to obtain the correct eigenvector. This regularization involves a parameter that can be determined using a generalization of the Bethe equations. It follows that this solution must be excluded for odd N.
Quantum Computing via The Bethe Ansatz
Zhang, Yong,
2011-01-01
We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our perspectives on quantum computation, we study quantum computing in one-dimensional nonrelativistic system with delta-function interaction, where the two-body scattering matrix satisfies the factorisation equation (the quantum Yang--Baxter equation) and acts as a para...
Bethe ansatz and Isomonodromic deformations
Talalaev, D
2008-01-01
We study symmetries of the Bethe equations for the Gaudin model appeared naturally in the framework of the geometric Langlands correspondence under the name of Hecke operators and under the name of Schlesinger transformations in the theory of isomonodromic deformations, and particularly in the theory of Painlev\\'e transcendents.
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...
Coordinate Bethe ansatz for the string S-matrix
Energy Technology Data Exchange (ETDEWEB)
Leeuw, M de [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)
2007-11-30
We use the coordinate Bethe ansatz approach to derive the nested Bethe equations corresponding to the recently found S-matrix for strings in AdS{sub 5} x S{sup 5}, compatible with centrally extended su(2 vertical bar 2) symmetry.
All-loop Bethe ansatz equations for AdS3/CFT2
Borsato, Riccardo; Sfondrini, Alessandro
2012-01-01
Using the S-matrix for the d(2,1;alpha)^2 symmetric spin-chain of AdS3/CFT2, we propose a new set of all-loop Bethe equations for the system. These equations differ from the ones previously found in the literature by the choice of relative grading between the two copies of the d(2,1;alpha) superalgebra, and involve four undetermined scalar factors that play the role of dressing phases. Imposing crossing symmetry and comparing with the near-BMN form of the S-matrix found in the literature, we find several novel features. In particular, the scalar factors must differ from the Beisert-Eden-Staudacher phase, and should couple nodes of different masses to each other. In the semiclassical limit the phases are given by a suitable generalization of Arutyunov-Frolov-Staudacher phase.
All-loop Bethe ansatz equations for AdS3/CFT2
Borsato, Riccardo; Sax, Olof Ohlsson; Sfondrini, Alessandro
2013-04-01
Using the S-matrix for the {d}{{( {2, 1; α } )}^2} symmetric spin-chain of AdS3/CFT2, we propose a new set of all-loop Bethe equations for the system. These equations differ from the ones previously found in the literature by the choice of relative grading between the two copies of the {d}( {2, 1; α } ) superalgebra, and involve four undetermined scalar factors that play the role of dressing phases. Imposing crossing symmetry and comparing with the near-BMN form of the S-matrix found in the literature, we find several novel features. In particular, the scalar factors must differ from the Beisert-Eden-Staudacher phase, and should couple nodes of different masses to each other. In the semiclassical limit the phases are given by a suitable generalization of Arutyunov-Frolov-Staudacher phase.
Quelques applications de l'Ansatz de Bethe (Some applications of the Bethe Ansatz)
Zinn-Justin, P
1998-01-01
The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex models) and relativistic field theories with 1 space dimension and 1 time dimension. The connection with quantum groups is expounded. Several applications are then presented. Finite size corrections are calculated via two methods: The Non-Linear Integral Equations, which are applied to the study of the states of the affine Toda model with imaginary coupling, and their interpolation between the high energy (ultra-violet) and low energy (infra-red) regions; and the Thermodynamic Bethe Ansatz Equations, along with the associated Fusion Equations, which are used to determine the thermodynamic properties of the generalized multi-channel Kondo model. The latter is then studied in more detail, still using the Bethe Ansatz and quantum groups, so as to characterize the spectrum of th...
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.
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 in Stringy Sigma Models
Klose, T.; Zarembo, K.
2006-01-01
We compute the exact S-matrix and give the Bethe ansatz solution for three sigma-models which arise as subsectors of string theory in AdS(5)xS(5): Landau-Lifshitz model (non-relativistic sigma-model on S(2)), Alday-Arutyunov-Frolov model (fermionic sigma-model with su(1|1) symmetry), and Faddeev-Reshetikhin model (string sigma-model on S(3)xR).
The Bethe ansatz for AdS5 × S5 bound states
de Leeuw, M.
2009-01-01
We reformulate the nested coordinate Bethe ansatz in terms of coproducts of Yangian symmetry generators. This allows us to derive the nested Bethe equations for arbitrary bound state string S-matrices. The bound state number dependence in the Bethe equations appears through the parameters x± and the
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
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.
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
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.
Kundu, Anjan
2016-12-01
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.
Algebraic Bethe ansatz for Q-operators: The Heisenberg spin chain
Frassek, Rouven
2015-01-01
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
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
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.
Spin-12 XYZ model revisit: General solutions via off-diagonal Bethe ansatz
Directory of Open Access Journals (Sweden)
Junpeng Cao
2014-09-01
Full Text Available The spin-12 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.
Directory of Open Access Journals (Sweden)
Xiaotian Xu
2015-09-01
Full Text Available The small polaron, a one-dimensional lattice model of interacting spinless fermions, with generic non-diagonal boundary terms is studied by the off-diagonal Bethe ansatz method. The presence of the Grassmann valued non-diagonal boundary fields gives rise to a typical U(1-symmetry-broken fermionic model. The exact spectra of the Hamiltonian and the associated Bethe ansatz equations are derived by constructing an inhomogeneous T–Q relation.
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.
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.
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
Directory of Open Access Journals (Sweden)
Samuel Belliard
2013-11-01
Full Text Available We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations formally similar to the ones obtained in the periodic case or with diagonal boundaries.
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.
Algebraic Bethe ansatz for the Temperley–Lieb spin-1 chain
Directory of Open Access Journals (Sweden)
Rafael I. Nepomechie
2016-09-01
Full Text Available 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.
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.
Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain
Nepomechie, Rafael I.; Pimenta, Rodrigo A.
2016-09-01
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.
Algebraic Bethe Ansatz Solution to CN Vertex Model with Open Boundary Conditions
Institute of Scientific and Technical Information of China (English)
LI Guang-Liang; SHI Kang-Jie; YUE Rui-Hong
2005-01-01
We present three diagonal reflecting matrices for the CN vertex model with open boundary conditions and exactly solve the model by using the algebraic Bethe ansatz. The eigenvector is constructed and the eigenvalue and the associated Bethe equations are achieved. All the unwanted terms are cancelled out by three kinds of identities.
Modified algebraic Bethe ansatz for XXZ chain on the segment – II – general cases
Directory of Open Access Journals (Sweden)
S. Belliard
2015-05-01
Full Text Available The spectral problem of the Heisenberg XXZ spin-12 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.
Linking Chains Together: String Bits And The Bethe Ansatz
Lübcke, M
2004-01-01
This thesis is divided into two parts. In the first part we focus mainly on certain aspects of the AdS/CFT correspondence. The AdS/CFT correspondence is a proposed duality between Type IIB superstring theory on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. In the BMN limit string states located in the center of AdS5 rotate quickly around the equator of the S5 and correspond, in the dual theory, to operators constructed as long chains of sub-operators. This structure of the operators can be formulated as a spin chain and by using the Bethe ansatz their properties can be obtained by solving a set of Bethe equations. Having infinitely many sub-operators, there are methods for solving the Bethe equations in certain sectors. In paper III finite size corrections to the anomalous dimensions in the SU(2) sector are calculated to leading order. Inspired by the chain structure of the corresponding operators, the theory of string bits treats the strings as a discrete sets of points. This theory suffers...
Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases
Directory of Open Access Journals (Sweden)
Samuel Belliard
2015-03-01
Full Text Available The modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-12 chain on the segment with lower and upper triangular boundaries. The eigenvalues and the eigenvectors are conjectured. They are characterized 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. The conjecture follows from exact results for small chains. We also present a factorized formula for the Bethe vectors of the Heisenberg XXZ spin-12 chain on the segment with two upper triangular boundaries.
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.
Bethe ansatz solution of triangular trimers on the triangular lattice
Verberkmoes, A.; Nienhuis, B.
2001-01-01
Recently, a model consisting of triangular trimers covering the triangular lattice was introduced and its exact free energy given. In this paper we present the complete calculation leading to this exact result. The solution involves a coordinate Bethe ansatz with two kinds of particles. It is simila
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...
Universal Bethe ansatz solution for the Temperley-Lieb spin chain
Nepomechie, Rafael I.; Pimenta, Rodrigo A.
2016-09-01
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 appendix, we briefly consider the closed TL spin chain with periodic boundary conditions, and show how a previously-proposed solution can be improved so as to obtain the complete (albeit non-universal) spectrum.
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.
Reflection Amplitudes of ADE Toda Theories and Thermodynamic Bethe Ansatz
Ahn, C; Kim, C; Rim, C; Yang, B; Ahn, Changrim; Kim, Chanju; Rim, Chaiho; Yang, Bedl
2000-01-01
We study the ultraviolet asymptotics in affine Toda theories. These models are considered as perturbed non-affine Toda theories. We calculate the reflection amplitudes, which relate different exponential fields with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with thermodynamic Bethe ansatz results.
Hidden Relation between Reflection Amplitudes and Thermodynamic Bethe Ansatz
Ahn, C; Rim, C; Ahn, Changrim; Kim, Chanju; Rim, Chaiho
1999-01-01
In this paper we compute the scaling functions of the effective central charges for various quantum integrable models in a deep ultraviolet region $R\\to 0$ using two independent methods. One is based on the ``reflection amplitudes'' of the (super-)Liouville field theory where the scaling functions are given by the conjugate momentum to the zero-modes. The conjugate momentum is quantized for the sinh-Gordon, the Bullough-Dodd, and the super sinh-Gordon models where the quantization conditions depend on the size $R$ of the system and the reflection amplitudes. The other method is to solve the standard thermodynamic Bethe ansatz (TBA) equations for the integrable models in a perturbative series of $1/(const. - \\ln R)$. The constant factor which is not fixed in the lowest order computations can be identified {\\it only when} we compare the higher order corrections with the quantization conditions. Numerical TBA analysis shows a perfect match for the scaling functions obtained by the first method. Our results show ...
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.
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 (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, M; Lukowski, T; Zieme, S
2009-01-01
We present a formula for the five-loop anomalous dimension of N=4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Luescher 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 log^2 M/M^2 for large values of the spin.
Critical phenomena in one dimension from a Bethe ansatz perspective
Guan, Xiwen
2014-08-01
This article briefly reviews recent theoretical developments in quantum critical phenomena in one-dimensional (1D) integrable quantum gases of cold atoms. We present a discussion on quantum phase transitions, universal thermodynamics, scaling functions and correlations for a few prototypical exactly solved models, such as the Lieb-Liniger Bose gas, the spin-1 Bose gas with antiferromagnetic spin-spin interaction, the two-component interacting Fermi gas as well as spin-3/2 Fermi gases. We demonstrate that their corresponding Bethe ansatz solutions provide a precise way to understand quantum many-body physics, such as quantum criticality, Luttinger liquids (LLs), the Wilson ratio, Tan's Contact, etc. These theoretical developments give rise to a physical perspective using integrability for uncovering experimentally testable phenomena in systems of interacting bosonic and fermonic ultracold atoms confined to 1D.
Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions
Institute of Scientific and Technical Information of China (English)
WU Jun-Fang; ZHANG Chun-Min; YUE Rui-Hong; LI Run-Ling
2005-01-01
The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.
Bethe Ansatz solution of the small polaron with nondiagonal boundary terms
Karaiskos, Nikos; Frahm, Holger
2013-01-01
The small polaron with generic, nondiagonal boundary terms is investigated within the framework of quantum integrability. The eigenvalues of the model are extracted by using the fusion hierarchy of the transfer matrices and the corresponding Bethe Ansatz equations are presented. For particular values of the anisotropy parameter the fusion hierarchy truncates, giving rise to a set of functional relations for the transfer matrix. Exploiting the latter ones, the same set of eigenvalues is rederived, confirming our results. Finally, we comment on the eigenvectors of the model and explicitly compute the state with all sites unoccupied for arbitrary chain lengths.
Yangian symmetry, S-matrices and Bethe Ansatz for the AdS{sub 5} x S{sup 5} superstring
Energy Technology Data Exchange (ETDEWEB)
Leeuw, M. de [Institute for Theoretical Physics and Spinoza Institute, Utrecht University (Netherlands)
2009-05-15
We discuss the relation between the recently derived bound state S-matrices for the AdS{sub 5} x S{sup 5} superstring and Yangian symmetry. We will study the relation between this Yangian symmetry and the Bethe ansatz. In particular we can use it to derive the Bethe equations for bound states. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Functional Bethe ansatz methods for the open XXX chain
Energy Technology Data Exchange (ETDEWEB)
Frahm, Holger; Grelik, Jan H; Seel, Alexander; Wirth, Tobias, E-mail: Holger.Frahm@itp.uni-hannover.d, E-mail: Jan.Grelik@itp.uni-hannover.d, E-mail: Alexander.Seel@itp.uni-hannover.d [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstr. 2, 30167 Hannover (Germany)
2011-01-07
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.
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.
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.
BETHE ANSATZ FOR SUPERSYMMETRIC MODEL WITH?Uq[osp( 1｜2 ) ] SYMMETRY
Institute of Scientific and Technical Information of China (English)
杨文力
2001-01-01
Using the algebraic Bethe ansatz method, we obtain the eigenvalues of the transfer matrix of the supersymmetric model with Uq[osp(1｜2)] symmetry under periodic boundary and twisted boundary conditions.
Bethe ansatz solution of the small polaron with nondiagonal boundary terms
Karaiskos, Nikos; Grabinski, André M.; Frahm, Holger
2013-07-01
The small polaron with generic, nondiagonal boundary terms is investigated within the framework of quantum integrability. The fusion hierarchy of the transfer matrices and its truncation for particular values of the anisotropy parameter are both employed, so that the spectral problem is formulated in terms of a TQ equation. The solution of this equation for generic boundary conditions is based on a deformation of the diagonal case. The eigenvalues of the model are extracted and the corresponding Bethe ansatz equations are presented. Finally, we comment on the eigenvectors of the model and explicitly compute the eigenstate of the model which evolves into the Fock vacuum when the off-diagonal boundary terms are switched off.
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.
Masoero, Davide; Raimondo, Andrea; Valeri, Daniele
2016-09-01
We assess the ODE/IM correspondence for the quantum g -KdV model, for a non-simply laced Lie algebra g. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra g^{(1)} , and constructing the relevant {Ψ} -system among subdominant solutions. We then use the {Ψ} -system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum 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.
The algebraic Bethe ansatz for rational braid-monoid lattice models
Martins, M J
1997-01-01
In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_n and D_n Lie algebra and by the superalgebra Osp(n|2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvalues of the transfer matrix associated to the B_n, C_n, D_n, Osp(2n-1|2), Osp(2|2n-2), Osp(2n-2|2) and Osp(1|2n) models. The corresponding Bethe Ansatz equations can be formulated in terms of the root structure of the underlying algebra.
Energy Technology Data Exchange (ETDEWEB)
Mishra, A.K., E-mail: mishra@imsc.res.i [Insitituto Nacional de Pesquidas Espaciais - INPE, P.O. Box 103, CP 515, S. J. Campos, SP 12245-970 (Brazil); Kishore, R., E-mail: kishore@las.inpe.b [Insitituto Nacional de Pesquidas Espaciais - INPE, P.O. Box 103, CP 515, S. J. Campos, SP 12245-970 (Brazil)
2009-10-15
The exact nested Bethe ansatz solution for the one dimensional (1-D) U infinity Hubbard model show that the state vectors are a product of spin-less fermion and spin wavefunctions, or an appropriate superposition of such factorized wavefunctions. The spin-less fermion component of the wavefunctions ensures no double occupancy at any site. It had been demonstrated that the nested Bethe ansatz wavefunctions in the U infinity limit obey orthofermi statistics. Gutzwiller projection operator formalism is the another well known technique employed to handle U infinity Hubbard model. In general, this approach does not lead to spin-less fermion wavefunctions. Therefore, the nested Bethe ansatz and Gutzwiller projection operator approach give rise to different kinds of the wavefunctions for the U infinity limit of 1-D Hubbard Hamiltonian. To compare the consequences of this dissimilarity in the wavefunctions, we have obtained the ground state energy of a finite system consisting of three particles on a four site closed chain. It is shown that in the nested Bethe ansatz implemented through orthofermion algebra, all the permissible 2{sup 3} spin configurations are degenerate in the ground state. This eight fold degeneracy of the ground state is absent in the Gutzwiller projection operator approach. This finding becomes relevant in the context of known exact U infinity results, which require that all the energy levels are 2{sup N}-fold degenerate for an N particle system.
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.
Massless L\\"uscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz
Abbott, Michael C
2015-01-01
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 AdS3, as we demonstrate here by studying L\\"uscher F-terms with a massless particle running in the loop. We apply this to the classic test of Hern\\'andez & L\\'opez, in which the su(2) sector Bethe equations (including one-loop dressing phase) should match the semiclassical string theory result for a circular spinning string. These calculations did not agree in AdS3xS3xT4, and we show that the sum of all massless L\\"uscher F-terms can reproduce the difference.
Algebraic Bethe Ansatz for the Osp(1|2) Model with Reflecting Boundaries
Institute of Scientific and Technical Information of China (English)
YUE Rui-Hong; XIONG Chuan-Hua
2001-01-01
In the framework of graded quantum inverse scattering method, we obtain the eigenvalues and the eigenvectors of the Osp(l|2) model with reflecting boundary conditions in FBF background. The corresponding Bathe ansatz equations are obtained.
Energy Technology Data Exchange (ETDEWEB)
Kitanine, N
2007-09-15
Spin chains are the basic elements of integrable quantum models. These models have direct applications in condense matter theory, in statistical physics, in quantum optics, in field theory and even in string theory but they are also important because they enable us to solve, in an exact manner, non-perturbative phenomena that otherwise would stay unresolved. The method described in this work is based on the algebraic Bethe Ansatz. It is shown how this method can be used for the computation of null temperature correlation functions of the Heisenberg 1/2 spin chain. The important point of this approach is the solution of the inverse quantum problem given by the XXZ spin chain. This solution as well as a simple formulae for the scalar product of the Bethe states, have enabled us to get the most basic correlation functions under the form of multiple integrals. The formalism of multiple integrals open the way for asymptotic analysis for a few physical quantities like the probability of vacuum formation. It is worth noticing that this formalism can give exact results for two-point functions that are the most important correlation functions for applications. A relationship has been discovered between these multiple integrals and the sum of the form factors. The results have been extended to dynamical correlation functions. (A.C.)
"Generalized" algebraic Bethe ansatz, Gaudin-type models and Zp-graded classical r-matrices
Skrypnyk, T.
2016-12-01
We consider quantum integrable systems associated with reductive Lie algebra gl (n) and Cartan-invariant non-skew-symmetric classical r-matrices. We show that under certain restrictions on the form of classical r-matrices "nested" or "hierarchical" Bethe ansatz usually based on a chain of subalgebras gl (n) ⊃ gl (n - 1) ⊃ . . . ⊃ gl (1) is generalized onto the other chains or "hierarchies" of subalgebras. We show that among the r-matrices satisfying such the restrictions there are "twisted" or Zp-graded non-skew-symmetric classical r-matrices. We consider in detail example of the generalized Gaudin models with and without external magnetic field associated with Zp-graded non-skew-symmetric classical r-matrices and find the spectrum of the corresponding Gaudin-type hamiltonians using nested Bethe ansatz scheme and a chain of subalgebras gl (n) ⊃ gl (n -n1) ⊃ gl (n -n1 -n2) ⊃ gl (n - (n1 + . . . +np-1)), where n1 +n2 + . . . +np = n.
The single-particle density matrix of a quantum bright soliton from the coordinate Bethe ansatz
Ayet, Alex; Brand, Joachim
2017-02-01
We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in coordinate representation. A diagrammatic approach is developed to keep track of relevant terms and identify symmetries, which helps to reduce the number of terms that have to be evaluated numerically. As a first application we compute with modest numerical resources the single-particle density matrix and its eigenvalues including the condensate fraction for a quantum bright soliton with up to N = 10 bosons. The latter are constructed as superpositions of string-type Bethe-ansatz eigenstates of nonrelativistic bosons in one spatial dimension with attractive contact interaction. Upon delocalising the superposition in momentum space we find that the condensate fraction reaches maximum values larger than 97% with weak particle-number dependence in the range of particles studied. The presented approach is suitable for studying time-dependent problems and generalises to higher-order correlation functions.
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.
Hou, B; Yang, W L; Hou, Boyu; Sasaki, Ryu; Yang, Wen-Li
2004-01-01
Ruijsenaars-Schneider models associated with $A_{n-1}$ root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic" limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder et al [20].
Energy Technology Data Exchange (ETDEWEB)
Shuaibu, A. [Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia and Physics Department, Faculty of Science, Nigerian Defence Academy, P.M.B 2109, Kaduna (Nigeria); Rahman, M. M. [Physics Department, Faculty of Science, Nigerian Defence Academy, P.M.B 2109, Kaduna (Nigeria)
2014-03-05
We study the low temperature behavior of a triangular lattice quantum spin-1 Heisenberg antiferromagnet with single-site anisotropy by using coordinate Bethe ansatz method. We compute the standard two-particle Hermitian Hamiltonian, and obtain the eigenfunctions and eigenvalue of the system. The obtained results show a number of advantages in comparison with many results.
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.``
Reflection Amplitudes in Non-Simply Laced Toda Theories and Thermodynamic Bethe Ansatz
Ahn, C; Fateev, V A; Kim, C; Rim, C; Ahn, Changrim; Kim, Chanju; Rim, Chaiho
2000-01-01
We study the ultraviolet asymptotics in non-simply laced affine Toda theoriesconsidering them as perturbed non-affine Toda theories, which possess theextended conformal symmetry. We calculate the reflection amplitudes, innon-affine Toda theories and use them to derive the quantization condition forthe vacuum wave function, describing zero-mode dynamics. The solution of thisquantization conditions for the ground state energy determines the UVasymptotics of the effective central charge. These asymptotics are in a goodagreement with Thermodynamic Bethe Ansatz(TBA) results. To make the comparisonwith TBA possible, we give the exact relations between parameters of the actionand masses of particles as well as the bulk free energies for non-simply lacedaffine Toda theories.
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.
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.
Fioravanti, Davide; Rossi, Marco
2015-01-01
Moving from Beisert-Staudacher equations, the complete set of Asymptotic Bethe Ansatz equations and $S$-matrix for the excitations over the GKP vacuum is found. The resulting model on this new vacuum is an integrable spin chain of length $R=2\\ln s$ ($s=$ spin) with particle rapidities as inhomogeneities, two (purely transmitting) defects and $SU(4)$ (residual R-)symmetry. The non-trivial dynamics of ${\\cal N}=4$ SYM appears in elaborated dressing factors of the 2D two-particle scattering factors, all depending on the 'fundamental' one between two scalar excitations. From scattering factors we determine bound states. In particular, we study the strong coupling limit, in the non-perturbative, perturbative and giant hole regimes. Eventually, from these scattering data we construct the $4D$ pentagon transition amplitudes (perturbative regime). In this manner, we detail the multi-particle contributions (flux tube) to the MHV gluon scattering amplitudes/Wilson loops (OPE or BSV series) and re-sum them to the Thermo...
On The Ladder Bethe-Salpeter Equation
Efimov, G V
2003-01-01
The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a scalar theory: two scalar fields (constituents) with mass $m$ interacting via an exchange of a scalar field (tieon) with mass $\\mu$. The BS equation is written in the form of an integral equation in the configuration Euclidean $x$-space with the kernel which for stable bound states $M<2m$ is a self-adjoint positive operator. The solution of the BS equation is formulated as a variational problem. The nonrelativistic limit of the BS equation is considered. The role of so-called abnormal states is discussed. The analytical form of test functions for which the accuracy of calculations of bound state masses is better than 1% (the comparison with available numerical calculations is done) is determined. These test functions make it possible to calculate analytically vertex functions describing the interaction of bound states with constituents. As a by-product a simple solution of the Wick-Cutkosky model for the case of massless bound...
Castro-Alvaredo, Olalla; Chen, Yixiong; Doyon, Benjamin; Hoogeveen, Marianne
2014-03-01
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 Bernard and Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures Tl, Tr, and waiting for a long time. We evaluate the current J(Tl, Tr) using the exact QFT density matrix describing these non-equilibrium steady states and using 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-state TBA equations for three models: the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of non-equilibrium c-functions, associated with the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the ‘additivity’ property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT—that is, J(Tl, Tr) is not of the form f(Tl) - f(Tr).
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.
Solving Bethe-Salpeter scattering state equation in Minkowski space
Carbonell, J
2014-01-01
We present a method to directly solving the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the singularities which appear in the kernel, propagators and Bethe-Salpeter amplitude itself. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange is computed for the first time.
Scalar product of Bethe vectors from functional equations
Galleas, W.
2012-01-01
In this work the scalar product of Bethe vectors for the six-vertex model is studied by means of functional equations. The scalar products are shown to obey a system of functional equations originated from the Yang-Baxter algebra and its solution is given as a multiple contour integral.
Boundary Quantum Knizhnik-Zamolodchikov Equations and Bethe Vectors
Reshetikhin, N.; Stokman, J.; Vlaar, B.
2015-01-01
Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and only the 2-dimensional representation of Uq(slˆ2) is involved. We also consider their rational and classical degeneration
Twisting singular solutions of Betheʼs equations
Nepomechie, Rafael I.; Wang, Chunguang
2014-12-01
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.
Solving Bethe-Salpeter equation in Minkowski space
Karmanov, V A
2005-01-01
We develop a new method of solving Bethe-Salpeter (BS) equation for spinless particles. It is based on projecting the BS equation on the light-front plane and on the Nakanishi integral representation of the BS amplitude. The method is valid for any kernel given by the irreducible Feynman graphs and does not assume a transformation to the Euclidean space. For massless ladder exchange our approach reproduces analytically the Wick-Cutkosky equation. For massive ladder exchange the numerical results coincide with ones obtained by Wick rotation.
Bethe-Salpeter equation in non-commutative space
Directory of Open Access Journals (Sweden)
M. Haghighat
2005-06-01
Full Text Available We consider Bethe-Salpeter (BS equation for the bound state of two point particles in the non-commutative space-time. We subsequently explore the BS equation for spin0-spin0, spin1/2-spin1/2 and spin0-spin1/2 bound states. we show that the lowest order spin independent correction to energy spectrum in each case is of the order θ a 4 while the spin dependent one in NC space, is started at the order θ a 6.
An ansatz for solving nonlinear partial differential equations in mathematical physics.
Akbar, M Ali; Ali, Norhashidah Hj Mohd
2016-01-01
In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.
Solving the Bethe-Salpeter Equation in Euclidean Space
Dorkin, S M; Atti, C Ciofi degli; Kämpfer, B
2010-01-01
Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve numerically the resulting system of equations with realistic interaction kernels. Other representations can be obtained by performing proper unitary transformations. A generalization of the iteration method for finding the energy spectrum of the BS equation is discussed and examples of concrete calculations are presented. Comparison of relativistic calculations with available experimental data and with corresponding non relativistic results together with an analysis of the role of Lorentz boost effects and relativistic corrections are presented. A novel method related to the use of hyperspherical harmonics is considered for a representation of the vertex functions suitable for numerical calculations.
Solving the Bethe-Salpeter Equation in Euclidean Space
Dorkin, S. M.; Kaptari, L. P.; Ciofi degli Atti, C.; Kämpfer, B.
2011-03-01
Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve numerically the resulting system of equations with realistic interaction kernels. Other representations can be obtained by performing proper unitary transformations. A generalization of the iteration method for finding the energy spectrum of the BS equation is discussed and examples of concrete calculations are presented. Comparison of relativistic calculations with available experimental data and with corresponding non relativistic results together with an analysis of the role of Lorentz boost effects and relativistic corrections are presented. A novel method related to the use of hyperspherical harmonics is considered for a representation of the vertex functions suitable for numerical calculations.
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.
Hutsalyuk, A.; Liashyk, A.; Pakuliak, S. Z.; Ragoucy, E.; Slavnov, N. A.
2017-01-01
We study integrable models with 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. Dedicated to the memory of Petr Petrovich Kulish.
Bethe-Salpeter equation in Minkowski space with cross-ladder kernel
Karmanov, V A
2006-01-01
A new method for solving the Bethe-Salpeter equation is developed. It allows to find the Bethe-Salpeter amplitudes both in Minkowski and in Euclidean spaces and, as a by product, the light-front wave function. The method is valid for any kernel given by irreducible Feynman graphs. Bethe-Salpeter and Light-Front equations for scalar particles with ladder + cross-ladder kernel are solved.
Instantaneous Bethe-Salpeter Equation and Its Exact Solution
Institute of Scientific and Technical Information of China (English)
CHANG Chao-Hsi; CHEN Jiao-Kai; LI Xue-Qian; WANG Guo-Li
2005-01-01
We present an approach to solve Bethe-Salpeter (BS) equations exactly without any approximation if the kernel of the BS equations exactly is instantaneous, and take positronium as an example to illustrate the general features of the exact solutions. The key step for the approach is from the BS equations to derive a set of coupled and welldetermined integration equations in linear eigenvalue for the components of the BS wave functions equivalently, which may be solvable numerically under a controlled accuracy, even though there is no analytic solution. For positronium,the exact solutions precisely present corrections to those of the corresponding Schrodinger equation in order v1 (v is the relative velocity) for eigenfunctions, in order v2 for eigenvalues, and the mixing between S and D components in JPC = 1- states etc., quantitatively. Moreover, we also point out that there is a questionable step in some existent derivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, we emphasize that one should take the O(v) corrections emerging in the exact solutions into account accordingly if one is interested in the relativistic corrections for relevant problems to the bound states.
A systematic approach to sketch Bethe-Salpeter equation
Qin, Si-xue
2016-03-01
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 symmetry breaking (DCSB). The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.
A systematic approach to sketch Bethe-Salpeter equation
Directory of Open Access Journals (Sweden)
Qin Si-xue
2016-01-01
Full Text Available To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark–anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD’s gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symmetry breaking (DCSB. The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.
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...
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-Salpeter equation with cross-ladder kernel in Minkowski and Euclidean spaces
Karmanov, V A; Mangin-Brinet, M
2007-01-01
Some results obtained by a new method for solving the Bethe-Salpeter equation are presented. The method is valid for any kernel given by irreducible Feynman graphs. The Bethe-Salpeter amplitude, both in Minkowski and in Euclidean spaces, and the binding energy for ladder + cross-ladder kernel are found. We calculate also the corresponding electromagnetic form factor.
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...
Instantaneous Bethe-Salpeter Equation and Its Analog: Breit-like Equation
Institute of Scientific and Technical Information of China (English)
CHANG Chao-Hsi; CHEN Jiao-Kai
2005-01-01
We take the (μ士e干) system as an example, but restrict ourselves to highlight the states with quantum number JP = 0-, to explore the different contents of the instantaneous Bethe-Salpeter (BS) equation and its analog,the relativistic version of Breit equation, by solving them exactly. The results show that the two equations are not equivalent, although they are analogous. Furthermore, since the Breit equation contains extra un-physical solutions,so we point out that it should be abandoned if one wishes to have an accurate description of the bound states for the instantaneous interacting binding systems.
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.
Carbonell, J
2010-01-01
We present a new method for solving the two-body Bethe-Salpeter equation in Minkowski space. It is based on the Nakanishi integral representation of the Bethe-Salpeter amplitude and on subsequent projection of the equation on the light-front plane. The method is valid for any kernel given by the irreducible Feynman graphs and for systems of spinless particles or fermions. The Bethe-Salpeter amplitudes in Minkowski space are obtained. The electromagnetic form factors are computed and compared to the Euclidean results.
Solutions of the Bethe-Salpeter Equation in Minkowski space: a comparative study
Salme`, Giovanni; Viviani, Michele
2014-01-01
The Bethe-Salpeter Equation for a two-scalar, S-wave bound system, interacting through a massive scalar, is investigated within the ladder approximation. By assuming a Nakanishi integral representation of the Bethe-Salpeter amplitude, one can deduce new integral equations that can be solved and quantitatively studied, overcoming the analytic difficulties of the Minkowski space. Finally, it is shown that the Light-front distributions of the valence state, directly obtained from the Bethe-Salpeter amplitude, open an effective window for studying the two-body dynamics.
Yangian symmetry, S-Matrices and Bethe Ansats for the Ads5 x S5 superstring
de Leeuw, M.
2009-01-01
We discuss the relation between the recently derived bound state S-matrices for the AdS5× S5 superstring and Yangian symmetry. We will study the relation between this Yangian symmetry and the Bethe ansatz. In particular we can use it to derive the Bethe equations for bound states.
Bethe states for the two-site Bose–Hubbard model: A binomial approach
Directory of Open Access Journals (Sweden)
Gilberto Santos
2015-06-01
Full Text Available 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.
Numerical solution of the spinor Bethe-Salpeter equation and the Goldstein problem
L.G. Suttorp
1978-01-01
The spinor Bethe-Salpeter equation describing bound states of a fermion-antifermion pair with massless-boson exchange reduces to a single (uncoupled) partial differential equation for special combinations of the fermion-boson couplings. For spinless bound states with positive or negative parity this
The Spin Symmetry of Heavy Baryons in the Framework of the Bethe-Salpeter Equation
Institute of Scientific and Technical Information of China (English)
CUI Jian-Ying; JIN Hong-Ying; WU Ji-Min
2001-01-01
We study the baryons containing a heavy quark in the framework of Bethe-Salpeter (BS) equation. The most general forms of the BS wavefunctions are given. In the heavy-quark limit we simplify the BS equations and we show clearly that the spin symmetry exists in heavy baryon states.``
A Novel Approach in Solving the Spinor-Spinor Bethe-Salpeter Equation
Dorkin, S M; Semikh, S S; Kaptari, L P
2008-01-01
To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is suitable for a representation of the vertex functions. We present a numerical algorithm to solve the Bethe-Salpeter equation and investigate in detail the properties of the solution for the scalar, pseudoscalar and vector meson exchange kernels including the stability of bound states. We also compare our results to the non relativistic ones and to the results given by light front dynamics.
Exact solutions of the spinor Bethe-Salpeter equation for tightly bound states
Suttorp, L.G.
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
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
Solutions of Bethe-Salpeter and Light-Front equations with cross-ladder kernel
Carbonell, J
2005-01-01
By method developed in our previous paper we solve the Bethe-Salpeter (BS) equation for the kernel given by sum of ladder and cross-ladder exchanges. We solve also corresponding equation in light-front dynamics (LFD), where we add the time-ordered stretched boxes. Cross-ladder contribution is large and attractive, whereas the influence of stretched boxes is negligible. Both approaches -- BS and LFD -- give very close results.
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...
Solving Bethe-Salpeter equation for two fermions in Minkowski space
Carbonell, J
2010-01-01
The method of solving the Bethe-Salpeter equation in Minkowski space, which we developed previously for spinless particles, is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the amplitude and on projecting the equation on the light-front plane. The singularities in the projected two-fermion kernel are regularized without modifying the original Bethe-Salpeter amplitudes. The numerical solutions for the J=0 bound state with the scalar, pseudoscalar and massless vector exchange kernels are found. The stability of the scalar and positronium states without vertex form factor is discussed. Binding energies are in close agreement with the Euclidean results. Corresponding amplitudes in Minkowski space are obtained.
Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
Frederico, Tobias; Viviani, Michele
2013-01-01
The Bethe-Salpeter Equation for a bound system, composed by two massive scalars exchanging a massive scalar, is quantitatively investigated in ladder approximation, within the Nakanishi integral representation approach. For the S-wave case, numerical solutions with a form inspired by the Nakanishi integral representation, have been calculated. The needed Nakanishi weight functions have been evaluated by solving two different eigenequations, obtained directly from the Bethe-Salpeter equation applying the Light-Front projection technique. A remarkable agreement, in particular for the eigenvalues, has been achieved, numerically confirming that the Nakanishi uniqueness theorem for the weight functions, demonstrated in the context of the perturbative analysis of the multi-leg transition amplitudes and playing a basic role in suggesting one of the two adopted eigenequations, can be extended to a non perturbative realm. The detailed, quantitative studies are completed by presenting both probabilities and Light-Front...
Numerical Studies of the Zero-Energy Bethe-Salpeter Equation in Minkowski Space
Viviani, Michele; Frederico, Tobias; Salmè, Giovanni
2015-09-01
The inhomogeneous Bethe-Salpeter equation describing the zero-energy scattering of a system composed by two massive scalars exchanging a massive scalar is numerically investigated in ladder approximation, directly in Minkowski space. The solution is obtained by using the Nakanishi integral representation, as performed in Frederico et al. (Phys Rev D 89:016010, 2014) where the method was successfully applied to bound states. The scattering lengths are quantitatively investigated and the results compared with the corresponding ones present in literature.
Calculation of Spin Observables for Proton-Proton Elastic Scattering in the Bethe-Salpeter Equation
Kinpara, Susumu
2015-01-01
Bethe-Salpeter equation is applied to $p$-$p$ elastic scattering. The observables of spin are calculated in the framework of the M matrix using the two-body interaction potential. The parameter of the pseudovector coupling constant is adjusted so as to reproduce the spin singlet part. It is shown that the spin rotation $R(\\theta)$ and $A(\\theta)$ are improved by the resonance effect for ${}^{\\rm 1}S_{\\rm 0}$.
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.
Solution of the Bethe-Salpeter equation in Minkowski space for a two fermion system
Carbonell, J
2010-01-01
The method of solving the Bethe-Salpeter equation in Minkowski space, developed previously for spinless particles, is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the amplitude and on projecting the equation on the light-front plane. The singularities in the projected two-fermion kernel are regularized without modifying the original BS amplitudes. The numerical solutions for the J=0 bound state with the scalar, pseudoscalar and massless vector exchange kernels are found. Binding energies are in close agreement with the Euclidean results. Corresponding amplitudes in Minkowski space are obtained.
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.
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.
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...
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.
Abe, Yuya; Fukushima, Kenji
2016-11-01
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 when they converge to the exact answer, as well as the border of 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.
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.
Solution to Bethe-Salpeter equation via Mellin-Barnes transform
Allendes, Pedro; Kondrashuk, Igor; Cuello, Eduardo A Notte; Medar, Marko Rojas
2012-01-01
We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in d=4 dimensions. It is shown how multi-fold MB transform of the momentum integral corresponding to any number of rungs is reduced to two-fold MB transform. For this purpose we use Belokurov-Usyukina reduction method for four-dimensional scalar integrals in the position space. The result is represented in terms of Euler 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 ...
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.
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...
Meson masses in large Nf QCD from Bethe-Salpeter equation
Harada, M; Yamawaki, K; Harada, Masayasu; Kurachi, Masafumi; Yamawaki, Koichi
2003-01-01
We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector and axial-vector bound states of quark and anti-quark in large Nf QCD with the improved ladder approximation in the Landau gauge. Quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for the consistency with the chiral symmetry. Amazingly, due to the fact that the two-loop running coupling of large Nf QCD is explicitly written in terms of an analytic function, large Nf QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large Nf QCD.
Topics in dual models and extended solutions. [Bethe-Salpeter equation
Energy Technology Data Exchange (ETDEWEB)
Roth, R.S.
1977-06-01
Two main topics are explored. The first deals with the infinities arising from the one loop planar string diagram of the standard dual model. It is shown that for the number of dimensions d = 25 or 26, these infinities lead to a renormalization of the slope of the Regge trajectories, in addition to a renormalization of the coupling constant. The second topic deals with the propagator for a confined particle (monopole) in a field theory. When summed to all orders, this propagator is altogether free of singularities in the finite momentum plane, and an attempt is made to illustrate this. One examines the Bethe-Salpeter equation and shows that ladder diagrams are not sufficient to obtain this result. However, in a nonrelativistic approximation confinement is obtained and all poles disappear.
Institute of Scientific and Technical Information of China (English)
XIE Chuan-Mei; LI Heng-Mei; WAN Shao-Long
2009-01-01
The wave functions and electromagnetic form factor of charged scalar mesons are studied with a modified vector-vector flat-bottom potential model under the framework of the Schwinger-Dyeon and Bethe-Salpeter equations.The obtained results agree well with other theories.
Pressure-velocity relations in reservoir rocks: Modified MacBeth's equation
Grana, Dario
2016-09-01
The knowledge of the saturation and pressure effects on elastic properties is a key factor in reservoir monitoring. The relation between saturation changes and velocity variations is well known in rock physics and at seismic frequency it can be satisfactorily described by Gassmann's equations. The pressure effect still requires deeper investigations in order to be included in rock physics models for 4D studies. Theoretical models of velocity-pressure relations often do not match lab measurements, or contain empirical constants or theoretical parameters that are difficult to calibrate or do not have a precise physical meaning. In this work, I present a new model to describe the pressure sensitivity of elastic moduli for clastic rocks. The proposed model is an extension of MacBeth's relations. These equations are then integrated within a complete rock physics model to describe the relation between rock properties (porosity and clay content), dynamic attributes (saturation and pressure) and elastic properties. The proposed model is calibrated with laboratory measurements of dry samples over a wide range of pressure variations and then applied to well data to simulate different production scenarios. The complete rock physics model can then be used in time-lapse inversion to predict the distribution of dynamic property changes in the reservoir within an inversion workflow for reservoir monitoring.
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.)
Loginov, A Y
2002-01-01
Bethe-Salpeter equation for the massive particles with spin 1 is considered. The scattering amplitude decomposition of the particles with spin 1 by relativistic tensors is derived. The transformation coefficients from helicity amplitudes to invariant functions is found. The integral equations system for invariant functions is obtained and partial decomposition of this system is performed. Equivalent system of the integral equation for the partial helicity amplitudes is presented.
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.
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.
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.
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.
Efficient implementation of core-excitation Bethe-Salpeter equation calculations
Gilmore, K.; Vinson, John; Shirley, E. L.; Prendergast, D.; Pemmaraju, C. D.; Kas, J. J.; Vila, F. D.; Rehr, J. J.
2015-12-01
We present an efficient implementation of the Bethe-Salpeter equation (BSE) method for obtaining core-level spectra including X-ray absorption (XAS), X-ray emission (XES), and both resonant and non-resonant inelastic X-ray scattering spectra (N/RIXS). Calculations are based on density functional theory (DFT) electronic structures generated either by ABINIT or QuantumESPRESSO, both plane-wave basis, pseudopotential codes. This electronic structure is improved through the inclusion of a GW self energy. The projector augmented wave technique is used to evaluate transition matrix elements between core-level and band states. Final two-particle scattering states are obtained with the NIST core-level BSE solver (NBSE). We have previously reported this implementation, which we refer to as OCEAN (Obtaining Core Excitations from Ab initio electronic structure and NBSE) (Vinson et al., 2011). Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previously possible; containing up to a few thousand electrons. These improvements include the implementation of optimal basis functions that reduce the cost of the initial DFT calculations, more complete parallelization of the screening calculation and of the action of the BSE Hamiltonian, and various memory reductions. Scaling is demonstrated on supercells of SrTiO3 and example spectra for the organic light emitting molecule Tris-(8-hydroxyquinoline)aluminum (Alq3) are presented. The ability to perform large-scale spectral calculations is particularly advantageous for investigating dilute or non-periodic systems such as doped materials, amorphous systems, or complex nano-structures.
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...
Institute of Scientific and Technical Information of China (English)
CHANG; ChaoHsi
2010-01-01
Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) are still missing in experimental observations and potential applications of the relevant wave functions of the bound states,we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCDinspired kernel.Such a kernel for the heavy quarkonia,relating to potential of the non-relativistic quark model,is instantaneous,so we call the corresponding B.S.equation as BS-In equation throughout the paper.Particularly,a new way to solve the B.S.equation,which is different from the traditional ones,is proposed here,and with it not only the known spectrum for the heavy quarkonia is re-generated,but also an important issue is brought in,i.e.,the obtained solutions of the equation ‘automatically’ include the ‘fine’,‘hyperfine’ splittings and the wave function mixture,such as S-D wave mixing in J PC = 1-states,P-F wave mixing in J PC = 2 ++ states for charmonium,bottomonium etc.It is pointed out that the best place to test the wave mixture probably is at Z-factory (e + e-collider running at Z-boson pole with extremely high luminosity).
Attaccalite, C.; Grüning, M.; Marini, A.
2011-12-01
Many-body effects are known to play a crucial role in the electronic and optical properties of solids and nanostructures. Nevertheless, the majority of theoretical and numerical approaches able to capture the influence of Coulomb correlations are restricted to the linear response regime. In this work, we introduce an approach based on a real-time solution of the electronic dynamics. The proposed approach reduces to the well-known Bethe-Salpeter equation in the linear limit regime and it makes it possible, at the same time, to investigate correlation effects in nonlinear phenomena. We show the flexibility and numerical stability of the proposed approach by calculating the dielectric constants and the effect of a strong pulse excitation in bulk h-BN.
DEFF Research Database (Denmark)
Yan, Jun; Jacobsen, Karsten W.; Thygesen, Kristian S.
2012-01-01
We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method Grid-based projector-augmented wave method (GPAW). Single-particle energies and wave functions are obtained from the Gritsenko, Leeuwen, Lenthe...
Rebolini, Elisa; Savin, Andreas
2013-01-01
We review the Bethe-Salpeter equation (BSE) approach to the calculation of electronic excitation energies of molecular systems. We recall the general Green's function many-theory formalism and give the working equations of the BSE approach within the static GW approximation with and without spin adaptation in an orbital basis. We apply the method to the pedagogical example of the H2 molecule in a minimal basis, testing the effects of the choice of the starting one-particle Green's function. Using the non-interacting one-particle Green's function leads to incorrect energy curves for the first singlet and triplet excited states in the dissociation limit. Starting from the exact one-particle Green's function leads to a qualitatively correct energy curve for the first singlet excited state, but still an incorrect energy curve for the triplet excited state. Using the exact one-particle Green's function in the BSE approach within the static GW approximation also leads to a number of additional excitations, all of t...
Anisovich, A V; Markov, V N; Matveev, M A; Sarantsev, A V
2004-01-01
The Bethe--Salpeter equations for the quark-antiquark composite systems with different quark masses, such as $q\\bar s$ (with $q=u$,$d$), $q\\bar Q$ and $s \\bar Q$ (with $Q=c$,$b$), are written in terms of spectral integrals. For the mesons characterized by the mass $M$, spin $J$ and radial quantum number $n$, the equations are presented for the $(n,M^2)$-trajectories with fixed $J$. In the spectral-integral technique one can use the energy-dependent forces and get beyond instantaneous approximation. The mixing between states with different quark spin $S$ and angular momentum $L$ are also discussed.
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.
Differential equations and integrable models the $SU(3)$ case
Dorey, P; Dorey, Patrick; Tateo, Roberto
2000-01-01
We exhibit a relationship between the massless $a_2^{(2)}$ integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schrödinger equation. This forms part of a more general correspondence involving $A_2$-related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the nonlinear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators $\\phi_{12}$, $\\phi_{21}$ and $\\phi_{15}$. This is checked against previous results obtained using the thermodynamic Bethe ansatz.
Energy Technology Data Exchange (ETDEWEB)
Maglevanny, I.I., E-mail: sianko@list.ru [Volgograd State Social Pedagogical University, 27 Lenin Avenue, Volgograd 400131 (Russian Federation); Smolar, V.A.; Nguyen, H.T.T. [Volgograd State Technical University, 28 Lenin Avenue, Volgograd 400131 (Russian Federation)
2013-12-01
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.
Bhatnagar, Shashank; Mengesha, Yikdem
2013-01-01
In this work we have employed Bethe-Salpeter equation (BSE) under covariant instantaneous ansatz (CIA) to study electromagnetic decays of ground state equal mass vector mesons: $\\rho$, $\\omega$, $\\phi$, $\\psi$ and $Y$ through the process $V\\rightarrow\\gamma*\\rightarrow e^+ + e^-$. We employ the generalized structure of hadron-quark vertex function $\\Gamma$ which incorporates various Dirac structures from their complete set order-by-order in powers of inverse of meson mass. The electromagnetic decay constants for the above mesons are calculated using the leading order (LO) and the next-to-leading order (NLO) Dirac structures. The relevance of various Dirac structures in this calculation is studied.
Bhatnagar, S; Bhatnagar, Shashank; Li, Shi-Yuan
2006-01-01
We employ the framework of Bethe-Salpeter equation under Covariant Instantaneous Ansatz (CIA) to study the leptonic decays of vector mesons. The calculations of decay constants f_v for rho, phi and omega mesons have been performed adopting a generalized structure of the hadron-quark vertex function Gamma which is generalized to include various Dirac covariants (other than the leading covariant i gamma cdot epsilon) from the complete set of covariants in accordance with a naive power counting rule, which allows the incorporation of them order by order in powers of the inverse of the meson mass.
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.
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.
Yan, Jun; Jacobsen, Karsten W.; Thygesen, Kristian S.
2012-07-01
We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method Grid-based projector-augmented wave method (GPAW). Single-particle energies and wave functions are obtained from the Gritsenko, Leeuwen, Lenthe, and Baerends potential [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.51.1944 51, 1944 (1995)] with the modifications from Kuisma [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.82.115106 82, 115106 (2010)] GLLBSC functional which explicitly includes the derivative discontinuity, is computationally inexpensive, and yields excellent fundamental gaps. Electron-hole interactions are included through the BSE using the statically screened interaction evaluated in the random phase approximation. For a representative set of semiconductors and insulators we find excellent agreement with experiments for the dielectric functions, onset of absorption, and lowest excitonic features. For the two-dimensional systems of graphene and hexagonal boron-nitride (h-BN) we find good agreement with previous many-body calculations. For the graphene/h-BN interface we find that the fundamental and optical gaps of the h-BN layer are reduced by 2.0 and 0.7 eV, respectively, compared to freestanding h-BN. This reduction is due to image charge screening which shows up in the GLLBSC calculation as a reduction (vanishing) of the derivative discontinuity.
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...
Energy Technology Data Exchange (ETDEWEB)
Hilger, Thomas Uwe
2012-04-11
The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D- anti D and B- anti B mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D{sub s} and D{sup *}{sub 0} mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the ρ meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpeter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.
An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
DEFF Research Database (Denmark)
Andersen, Molte Emil Strange; Salami Dehkharghani, Amin; Volosniev, A. G.;
2016-01-01
beyond the Bethe ansatz and bosonisation allow us to predict the behaviour of one-dimensional confined systems with strong short-range interactions, and new experiments with cold atomic Fermi gases have already confirmed these theories. Here we demonstrate that a simple linear combination of the strongly...
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.
The Dirac equation in the Kerr-de Sitter metric
Batic, D; Nowakowski, M; Medina, S Bravo
2015-01-01
We consider a fermion in the presence of a rotating black hole immersed in a universe with positive cosmological constant. After deriving new formulae for the event, Cauchy and cosmological horizons we adopt the Carter tetrad to separate the aforementioned equation into a radial and angular equation. We show how the Chandrasekhar ansatz leads to the construction of a symmetry operator that can be interpreted as the square root of the squared total angular momentum operator. Furthermore, we prove that the the spectrum of the angular operator is discrete and consists of simple eigenvalues and by means of the functional Bethe ansatz method we also derive a set of necessary and sufficient conditions for the angular operator to have polynomial solutions. Finally, we show that there exist no bound states for the Dirac equation in the non-extreme case.
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.
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)
Gaudin, M.; Caux, J.-S.
2014-01-01
Michel Gaudin's book La fonction d'onde de Bethe is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics. Available in English for the first time, this translation brings his classic work to a new generation of graduate students and researchers i
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
An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems.
Andersen, M E S; Dehkharghani, A S; Volosniev, A G; Lindgren, E J; Zinner, N T
2016-01-01
Interacting one-dimensional quantum systems play a pivotal role in physics. Exact solutions can be obtained for the homogeneous case using the Bethe ansatz and bosonisation techniques. However, these approaches are not applicable when external confinement is present. Recent theoretical advances beyond the Bethe ansatz and bosonisation allow us to predict the behaviour of one-dimensional confined systems with strong short-range interactions, and new experiments with cold atomic Fermi gases have already confirmed these theories. Here we demonstrate that a simple linear combination of the strongly interacting solution with the well-known solution in the limit of vanishing interactions provides a simple and accurate description of the system for all values of the interaction strength. This indicates that one can indeed capture the physics of confined one-dimensional systems by knowledge of the limits using wave functions that are much easier to handle than the output of typical numerical approaches. We demonstrate our scheme for experimentally relevant systems with up to six particles. Moreover, we show that our method works also in the case of mixed systems of particles with different masses. This is an important feature because these systems are known to be non-integrable and thus not solvable by the Bethe ansatz technique.
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."
Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion
Energy Technology Data Exchange (ETDEWEB)
Bajnok, Zoltán; Balog, János [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary); Correa, Diego H. [Instituto de Física La Plata, CONICET, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata (Argentina); Hegedűs, Árpád [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary); Massolo, Fidel I. Schaposnik [Instituto de Física La Plata, CONICET, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata (Argentina); Tóth, Gábor Zsolt [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary)
2014-03-11
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.
Note on Nonlinear Schr\\"odinger Equation, KdV Equation and 2D Topological Yang-Mills-Higgs Theory
Nian, Jun
2016-01-01
In this paper we discuss the relation between the (1+1)D nonlinear Schr\\"odinger equation and the KdV equation. By applying the boson/vortex duality, we can map the classical nonlinear Schr\\"odinger equation into the classical KdV equation in the small coupling limit, which corresponds to the UV regime of the theory. At quantum level, the two theories satisfy the Bethe Ansatz equations of the spin-$\\frac{1}{2}$ XXX chain and the XXZ chain in the continuous limit respectively. Combining these relations with the dualities discussed previously in the literature, we propose a duality web in the UV regime among the nonlinear Schr\\"odinger equation, the KdV equation and the 2D $\\mathcal{N}=(2,2)^*$ topological Yang-Mills-Higgs theory.
Hutsalyuk, A.; Liashyk, A.; Pakuliak, S. Z.; Ragoucy, E.; Slavnov, N. A.
2016-11-01
We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing {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 {gl}(1| 1) symmetry. Dedicated to the memory of Petr Petrovich Kulish.
Correlation Function and Simplified TBA Equations for XXZ Chain
Directory of Open Access Journals (Sweden)
Minoru Takahashi
2011-01-01
Full Text Available The calculation of the correlation functions of Bethe ansatz solvable models is very difficult problem. Among these solvable models spin 1/2 XXX chain has been investigated for a long time. Even for this model only the nearest neighbor and the second neighbor correlations were known. In 1990's multiple integral formula for the general correlations is derived. But the integration of this formula is also very difficult problem. Recently these integrals are decomposed to products of one dimensional integrals and at zero temperature, zero magnetic field and isotropic case, correlation functions are expressed by log 2 and Riemann's zeta functions with odd integer argument ς(3,ς(5,ς(7,.... We can calculate density sub-matrix of successive seven sites. Entanglement entropy of seven sites is calculated. These methods can be extended to XXZ chain up to n=4. Correlation functions are expressed by the generalized zeta functions. Several years ago I derived new thermodynamic Bethe ansatz equation for XXZ chain. This is quite different with Yang-Yang type TBA equations and contains only one unknown function. This equation is very useful to get the high temperature expansion. In this paper we get the analytic solution of this equation at Δ=0.
The Kerr-Schild ansatz revised
Bini, Donato; Kerr, Roy P
2014-01-01
Kerr-Schild metrics have been introduced as a linear superposition of the flat spacetime metric and a squared null vector field, say $\\boldsymbol{k}$, multiplied by some scalar function, say $H$. The basic assumption which led to Kerr solution was that $\\boldsymbol{k}$ be both geodesic and shearfree. This condition is relaxed here and Kerr-Schild ansatz is revised by treating Kerr-Schild metrics as {\\it exact linear perturbations} of Minkowski spacetime. The scalar function $H$ is taken as the perturbing function, so that Einstein's field equations are solved order by order in powers of $H$. It turns out that the congruence must be geodesic and shearfree as a consequence of third and second order equations, leading to an alternative derivation of Kerr solution.
The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing
De Baerdemacker, Stijn
2010-01-01
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.
Stripe Ansatzs from Exactly Solved Models
2001-01-01
Using the Boltzmann weights of classical Statistical Mechanics vertex models we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems, characterized by a strong anisotropy, which gives rise to stripe like structures. In the case of the six vertex model we compute exactly, in the thermodynamic limit, the norm of the ansatz and other observables. Employing this ansatz we study the phase diagram of a Hamiltonian given by the sum of XXZ Hamiltonians along the legs coupled by...
Differential-algebraic solutions of the heat equation
Buchstaber, Victor M.; Netay, Elena Yu.
2014-01-01
In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of a special form. The ansatz for such solutions is called the $n$-ansatz, where $n+1$ is the order of the differential equation.
Transition electromagnetic form factor in the Minkowski space Bethe-Salpeter approach
Carbonell, J
2013-01-01
Using the solutions of the Bethe-Salpeter equation in Minkowski space for bound and scattering states found in previous works, we calculate the transition electromagnetic form factor describing the electro-disintegration of a bound system.
Instantaneous Bethe-Salpeter Kernel for the Lightest Pseudoscalar Mesons
Lucha, Wolfgang
2016-01-01
Starting from a phenomenologically successful, numerical solution of the Dyson-Schwinger equation that governs the quark propagator, we reconstruct in detail the interaction kernel that has to enter the instantaneous approximation to the Bethe-Salpeter equation to allow us to describe the lightest pseudoscalar mesons as quark-antiquark bound states exhibiting the (almost) masslessness necessary for them to be interpretable as the (pseudo) Goldstone bosons related to the spontaneous chiral symmetry breaking of quantum chromodynamics.
Newman-Janis Ansatz in conformastatic spacetimes
Gutiérrez-Piñeres, Antonio C.; Quevedo, Hernando
2016-11-01
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 a further indication of its applicability limitations.
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.
3D-4D Interlinkage Of qqq Wave Functions Under 3D Support For Pairwise Bethe-Salpeter Kernels
Mitra, A N
1998-01-01
Using the method of Green's functions within a Bethe-Salpeter framework characterized by a pairwise qq interaction with a Lorentz-covariant 3D support to its kernel, the 4D BS wave function for a system of 3 identical relativistic spinless quarks is reconstructed from the corresponding 3D form which satisfies a fully connected 3D BSE. This result is a 3-body generalization of a similar 2-body result found earlier under identical conditions of a 3D support to the corresponding qq-bar BS kernel under Covariant Instaneity (CIA for short). (The generalization from spinless to fermion quarks is straightforward). To set the CIA with 3D BS kernel support ansatz in the context of contemporary approaches to the qqq baryon problem, a model scalar 4D qqq BSE with pairwise contact interactions to simulate the NJL-Faddeev equations is worked out fully, and a comparison of both vertex functions shows that the CIA vertex reduces exactly to the NJL form in the limit of zero spatial range. This consistency check on the CIA ve...
Integrability of a New Type of Deformed XXZ Model
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model.
Directory of Open Access Journals (Sweden)
Jon Links
2017-03-01
Full Text Available Solutions of the classical Yang–Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang–Baxter equation, from which commuting transfer matrices may be constructed. This procedure is reviewed, specifically for solutions without skew-symmetry. A particular solution with an exotic symmetry is identified, which is not obtained as a limiting expansion of the usual Yang–Baxter equation. This solution facilitates the construction of commuting transfer matrices which will be used to establish the integrability of a multi-species boson tunnelling model. The model generalises the well-known two-site Bose–Hubbard model, to which it reduces in the one-species limit. Due to the lack of an apparent reference state, application of the algebraic Bethe Ansatz to solve the model is prohibitive. Instead, the Bethe Ansatz solution is obtained by the use of operator identities and tensor product decompositions.
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.
Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras
Zinn-Justin, P
1998-01-01
A set of coupled non-linear integral equations is derived for a class of models connected with the quantum group $U_q(\\hat g)$ ($q=e^{i\\gamma}$ and $g$ simply laced Lie algebra), which are solvable using the Bethe Ansatz; these equations describe arbitrary excited states of a system with finite spatial length $L$. They generalize the Destri-De Vega equation for the Sine-Gordon/massive Thirring model to affine Toda field theory with imaginary coupling constant. As an application, the central charge and all the conformal weights of the UV conformal field theory are extracted in a straightforward manner. The quantum group truncation for rational values of $\\gamma/\\pi$ is discussed in detail; in the UV limit we recover through this procedure the RCFTs with extended $W(g)$ conformal symmetry.
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.
ODE/IM correspondence for modified B2(1) affine Toda field equation
Ito, Katsushi; Shu, Hongfei
2017-03-01
We study the massive ODE/IM correspondence for modified B2(1) affine Toda field equation. Based on the ψ-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 A3 /Z2 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.
Novel ansatzes and scalar quantities in gravito-electromagnetism
Bakopoulos, A.; Kanti, P.
2017-03-01
In this work, we focus on the theory of gravito-electromagnetism (GEM)—the theory that describes the dynamics of the gravitational field in terms of quantities met in electromagnetism—and we propose two novel forms of metric perturbations. The first one is a generalisation of the traditional GEM ansatz, and succeeds in reproducing the whole set of Maxwell's equations even for a dynamical vector potential A. The second form, the so-called alternative ansatz, goes beyond that leading to an expression for the Lorentz force that matches the one of electromagnetism and is free of additional terms even for a dynamical scalar potential Φ. In the context of the linearised theory, we then search for scalar invariant quantities in analogy to electromagnetism. We define three novel, 3rd-rank gravitational tensors, and demonstrate that the last two can be employed to construct scalar quantities that succeed in giving results very similar to those found in electromagnetism. Finally, the gauge invariance of the linearised gravitational theory is studied, and shown to lead to the gauge invariance of the GEM fields E and B for a general configuration of the arbitrary vector involved in the coordinate transformations.
Novel Ansatzes and Scalar Quantities in Gravito-Electromagnetism
Bakopoulos, Athanasios
2016-01-01
In this work, we focus on the theory of Gravito-Electromagnetism (GEM) -- the theory that describes the dynamics of the gravitational field in terms of quantities met in Electromagnetism -- and we propose two novel forms of metric perturbations. The first one is a generalisation of the traditional GEM ansatz, and succeeds in reproducing the whole set of Maxwell's equations even for a dynamical vector potential A. The second form, the so-called alternative ansatz, goes beyond that leading to an expression for the Lorentz force that matches the one of Electromagnetism and is free of additional terms even for a dynamical scalar potential \\Phi. In the context of the linearised theory, we then search for scalar invariant quantities in analogy to Electromagnetism. We define three novel, 3rd-rank gravitational tensors, and demonstrate that the last two can be employed to construct scalar quantities that succeed in giving results very similar to those found in Electromagnetism. Finally, the gauge invariance of the li...
Scaling ansatz for the jamming transition.
Goodrich, Carl P; Liu, Andrea J; Sethna, James P
2016-08-30
We propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.
Scaling ansatz for the jamming transition
Goodrich, Carl P.; Liu, Andrea J.; Sethna, James P.
2016-08-01
We propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.
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.
Spectra of Free Diquark in the Bethe-Salpeter Approach
Institute of Scientific and Technical Information of China (English)
YU Yan-Ming; KE Hong-Wei; DING Yi-Bing; GUO Xin-Heng; JIN Hong-Ying; LI Xue-Qian; SHEN Peng-Nian; WANG Guo-Li
2006-01-01
In this work, we employ the Bethe-Salpeter (B-S) equation to investigate the spectra of free diquarks and their B-S wave functions. We find that the B-S approach can be consistently applied to study the diqaurks with two heavy quarks or one heavy and one light quarks, but for two light-quark systems, the results are not reliable. There are a few free parameters in the whole scenario which can only be fixed phenomenologically. Thus, to determine them, one has to study baryons which are composed of quarks and diquarks.
Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz
Chua, Victor; Tiwari, Apoorv; Ryu, Shinsei
2016-01-01
The Multiscale Entanglement Renormalization Ansatz (MERA) is a tensor network based variational ansatz that is capable of capturing many of the key physical properties of strongly correlated ground states such as criticality and topological order. MERA also shares many deep relationships with the AdS/CFT (gauge-gravity) correspondence by realizing a UV complete holographic duality within the tensor networks framework. Motivated by this, we have re-purposed the MERA tensor network as an analysis tool to study the real-time evolution of the 1D transverse Ising model in its low energy excited state sector. We performed this analysis by allowing the ancilla qubits of the MERA tensor network to acquire quantum fluctuations, which yields a unitary transform between the physical (boundary) and ancilla qubit (bulk) Hilbert spaces. This then defines a reversible quantum circuit which is used as a `holographic transform' to study excited states and their real-time dynamics from the point of the bulk ancillae. In the ga...
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
Counting independent sets using the Bethe approximation
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Laboratory; Chandrasekaran, V [MIT; Gamarmik, D [MIT; Shah, D [MIT; Sin, J [MIT
2009-01-01
The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.
Obituary: Hans Albrecht Bethe, 1906-2005
Wijers, R.
2007-01-01
One of the unquestioned giants of physics and astrophysics, Hans Bethe, died on 6 March 2005, at the venerable age of 98, in his home town of Ithaca, New York. Seven decades of contributing to research and a Nobel Prize for his work on stellar hydrogen burning make a listing of his honors superfluou
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.
A variational matrix product ansatz for dispersion relations
Haegeman, Jutho; Weir, David J; Cirac, J Ignacio; Osborne, Tobias J; Verschelde, Henri; Verstraete, Frank
2011-01-01
A variational ansatz for momentum eigenstates of translation invariant quantum spin chains is formulated. The matrix product state ansatz works directly in the thermodynamic limit and allows for an efficient and stable implementation of the variational principle. Unlike previous approaches, the ansatz includes topologically non-trivial states (kinks, domain walls) for systems with symmetry breaking. The method is benchmarked using the S=1/2 XXZ antiferromagnet, the S=1 Heisenberg antiferromagnet and the S=1 XXZ antiferromagnet, and we obtain surprisingly accurate results.
Deng-Fan Potential for Relativistic Spinless Particles -- an Ansatz Solution
Institute of Scientific and Technical Information of China (English)
H. Hassanabadi; B.H. Yazarloo; S. Zarrinkamar; H. Rahimov
2012-01-01
Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.
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.
Bethe logarithm and QED shift for lithium.
Yan, Zong-Chao; Drake, G W F
2003-09-12
A novel finite basis set method is used to calculate the Bethe logarithm for the ground 2 (2)S(1/2) and excited 3 (2)S(1/2) states of lithium. The basis sets are constructed to span a huge range of distance scales within a single calculation, leading to well-converged values for the Bethe logarithm. The results are used to calculate an accurate value for the complete quantum electrodynamic energy shift up to order alpha(3) Ry. The calculated 3 (2)S(1/2)-2 (2)S(1/2) transition frequency for 7Li is 27 206.092 6(9) cm(-1), and the ionization potential for the 2 (2)S(1/2) state is 43 487.158 3(6) cm(-1). The 7Li-6Li isotope shift is also considered, and all the results compared with experiment.
Hyperon stars in the Brueckner-Bethe-Goldstone theory
Baldo, Marcello; Schulze, H J
2000-01-01
In the framework of the Brueckner-Bethe-Goldstone theory, we determine a fully microscopic equation of state for asymmetric and $\\beta$-stable nuclear matter containing $\\sim$ and $\\la$ hyperons. We use the Paris and the new Argonne $Av_{18}$ two-body nucleon interaction, whereas the nucleon-hyperon interaction is described by the Njimegen soft-core model. We stress the role played by the three-body nucleon interaction, which produces a strong repulsion at high densities. This enhances enormously the hyperon population, and produces a strong softening of the equation of state, which turns out almost independent on the nucleon-nucleon interaction. We use the new equation of state in order to calculate the structure of static neutron stars. We obtain a maximum mass configuration with $M_{\\rm max}$ = 1.26 (1.22) when the Paris ($Av_{18}$) nucleon potential is adopted. Central densities are about 10 times normal nuclear matter density. Stellar rotations, treated within a perturbative approach, increase the value ...
The Generalized Coherent State ansatz: Application to quantum electron-vibrational dynamics
Borrelli, Raffaele; Gelin, Maxim F.
2016-12-01
A new ansatz for molecular vibronic wave functions based on a superposition of time-dependent Generalized Coherent States is developed and analysed. The methodology is specifically tailored to describe the time evolution of the wave function of a system in which several interacting electronic states are coupled to a bath of harmonic oscillators. The equations of motion for the wave packet parameters are obtained by using the Dirac-Frenkel time-dependent variational principle. The methodology is used to describe the quantum dynamical behavior of a model polaron system and its scaling and convergence properties are discussed and compared with numerically exact results.
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.
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.
Centenary Birth Anniversary of E. W. Beth (1908-1964)
Bagni, Giorgio T.
2008-01-01
Evert Willem Beth (1908-1964) was a Dutch logician, mathematician and philosopher, whose work mainly concerned the foundations of mathematics. Beth was among the founders of the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques and was a member of the Central Committee of the International Commission on…
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
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.
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.
Transition electromagnetic form factor and current conservation in the Bethe-Salpeter approach
Carbonell, J
2015-01-01
The transition form factor for electrodisintegration of a two-body bound system is calculated in the Bethe-Salpeter framework. For the initial (bound) and the final (scattering) states, we use our solutions of the Bethe-Salpeter equation in Minkowski space which were first obtained recently. The gauge invariance, which manifests itself in the conservation of the transition electromagnetic current Jq = 0, is studied numerically. It results from a cancellation between the plane wave and the final state interaction contributions. This cancellation takes place only if the initial bound state BS amplitude, the final scattering state and the operator of electromagnetic current are strictly consistent with each other, that is if they are found in the same dynamical framework. A reliable result for the transition form factor can be obtained in this case only.
Current conservation in electrodisintegration of a bound system in the Bethe-Salpeter approach
Karmanov, V A
2014-01-01
Using our solutions of the Bethe-Salpeter equation with OBE kernel in Minkowski space both for the bound and scattering states, we calculate the transition form factors for electrodisintegration of the bound system which determine the electromagnetic current J of this process. Special emphasis is put on verifying the gauge invariance which should manifest itself in the current conservation. We find that for any value of the momentum transfer q the contributions of the plane wave and the final state interaction to the quantity J.q cancel each other thus providing J.q=0. However, this cancellation is obtained only if the initial Bethe-Salpeter amplitude (bound state), the final one (scattering state) and the current operator are strictly consistent with each other. A reliable result for the transition form factor can be found only in this case.
Institute of Scientific and Technical Information of China (English)
WANG ZhiGang; WAN ShaoLong; WANG KeLin
2001-01-01
The kaon electromagnetic form factor is calculated in the framework of coupled Schwinger-Dyson equation in rainbow approximation and Bethe-Salpeter equation in ladder approximation with the modified fiat-bottom potential,which is the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviours of the effective quark-gluon coupling. All our numerical results give good fit to experimental values and other theoretical results.``
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
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...
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.
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.
Two-loop Bethe-logarithm correction in hydrogenlike atoms.
Pachucki, Krzysztof; Jentschura, Ulrich D
2003-09-12
We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogenlike systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited atomic states. Although much smaller in absolute magnitude than the well-known one-loop Bethe logarithm, the two-loop analog is quite significant when compared to the current experimental accuracy of the 1S-2S transition: It contributes -8.19 and -0.84 kHz for the 1S and the 2S state, respectively. The two-loop Bethe logarithm has been the largest unknown correction to the hydrogen Lamb shift to date. Together with the ongoing measurement of the proton charge radius at the Paul Scherrer Institute, its calculation will bring theoretical and experimental accuracy for the Lamb shift in atomic hydrogen to the level of 10(-7).
Model of pair aggregation on the Bethe lattice
DEFF Research Database (Denmark)
Baillet, M.V.-P.; Pacheco, A.F.; Gómez, J.B.
1997-01-01
We extend a recent model of aggregation of pairs of particles, analyzing the case in which the supporting framework is a Bethe lattice. The model exhibits a critical behavior of the percolation theory type....
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...
Isothermal vs. isentropic description of protoneutron stars in the Brueckner-Bethe-Goldstone theory
Burgio, G F
2009-01-01
We study the structure of hadronic protoneutron stars within the finite temperature Brueckner-Bethe-Goldstone theoretical approach. Assuming beta-equilibrated nuclear matter with nucleons and leptons in the stellar core, with isothermal or isentropic profile, we show that particle populations and equation of state are very similar. As far as the maximum mass is concerned, we find that its value turns out to be almost independent on T, while a slight decrease is observed in the isentropic case, due to the enhanced proton fraction in the high density range.
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.
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...
Exact results in the Skyrme model in (3+1) dimensions via the generalized hedgehog ansatz
Canfora, Fabrizio
2016-09-01
We present exact results in the (3 + 1) -dimensional Skyrme model. First of all, it will be shown that, in the Pionic sector, a quite remarkable phenomenon for a non-integrable (3 + 1) -dimensional field theory appears: a non-linear superposition law is available allowing the composition of solutions in order to generate new solutions of the full field equations keeping alive, at the same time, the interactions terms in the energy-density. Secondly, it will be shown that the generalized hedgehog ansatz can be extended to suitable curved backgrounds. Interestingly, one can choose the background metric in such a way to describe finite-volume effects and, at the same time, to simplify the Skyrme field equations. In this way, it is possible to construct the first exact multi-Skyrmionic configurations of the (3 + 1) -dimensional Skyrme model with arbitrary high winding number and living at finite volume. Last but not least, a novel BPS bound (which is sharper than the usual one in term of the winding number) will be derived which can be saturated and reduces the field equations to a first-order equation for the profile.
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.
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.
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.
Evaluations of energy coefficients of Bethe-Weizsacker mass formula
Basu, D N
2004-01-01
A mass fit to the liquid drop model is presented. Coefficients of the volume, surface, coulomb, asymmetry and pairing energy terms of the semiemirical Bethe-Weizsacker mass formula have been determined by furnishing best fit to the observed mass excesses. Different sets of the weighting parameters for liquid drop model Bethe-Weizsacker mass formula have been obtained from minimizations of chisquare and mean square deviation. The recent exerimental and estimated mass excesses from Audi-Wapstra-Thibault atomic mass table have been used for the least square fitting procedure. Some implications of the modifications of parameters have been discussed.
Quantum Waveguide Properties of Bethe Lattices with a Ring
Institute of Scientific and Technical Information of China (English)
LIN Zhi-Ping; HOU Zhi-Lin; LIU You-Yan
2008-01-01
Based on waveguide theory we investigate electronic transport properties of Bethe lattices with a mesoscopic ring threaded by a magnetic flux. The generalized eigen-function method (GEM) is used to calculate the transmission and reflection coefficients up to the fifth generation of Bethe lattices. The relationships among the transmission coefficient T, magnetic flux φ and wave vector kl axe investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux φ are observed and discussed.
Relativistic bound-state equations for fermions with instantaneous interactions
Suttorp, L.G.
1979-01-01
Three types of relativistic bound-state equations for a fermion pair with instantaneous interaction are studied, viz., the instantaneous Bethe-Salpeter equation, the quasi-potential equation, and the two-particle Dirac equation. General forms for the equations describing bound states with arbitrary
Faber, C; Boulanger, P; Attaccalite, C; Duchemin, I; Blase, X
2014-03-13
Many-body Green's function perturbation theories, such as the GW and Bethe-Salpeter formalisms, are starting to be routinely applied to study charged and neutral electronic excitations in molecular organic systems relevant to applications in photovoltaics, photochemistry or biology. In parallel, density functional theory and its time-dependent extensions significantly progressed along the line of range-separated hybrid functionals within the generalized Kohn-Sham formalism designed to provide correct excitation energies. We give an overview and compare these approaches with examples drawn from the study of gas phase organic systems such as fullerenes, porphyrins, bacteriochlorophylls or nucleobases molecules. The perspectives and challenges that many-body perturbation theory is facing, such as the role of self-consistency, the calculation of forces and potential energy surfaces in the excited states, or the development of embedding techniques specific to the GW and Bethe-Salpeter equation formalisms, are outlined.
Energy Technology Data Exchange (ETDEWEB)
Ruban, V. P., E-mail: ruban@itp.ac.ru [Russian Academy of Sciences, Landau Institute for Theoretical Physics (Russian Federation)
2015-05-15
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.
Strange hadronic stellar matter within the Brueckner-Bethe-Goldstone theory
Baldo, Marcello; Schulze, H J
2000-01-01
In the framework of the non-relativistic Brueckner-Bethe-Goldstone theory, we derive a microscopic equation of state for asymmetric and $\\beta$-stable matter containing $\\Sigma^-$ and $\\Lambda$ hyperons. We mainly study the effects of three-body forces (TBFs) among nucleons on the hyperon formation and the equation of state (EoS). We find that, when TBFs are included, the stellar core is almost equally populated by nucleons and hyperons. The resulting EoS, which turns out to be extremely soft, has been used in order to calculate the static structure of neutron stars. We obtain a value of the maximum mass of 1.26 solar masses (1 solar mass $M_o \\simeq 1.99 \\cdot 10^{33} g$). Stellar rotations increase this value by about 12%.
Helium atom excitations by the GW and Bethe-Salpeter many-body formalism
Li, Jing; Duchemin, Ivan; Blase, Xavier; Olevano, Valerio
2016-01-01
Helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schr\\"odinger equation is known for helium ground and excited states, and represents a workbench for any many-body methodology. Here we check ab initio many-body GW approximation and Bethe-Salpeter equation (BSE) against helium exact solution. Starting from Hartree-Fock, we show that GW and BSE yield impressingly accurate results on excitation energies and oscillator strength. These findings suggest that the accuracy of BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.
Approximate Solutions of Klein-Gordon Equation with Kratzer Potential
Directory of Open Access Journals (Sweden)
H. Hassanabadi
2011-01-01
Full Text Available Approximate solutions of the D-dimensional Klein-Gordon equation are obtained for the scalar and vector general Kratzer potential for any l by using the ansatz method. The energy behavior is numerically discussed.
Pionierin der Religionspsychologie: Marianne Beth (1890-1984)
Belzen, J.A.
2010-01-01
This article deals with the contributions to the psychology of religion made by Dr. Marianne Beth (1890-1984), an almost totally forgotten pioneer of the psychology of religion. The article especially contextualizes her initiative to turn "unbelief" into a topic for research in psychology of religio
Mean values of local operators in highly excited Bethe states
Pozsgay, B.
2011-01-01
We consider expectation values of local operators in (continuum) integrable models in a situation when the mean value is calculated in a single Bethe state with a large number of particles. We develop a form factor expansion for the thermodynamic limit of the mean value, which applies whenever the d
Gravitational instantons of type $D_k$ and a generalization of the Gibbons-Hawking Ansatz
Ionas, Radu A
2016-01-01
We describe a quaternionic-based Ansatz generalizing the Gibbons-Hawking Ansatz to a class of hyperk\\"ahler metrics with hidden symmetries. We then apply it to obtain explicit expressions for gravitational instanton metrics of type $D_k$.
Exact satisfiability threshold for k -satisfiability problems on a Bethe lattice
Krishnamurthy, Supriya; Sumedha
2015-10-01
The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large system limit. Two different approaches to obtaining this threshold have been discussed in the literature: using first or second moment methods which give rigorous bounds or using the nonrigorous but powerful replica-symmetry-breaking (RSB) approach, which gives very accurate predictions on random graphs. In this paper, we lay out a different route to obtaining this threshold on a Bethe lattice. We need make no assumptions about the solution-space structure, a key assumption in the RSB approach. Despite this, our expressions and threshold values exactly match the best predictions of the cavity method under the one-step RSB hypothesis. In addition we can use the same procedure to obtain other useful quantities on the Bethe lattice such as the second moment of the number of solutions. Our method hence provides alternate interpretations as well as motivations for the key equations in the RSB approach.
Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz
Evenbly, G.; Vidal, G.
2015-11-01
We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e-β H for infinite β . This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β , produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.
Discontinuities of BFKL amplitudes and the BDS ansatz
Directory of Open Access Journals (Sweden)
V.S. Fadin
2015-12-01
Full Text Available 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.
Discontinuites of BFKL amplitudes and the BDS ansatz
Fadin, V S
2015-01-01
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 $\\to$ 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 colours starting with n = 2. Explicit expressions for the discontinuities of the 2 $\\to$ 3 and 2 $\\to$ 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.
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.
Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz.
Evenbly, G; Vidal, G
2015-11-13
We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e(-βH) for infinite β. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β, produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.
Ein Integraler Gestalt-Ansatz fuer Therapie und Beratung
Directory of Open Access Journals (Sweden)
Martina Gremmler-Fuhr
2005-06-01
Full Text Available Zusammenfassung: In diesem Text stellen wir unseren Ansatz für Psychotherapie und Beratung auf dem Hintergrund des integralen Paradigmas dar. Wir erläutern zunächst kurz vier Anforderungen an ein integrales Konzept in diesem professionellen Bereich: Umgang mit Komplexität und Vielperspektivität, Berücksichtigung gerichteter, vieldimensionaler Entwicklung, Orientierungs- und Sinngebungsfunktion, Realisierung relationaler Qualitäten in der Arbeit. Nach einer Begriffsbestimmung von „Therapie“, „Beratung“ und „Bildung“ charakterisieren wir das seit vielen Jahren von uns entwickelte Konzept für den Integralen Gestalt-Ansatz unter den Fragen nach (1 den Intentionen und Aufgaben von Therapie und Beratung, (2 der Gestaltung der Kommunikation und Beziehung, (3 der Art der Problemdefinition und dem Umgang mit Diagnostik sowie (4 den Strategien und Methoden – alle unter Rückkopplung an die zuvor erläuterten Anforderungen an ein integrales Konzept. Abstract: In this text we present our approach to psychotherapy and counseling on the background of the integral paradigm. We shortly explain four major requirements for such an integral concept: handling complexity and multi-perspectivity, considering directed and multi-dimensional development, offering orientation and meaning, relational qualities. After defining the terms „psychotherapy“, „counselling“, and „education“ we present our concept for the Integral Gestalt Approach which we have developed and evaluated for many years by dealing with four questions: (1 the intentions and tasks of therapy and counselling, (2 the formation of communication and relationship, (3 the specific way of defining problems and using diagnostics, and (4 the strategies and methods – all related back to the major requirements of an integral concept.
Institute of Scientific and Technical Information of China (English)
JianlanHU; X.FENG; ZhiLi
2000-01-01
New exact traveling wave solutions are derived for the fifth order KdV type equations by using a delicate way of rank analysis two-step ansatz method. Solitary shallowwater waves described by the above equation are discussed.
GW and Bethe-Salpeter study of small water clusters
Blase, Xavier; Boulanger, Paul; Bruneval, Fabien; Fernandez-Serra, Marivi; Duchemin, Ivan
2016-01-01
We study within the GW and Bethe-Salpeter many-body perturbation theories the electronic and optical properties of small (H2O)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 G0W0@PBE or G0W0@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 G0W0 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 G0W0 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.
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.
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...
Variational ansatz for the nonlinear Landau-Zener problem for cold atom association
Energy Technology Data Exchange (ETDEWEB)
Ishkhanyan, A [Institute for Physical Research NAS of Armenia, 0203 Ashtarak-2 (Armenia); Joulakian, B [LPMC, Universite Paul Verlaine-Metz, 1 Bld Arago, 57078 Metz Cedex 3 (France); Suominen, K-A [Department of Physics and Astronomy, University of Turku, 20014 Turun yliopisto (Finland)
2009-11-28
We present a rigorous analysis of the Landau-Zener linear-in-time term crossing problem for quadratic-nonlinear systems relevant to the coherent association of ultracold atoms in degenerate quantum gases. Our treatment is based on an exact third-order nonlinear differential equation for the molecular state probability. Applying a variational two-term ansatz, we construct a simple approximation that accurately describes the whole-time dynamics of the coupled atom-molecular system for any set of involved parameters. Ensuring an absolute error of less than 10{sup -5} for the final transition probability, the resultant solution improves by several orders of magnitude the accuracy of the previous approximations by A Ishkhanyan et al developed separately for the weak coupling (2005 J. Phys. A: Math. Gen. 38 3505) and strong interaction (2006 J. Phys. A: Math. Gen. 39 14887) limits. In addition, the constructed approximation covers the whole moderate-coupling regime, providing this intermediate regime with the same accuracy as the two mentioned limits. The obtained results reveal the remarkable observation, that for the strong-coupling limit the resonance crossing is mostly governed by the nonlinearity, while the coherent atom-molecular oscillations arising soon after the resonance has been crossed are basically of a linear nature. This observation is supposed to be of a general character, due to the basic attributes of the resonance-crossing processes in the nonlinear quantum systems of the discussed type of involved quadratic nonlinearity. (fast track communication)
Renormalization group flow equations from the 4PI equations of motion
Carrington, M E
2013-01-01
The 4PI effective action provides a a hierarchy of integral equations which have the form of Bethe-Salpeter equations. The vertex functions obtained from these equations can be used to truncate the exact renormalization group flow equations. This truncation has the property that the flow is a total derivative with respect to the flow parameter and is equivalent to solving the nPI equations of motion. This result establishes a direct connection between two non-perturbative methods.
Electromagnetic form factor via Minkowski and Euclidean Bethe-Salpeter amplitudes
Karmanov, V A; Mangin-Brinet, M
2007-01-01
The electromagnetic form factors calculated through Euclidean Bethe-Salpeter amplitude and through the light-front wave function are compared with the one found using the Bethe-Salpeter amplitude in Minkowski space. The form factor expressed through the Euclidean Bethe-Salpeter amplitude (both within and without static approximation) considerably differs from the Minkowski one, whereas form factor found in the light-front approach is almost indistinguishable from it.
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.
Golinelli, Olivier; Mallick, Kirone
2006-10-01
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by the Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by the Bethe ansatz.
Energy Technology Data Exchange (ETDEWEB)
Golinelli, Olivier [Service de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex (France); Mallick, Kirone [Service de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex (France)
2006-10-13
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by the Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by the Bethe ansatz.
REDUCTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATION AND EXACT SOLUTIONS
Institute of Scientific and Technical Information of China (English)
YeCaier; PanZuliang
2003-01-01
Nonlinear partial differetial equation(NLPDE)is converted into ordinary differential equation(ODE)via a new ansatz.Using undetermined function method,the ODE obtained above is replaced by a set of algebraic equations which are solved out with the aid of Mathematica.The exact solutions and solitary solutions of NLPDE are obtained.
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
About the seventh-order Kaup-Kupershmidt equation and its solutions
Salas, Alvaro; Lugo, Jose Gonzalo Escobar
2008-01-01
In this letter we obtain exact soliton and periodic solutions to the seventh-order Kaup-Kupershmidt equation. We make use of the Cole-Hopf transformation and two particular rational hyperbolic functions ansatze.
Nieves, J
2001-01-01
Heavy Baryon Chiral Perturbation Theory (HBChPT) to leading order provides a kernel to solve the Bethe-Salpeter equation for the $P_{33}$ ($\\Delta(1232)$-channel) $\\pi-N$ system, in the infinite nucleon mass limit. Crossed Born terms include, when iterated within the Bethe-Salpeter equation, both {\\it all} one- and {\\it some} two-pion intermediate states, hence preserving elastic unitarity below the two-pion production threshold. This suggests searching for a solution with the help of dispersion relations and suitable subtraction constants, when all in-elasticities are explicitly neglected. The solution allows for a successful description of the experimental phase shift from threshold up to $\\sqrt{s}=1500$ MeV in terms of four subtraction constants. Next-to-leading order HBChPT calculations are also used to estimate the unknown subtraction constants which appear in the solution. Large discrepancies are encountered which can be traced to the slow convergence rate of HBChPT.
The Bethe Sum Rule and Basis Set Selection in the Calculation of Generalized Oscillator Strengths
DEFF Research Database (Denmark)
Cabrera-Trujillo, Remigio; Sabin, John R.; Oddershede, Jens;
1999-01-01
Fulfillment of the Bethe sum rule may be construed as a measure of basis set quality for atomic and molecular properties involving the generalized oscillator strength distribution. It is first shown that, in the case of a complete basis, the Bethe sum rule is fulfilled exactly in the random phase...
In Defense of Today's Struggling Reader: What Policymakers Can Learn from Beth
Spencer, Tamara
2012-01-01
Beth attends a New York City K-8, dual-language (Spanish/English) public school where 96% of the students qualify as low-income, based on participation in the federally funded lunch program. Early in Beth's 1st-grade year, she was classified as a struggling reader, based on district-wide assessments that identified academic deficits in such skill…
Loop Equations in Abelian Gauge Theories
Di Bartolo, C; Pe~na, F; Bartolo, Cayetano Di; Leal, Lorenzo; Peña, Francisco
2005-01-01
The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme for studying these loop-equations for lattice Maxwell theory is presented. The approximation leads to a partial difference equation in the area and length variables of the loop, and certain physically motivated ansatz is seen to reproduce the mean field results from a geometrical perspective.
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...
Y-system for $\\gamma$-deformed ABJM Theory
Chen, Hui-Huang; Wu, Jun-Bao
2016-01-01
We investigate the integrable aspects of the planar $\\gamma$-deformed ABJM theory and proposed the twisted asymptotic Bethe ansatz equations. A more general method through a twist generating functional was discussed, based on which, the asymptotic large L solution of Y-system is modified in order to match the asymptotic Bethe ansatz equations. Serval applications of our method were made in $sl(2)$ sector and some important examples in $\\beta$-deformed ABJM were present as well.
Single-Field Inflation and the Local Ansatz: Distinguishability and Consistency
de Putter, Roland; Green, Daniel; Meyers, Joel
2016-01-01
The single-field consistency conditions and the local ansatz have played separate but important roles in characterizing the non-Gaussian signatures of single- and multifield inflation respectively. We explore the precise relationship between these two approaches and their predictions. We demonstrate that the predictions of the single-field consistency conditions can never be satisfied by a general local ansatz with deviations necessarily arising at order $(n_s-1)^2$. This implies that there is, in principle, a minimum difference between single- and (fully local) multifield inflation in observables sensitive to the squeezed limit such as scale-dependent halo bias. We also explore some potential observational implications of the consistency conditions and its relationship to the local ansatz. In particular, we propose a new scheme to test the consistency relations. In analogy with delensing of the cosmic microwave background, one can deproject the coupling of the long wavelength modes with the short wavelength ...
Phase Diagram for Ashkin-Teller Model on Bethe Lattice
Institute of Scientific and Technical Information of China (English)
LE Jian-Xin; YANG Zhan-Ru
2005-01-01
Using the recursion method, we study the phase transitions of the Ashkin-Teller model on the Bethe lattice,restricting ourselves to the case of ferromagnetic interactions. The isotropic Ashkin-Teller model and the anisotropic one are respectively investigated, and exact expressions for the free energy and the magnetization are obtained. It can be found that each of the three varieties of phase diagrams, for the anisotropic Ashkin-Teller model, consists of four phases, I.e., the fully disordered paramagnetic phase Para, the fully ordered ferromagnetic phase Ferro, and two partially ordered ferromagnetic phases and , while the phase diagram, for the isotropic Ashkin-Teller model,contains three phases, I.e., the fully disordered paramagnetic phase Para, the fully ordered ferromagnetic phase Baxter Phase, and the partially ordered ferromagnetic phase .
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.
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.
Testing an ansatz for the leading secular loop corrections from quantum gravity during inflation
Basu, S.; Woodard, R. P.
2016-10-01
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.
Graph Zeta Function in the Bethe Free Energy and Loopy Belief Propagation
Watanabe, Yusuke
2010-01-01
We propose a new approach to the analysis of Loopy Belief Propagation (LBP) by establishing a formula that connects the Hessian of the Bethe free energy with the edge zeta function. The formula has a number of theoretical implications on LBP. It is applied to give a sufficient condition that the Hessian of the Bethe free energy is positive definite, which shows non-convexity for graphs with multiple cycles. The formula clarifies the relation between the local stability of a fixed point of LBP and local minima of the Bethe free energy. We also propose a new approach to the uniqueness of LBP fixed point, and show various conditions of uniqueness.
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.
Exact travelling wave solutions for a class of nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Xie Fuding E-mail: xiefd@sohu.com; Gao Xiaoshan
2004-03-01
In this paper, the tanh-method is improved by means of a proper rational transformation based upon a coupled projective Riccati equations. The ansatz can be applied to find more and new exact solutions of the partial differential equations with the aid of symbolic computation system, Maple. We choose an example, which includes phi{sup 4} equation, Klein-Gordon equation, Duffing equation, Landau-Ginburg-Higgs equation and Sine-Gordon equation, to illustrate the method.
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...
A self-consistent determination of the RVB and SC gaps in the YRZ ansatz
Rao, Zi-Ye; Wang, Xiao-Min; Jiang, Hong-Min
2017-03-01
A correct understanding of the origin of the pseudogap in high temperature (high-T c) cuprate superconductors is considered to be a peripheral breakthrough in the understanding of the microscopic mechanism of the high-T c superconductivity. Yang-Rice-Zhang (YRZ) ansatz is an important phenomenological theory to describe the phenomenon of pseudogap. However, in the framework of YRZ, the pseudogap (resonant valence bond (RVB) gap) and the superconducting (SC) gap are unable to have a self-consistent determination at different doping concentrations, and this severely limits the application of the YRZ ansatz. Based on the YRZ ansatz, this study develops a technical method to determine the RVB and SC gaps in a self-consistent manner. It is revealed that the self-consistent calculations of the doping dependence of RVB, SC gaps and spectral function are not only consistent with the empirical gap formula in the YRZ framework, but also consistent with the doping evolution of the Fermi surface observed in the angle-resolved photoemission spectroscopy (ARPES) experiments. Our method will greatly extend the applications of the YRZ ansatz, and will deepen our understanding of the origin of pseudogap as well as the mechanism of high-T c superconductivity.
Decay of Bethe-Salpeter kernel and bound states for the lattice four Fermi model
Energy Technology Data Exchange (ETDEWEB)
Anjos, Petrus Henrique Ribeiro dos [Universidade Federal de Goias (UFG), Goiania, GO (Brazil)
2012-07-01
Full text: We consider an imaginary-time functional integral formulation of the the lattice four-Fermi or Gross-Neveu model in d + 1 space-time dimensions (d = 1, 2, 3) and with N-component fermions. Let 0 < {kappa} << 1 be the hopping parameter, {lambda} > 0 the four-fermion coupling, m > 0 the bare fermion mass and take s x s spin matrices (s = 2,4). In a previous work, we derive spectral representations for two- and four- point correlation functions and use this result to show that the low-lying energy-momentum spectrum of this model exhibits isolated dispersion curves which are identified as single particles, multi-particle bands and bound states. In this previous analysis, the one-particle energy-momentum spectrum is obtained rigorously and is manifested by sN/2 isolated and identical dispersion curves, and the mass of particles has asymptotic value order of order 1n {kappa}. The existence of two-particle bound states above or below the two-particle band depends on whether Gaussian domination does hold or does not, respectively. Two-particle bound states emerge from solutions to a lattice Bethe-Salpeter equation that we solve in a ladder approximation. Within this approximation, the bound states have O({kappa}{sup 0}) binding energies at zero system momentum and their masses are all equal, with value {approx} -2 1n {kappa}. In this work, using the hyperplane decoupling method, we provide a detailed analysis of the decay of the Bethe-Salpeter kernel and show how to use this decay to extend the spectral result obtained in the ladder approximation to the full model. In particular, we prove that if the two-point function decays faster than the four-point function (Gaussian subjugation) then the only point in the mass spectrum above the one-particle mass and below the two-particle band is the bound state mass. (author)
Exact solution of a generalized two-sites Bose-Hubbard model
Filho, Gilberto N Santos
2016-01-01
I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a $S^{N-1}$ sphere, where $N$ is the total number of atoms in the condensate.
Study of an anisotropic g-ology model
Wang, Y.; Pu, Fu-Cho
1997-01-01
The one-dimensional electron gas model in the strong coupling regime is considered. It is shown that this model is Bethe ansatz solvable and the exact spectrum of the Hamiltonian is obtained. The massive spin elementary excitations are established based on the Bethe ansatz equations. The magnetization near the onset at zero temperature is calculated. It is clarified that the Luther-Emergy model does represent a universal class of the one-D electron system.
Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Maillet, J.M. [UMR 5672 du CNRS, ENS Lyon (France). Lab. de Physique; Slavnov, N.A. [Steklov Mathematical Institute, Moscow (Russian Federation)
2010-12-15
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.)
The exact solution of an octagonal rectangle triangle random tiling
De Gier, J; Gier, Jan de; Nienhuis, Bernard
1996-01-01
We present a detailed calculation of the recently published exact solution of a random tiling model possessing an eight-fold symmetric phase. The solution is obtained using Bethe Ansatz and provides closed expressions for the entropy and phason elastic constants. Qualitatively, this model has the same features as the square-triangle random tiling model. We use the method of P. Kalugin, who solved the Bethe Ansatz equations for the square-triangle tiling, which were found by M. Widom.
Analyzing the DK molecular state in the Bethe-Salpeter approach%在Bethe-Salpeter方程框架下研究DK分子态
Institute of Scientific and Technical Information of China (English)
谢振兴
2012-01-01
本文研究了BaBar合作组在分析正负电子湮灭的不变质量时发现的一个很窄的峰结构,该峰结构被命名为D(*s0)+(2317).首先假定它是S波的DK分子束缚态,利用Bethe-Salpeter方程研究了其结构并研究了其同位旋破缺衰变过程D(*s0)+ (2317)→D(s+)+π0,同时在末态考虑了η-π0混合效应对衰变宽度的影响.研究结果表明,D(*s0)+(2317)可以具有DK的分子束缚态结构,而且η-π0混合效应对衰变宽度影响非常明显,D(*s0)+(2317)→D(s+)π0衰变宽度的理论结果与实验结果相符.其它的理论模型也对D(*s0)+(2317)的结构和性质进行了研究,认为D(*s0)+ (2317)可能存在其它形式的结构,并且得到的理论结果和实验结果相符.因此的结构存在多种形式,或者是几种结构的混合.该研究结果对未来的实验进一步确定D(*s0)(2317)的结构有指导意义.%We analyze the state D++s0 (2317) ,which was discovered as a very narrow peak by the Babar collaboration while analyzing the invariant mass distribution of the decay final state D++,0. Assuming D++s0(2317) that is composed of DK, we use the Bethe-Salpeter equation to study the structure of D++s0(2317) and the isospin breaking decay process D++s0 (2317)→Ds+π0. We also consider the η -π0 mixing effect in the decay. It is shown that D++s0 (2317) can be formed as a molecular bound state of DK and the mixing effect has significant influence on the decay. The decay width in our model agrees with the resolution of the detector. Other theoretical models are also used to study the property and the structure of D++s0(2317) .assuming that D++s0(2317) may have other forms, and the results agree with the experimental data too. So the structure of may be other forms or the mixing of them. Our results will give important instructions to the forthcoming experiments.
Self-Similar Solutions of Three-Dimensional Navier-Stokes Equation
Institute of Scientific and Technical Information of China (English)
I.F. Barna
2011-01-01
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 Kummer functions or strongly related. Our final formula is compared with other results obtained from group theoretical approaches.
Belief Propagation and Bethe approximation for Traffic Prediction
Furtlehner, C; Lasgouttes, J M; Fortelle, Arnaud De La; Furtlehner, Cyril; Lasgouttes, Jean-Marc
2007-01-01
We define and study an inference algorithm based on "belief propagation" (BP) and the Bethe approximation. The idea is to encode into a graph an a priori information composed of correlations or marginal probabilities of variables, and to use a message passing procedure to estimate the actual state from some extra real-time information. This method is originally designed for traffic prediction and is particularly suitable in settings where the only information available is floating car data. We propose a discretized traffic description, based on the Ising model of statistical physics, in order to both reconstruct and predict the traffic in real time. General properties of BP are addressed in this context. In particular, a detailed study of stability is proposed with respect to the a priori data and the graph topology. The behavior of the algorithm is illustrated by numerical studies on a simple traffic toy model. How this approach can be generalized to encode superposition of many traffic patterns is discussed...
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.
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.
Comment on ``New ansatz for metric operator calculation in pseudo-Hermitian field theory''
Bender, Carl M.; Benincasa, Gregorio; Jones, H. F.
2009-12-01
In a recent Brief Report by Shalaby, a new first-order perturbative calculation of the metric operator for an iϕ3 scalar field theory is given. It is claimed that the incorporation of derivative terms in the ansatz for the metric operator results in a local solution, in contrast to the nonlocal solution previously obtained by Bender, Brody, and Jones. Unfortunately, Shalaby’s calculation is not valid because of sign errors.
Institute of Scientific and Technical Information of China (English)
WANG Mei-Jiao; WANG Qi
2006-01-01
In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.
Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N.
2017-04-01
In this paper, we propose and study two approaches to approximate the solution of the Bethe-Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both approaches are based on the reduced basis method and low-rank factorizations of the generating matrices. We also propose to represent the static screen interaction part in the BSE matrix by a small active sub-block, with a size balancing the storage for rank-structured representations of other matrix blocks. We demonstrate by various numerical tests that the combination of the diagonal plus low-rank plus reduced-block approximation exhibits higher precision with low numerical cost, providing as well a distinct two-sided error estimate for the smallest eigenvalues of the Bethe-Salpeter operator. The complexity is reduced to O (Nb2) in the size of the atomic orbitals basis set, Nb, instead of the practically intractable O (Nb6) scaling for the direct diagonalization. In the second approach, we apply the quantized-TT (QTT) tensor representation to both, the long eigenvectors and the column vectors in the rank-structured BSE matrix blocks, and combine this with the ALS-type iteration in block QTT format. The QTT-rank of the matrix entities possesses almost the same magnitude as the number of occupied orbitals in the molecular systems, No
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.
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.
Nguyen-Truong, Hieu T
2015-02-01
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.
Miyaji, Masamichi; Numasawa, Tokiro; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento
2015-10-01
We present how the surface-state correspondence, conjectured by Miyaji and Takayanagi, works in the setup of AdS3/CFT2 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 AdS3 and bulk scalar propagators. We also calculate the information metric for a locally excited state and show that it reproduces the time slice of AdS3.
First-principles Theory of the Momentum-dependent Local Ansatz for Correlated Electron System
Chandra, Sumal; Kakehashi, Yoshiro
The momentum-dependent local-ansatz (MLA) wavefunction describes well correlated electrons in solids in both the weak and strong interaction regimes. In order to apply the theory to the realistic system, we have extended the MLA to the first-principles version using the tight-binding LDA+U Hamiltonian. We demonstrate for the paramagnetic Fe that the first-principles MLA can describe a reasonable correlation energy gain and suppression of charge fluctuations due to electron correlations. Furthermore, we show that the MLA yields a distinct momentum dependence of the momentum distribution, and thus improves the Gutzwiller wavefunction.
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
Testing Invisible Momentum Ansatze in Missing Energy Events at the LHC arXiv
Kim, Doojin; Moortgat, Filip; Pape, Luc
We consider SUSY-like events with two decay chains, each terminating in an invisible particle, whose true energy and momentum are not measured in the detector. Nevertheless, a useful educated guess about the invisible momenta can still be obtained by optimizing a suitable invariant mass function. We review and contrast several proposals in the literature for such ansatze: four versions of the M_T2-assisted on-shell reconstruction (MAOS), as well as several variants of the on-shell constrained M_2 variables. We compare the performance of these methods with regards to the mass determination of a new particle resonance along the decay chain from the peak of the reconstructed invariant mass distribution. For concreteness, we consider the event topology of dilepton ttbar events and study each of the three possible subsystems, in both a ttbar and a SUSY example. We find that the M_2 variables generally provide sharper peaks and therefore better ansatze for the invisible momenta. We show that the performance can be ...
Jacquemin, Denis; Duchemin, Ivan; Blase, Xavier
2017-03-21
Developing ab initio approaches able to provide accurate excited-state energies at a reasonable computational cost is one of the biggest challenges in theoretical chemistry. In that framework, the Bethe-Salpeter equation approach, combined with the GW exchange-correlation self-energy, which maintains the same scaling with system size as TD-DFT, has recently been the focus of a rapidly increasing number of applications in molecular chemistry. Using a recently proposed set encompassing excitation energies of many kinds [J. Phys. Chem. Lett. 2016, 7, 586-591], we investigate here the performances of BSE/GW. We compare these results to CASPT2, EOM-CCSD, and TD-DFT data and show that BSE/GW provides an accuracy comparable to the two wave function methods. It is particularly remarkable that the BSE/GW is equally efficient for valence, Rydberg, and charge-transfer excitations. In contrast, it provides a poor description of triplet excited states, for which EOM-CCSD and CASPT2 clearly outperform BSE/GW. This contribution therefore supports the use of the Bethe-Salpeter approach for spin-conserving transitions.
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.
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.
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)...
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.
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
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.
Numerical study of the mixed spin-1 and spin-5/2 BEG model on the Bethe lattice
Yessoufou, R. A.; Bekhechi, S.; Hontinfinde, F.
2011-05-01
The mixed spin- 1 and spin-5/2 ferromagnetic Ising model with bilinear ( J) and biquadratic ( K) nearest-neighbor exchange interactions and a single-ion potential or crystal-field interaction ( D) is studied on the Bethe lattice by means of exact recursion equations. First, the phase diagram of the system at zero temperature is obtained in the (D/Jq, K/Jq) plane, where q denotes the coordination number of the lattice. Second, the sublattice magnetizations as functions of the temperature, the crystal-field and the biquadratic interaction strengths are thoroughly investigated. For q = 3, the resulting phase diagrams show first and second order phase transitions as well as compensation points where the net magnetization of the whole lattice should vanish in the antiferromagnetic version of the model. One interesting feature of the model concerns the presence of tricritical points. Our calculations show that at non-zero temperature, none of the sublattice can order separately. However, under an external magnetic field, some interesting phase diagrams with partially ordered phases arise.
Mass matrix Ansatz and lepton flavor violation in the THDM-III
Díaz-Cruz, J L; Rosado, A
2004-01-01
Predictive Higgs-fermion couplings can be obtained when a specific texture for the fermion mass matrices is included in the general two-Higgs doublet model. We derive the form of these couplings in the charged lepton sector using a Hermitian mass matrix Ansatz with four-texture zeros. The presence of unconstrained phases in the vertices phi-li-lj modifies the pattern of flavor-violating Higgs interactions. Bounds on the model parameters are obtained from present limits on rare lepton flavor violating processes, which could be extended further by the search for the decay tau -> mu mu mu and mu-e conversion at future experiments. The signal from Higgs boson decays phi -> tau mu could be searched at the large hadron collider (LHC), while e-mu transitions could produce a detectable signal at a future e mu-collider, through the reaction e mu -> h0 -> tau tau.
Kakehashi, Yoshiro; Chandra, Sumal
2016-04-01
We have developed a first-principles local ansatz wavefunction approach with momentum-dependent variational parameters on the basis of the tight-binding LDA+U Hamiltonian. The theory goes beyond the first-principles Gutzwiller approach and quantitatively describes correlated electron systems. Using the theory, we find that the momentum distribution function (MDF) bands of paramagnetic bcc Fe along high-symmetry lines show a large deviation from the Fermi-Dirac function for the d electrons with eg symmetry and yield the momentum-dependent mass enhancement factors. The calculated average mass enhancement m*/m = 1.65 is consistent with low-temperature specific heat data as well as recent angle-resolved photoemission spectroscopy (ARPES) data.
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
Spectrum and Bethe-Salpeter amplitudes of $\\Omega$ baryons from lattice QCD
Liang, Jian; Chen, Ying; Chiu, Wei-Feng; Gong, Ming; Liu, Chuan; Liu, Yu-Bin; Liu, Zhaofeng; Ma, Jian-Ping; Zhang, Jian-Bo
2015-01-01
The $\\Omega$ baryons with $J^P=3/2^\\pm, 1/2^\\pm$ are studied on the lattice in the quenched approximation. Their mass levels are ordered as $M_{3/2^+}
The Beer/Bethe/Uexküll paper (1899) and misinterpretations surrounding 'vitalistic behaviorism'.
Mildenberger, Florian
2006-01-01
In the history of behaviorism the paper of the three physiologists Theodor Beer, Albrecht Bethe and Jakob von Uexküll from 1899 plays an important role. Many researchers were influenced by this paper and identified it as fundamental for objective psychological research. But during the period of its adoption (1900-1925) psychologists did not notice that Beer, Bethe and Uexküll had distanced themselves from their own paper, because it had been ignored in physiological and biological discussions. Moreover, one of the three (Beer) had to resign from the scientific community because of private scandal and another one (Uexküll) changed all of his views and left the base of objective science for subjective vitalism. However, this did not change his adoption of behaviorism.
Zero-Temperature Limit of a Convergent Algorithm to Minimize the Bethe Free Energy
Werner, Tomas
2011-01-01
After the discovery that fixed points of loopy belief propagation coincide with stationary points of the Bethe free energy, several researchers proposed provably convergent algorithms to directly minimize the Bethe free energy. These algorithms were formulated only for non-zero temperature (thus finding fixed points of the sum-product algorithm) and their possible extension to zero temperature is not obvious. We present the zero-temperature limit of the double-loop algorithm by Heskes, which converges a max-product fixed point. The inner loop of this algorithm is max-sum diffusion. Under certain conditions, the algorithm combines the complementary advantages of the max-product belief propagation and max-sum diffusion (LP relaxation): it yields good approximation of both ground states and max-marginals.
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.
Calculation of the relativistic Bethe logarithm in the two-center problem
Korobov, Vladimir I.; Hilico, L.; Karr, J.-Ph.
2013-06-01
We present a variational approach to evaluate relativistic corrections of order α2 to the Bethe logarithm for the ground electronic state of the Coulomb two-center problem. That allows us to estimate the radiative contribution at mα7 order in molecular-like three-body systems such as hydrogen molecular ions H2+ and HD+ or antiprotonic helium atoms. While we get ten 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 three to four significant digits starting from R=0.2 bohr, which will allow us to reach 10-10 relative uncertainty on transition frequencies.
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.
An exact solution on the ferromagnetic Face-Cubic spin model on a Bethe lattice
Ohanyan, V. R.; Ananikyan, L. N.; Ananikian, N. S.
2006-01-01
The lattice spin model with $Q$--component discrete spin variables restricted to have orientations orthogonal to the faces of $Q$-dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The partition function of the model with dipole--dipole and quadrupole--quadrupole interaction for arbitrary planar graph is presented in terms of double graph expansions. The latter is calculated exactly in case of trees. The system of two recurrent relations wh...
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 ...
Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation
Ma, W.
1996-05-01
Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and further two solutions to describe nonlinear interaction of traveling waves are generated. B\\"acklund transformations of the linear form and some special cases are considered.
Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation
Ma, Wen-Xiu; Fuchssteiner, Benno
1995-01-01
Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and further two solutions to describe nonlinear interaction of traveling waves are generated. B\\"acklund transformations of the linear form and some special cases are considered.
New Complexiton Solutions of (2+1)-Dimensional Nizhnik-Novikov-Veselov Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Yuan-Yuan; ZHENG Ying; ZHANG Hong-Qing
2006-01-01
In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.
Domain walls to Boussinesq-type equations in (2 + 1)-dimensions
Triki, H.; Kara, A. H.; Biswas, A.
2014-07-01
In this paper, two models with fourth-order dispersion in 2 + 1 dimensions are investigated. Based on Ansatz method, exact domain wall solutions are derived. Parametric conditions for the existence of the domain wall solutions are given. Lie symmetry analysis also retrieves conserved densities of governing nonlinear evolution equations.
New Families of Nontravelling Wave Solutions to Two (3+1)-Dimensional Equations
Institute of Scientific and Technical Information of China (English)
BAI Cheng-Lin; LIU Xi-Qiang; ZHAO Hong
2005-01-01
In this paper, two (3+1)-dimensional equations are investigated. A uto-Backlund 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.
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR GENERALIZED DRINFELD-SOKOLOV EQUATIONS
Institute of Scientific and Technical Information of China (English)
LONG Yao; RUI Wei-guo; HE Bin; CHEN Can
2006-01-01
Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups .of the parametric conditions, more solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions are obtained. Exact explicit parametric representations of these travelling wave solutions are given.
Compact and noncompact structures of the nonlinearly dispersive GNLS(m,n,k,l equation
Directory of Open Access Journals (Sweden)
Bülent Kılıç
2015-02-01
Full Text Available In this paper, we establish exact-special solutions of the generalized nonlinear dispersion GNLS(m,n,k,l equation. We use the ansatz method for acquiring the compactons, solitary patterns, solitons and other types of solutions.
1-Soliton solutions of complex modified KdV equation with time-dependent coefficients
Kumar, H.; Chand, F.
2013-09-01
In this paper, we have obtained exact 1-soliton solutions of complex modified KdV equation with variable—coefficients using solitary wave ansatz. Restrictions on parameters of the soliton have been observed in course of the derivation of soliton solutions. Finally, a few numerical simulations of dark and bright solitons have been given.
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.
Comments on Formulating Meson Bound-State Equations Beyond Rainbow-Ladder Approximation
Qin, Si-xue
2016-11-01
We study mesons through solving the coupled system of the gap equation for the quark propagator and the Bethe-Salpeter equation for the meson wavefunction. The gap equation and Bethe-Salpeter equation are in fact members of infinitely coupled Dyson-Schwinger equations of Green functions of QCD. To make it solvable, the system must be truncated. The simplest rainbow-ladder truncation is widely used but shows drawbacks in many aspects. To improve the simplest truncation, we analyze symmetries of the fundamental theory and solve the corresponding Ward-Green-Takahashi identities. Then, the elements of the coupled system, i.e., the quark-gluon vertex and the quark-antiquark scattering kernel, can be constructed accordingly.
非线性偏微分方程的约化和精确解%REDUCTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATION AND EXACT SOLUTIONS
Institute of Scientific and Technical Information of China (English)
叶彩儿; 潘祖梁
2003-01-01
Nonlinear partial differetial equation(NLPDE) is converted into ordinary differentialequation (ODE) via a new ansatzUsing undetermined function method ,the ODE obtained aboveis replaced by a set of algebraic equations which are solved out with the aid of MathematicaTheexact solutions and solitary solutions of NLPDE are obtained.
Electromagnetic form factor via Bethe-Salpeter amplitude in Minkowski space
Carbonell, J; Mangin-Brinet, M
2008-01-01
For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation in the form factor integral induces errors which increase with the momentum transfer Q^2. At JLab domain (Q^2=10 GeV^2/c^2), they are about 30%. Static approximation results in an additional and more significant error. On the contrary, the form factor calculated in light-front dynamics is almost indistinguishable from the Minkowski space one.
Study of BB ¯*/DD ¯* bound states in a Bethe-Salpeter approach
He, Jun
2014-10-01
In this work the BB ¯*/DD ¯* system is studied in the Bethe-Salpeter approach with quasipotential approximation. In our calculation both direct and cross diagrams are included in the one-boson-exchange potential. The numerical results indicate the existence of an isoscalar bound state DD ¯* with JPC=1++, which may be related to the X(3872). In the isovector sector, no bound state is produced from the interactions of DD ¯* and BB ¯*, which suggests the molecular state explanations for Zb(10610) and Zc(3900) are excluded.
Exact solutions for nonlinear foam drainage equation
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2017-02-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G)-expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Exact solutions for nonlinear foam drainage equation
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2016-09-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G) -expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Markov-Yukawa Transversality Principle And 3D-4D Interlinkage Of Bethe-Salpeter Amplitudes
Mitra, A N
2000-01-01
This article is designed to focus attention on the Markov-Yukawa Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D interlinkage between the corresponding BSE amplitudes, with a closely parallel treatment of $q{\\bar q}$ and $qqq$ systems, stemming from a common 4-fermion Lagrangian mediated by gluon (vector)-like exchange. This unique feature of MYTP owes its origin to a Lorentz- covariant 3D support to the BS kernel, which acts as a sort of `gauge principle' and distinguishes it from most other 3D approaches to strong interaction dynamics. Some of the principal approaches in the latter category are briefly reviewed so as to set the (less familiar) MYTP in their context. Two specific types of MYTP which provide 3D support to the BSE kernel, are considered: a) Covariant Instantaneity Ansatz (CIA); b) Covariant LF/NP ansatz (Cov.LF). Both lead to formaly identical 3D BSE reductions but produce sharply different 4D structures: Under CIA, the 4D loop integrals suffer from Lorentz mismatch of t...
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...
Gao, Fei; Liu, Yu-xin
2016-01-01
We propose a new numerical method to compute parton distribution amplitude(PDA) from the Euclidean Bethe-Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe-Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method(MEM). The Nakanishi weight function as well as the corresponding light-front PDA can be well determined. We confirm the previous works on PDA computation therein the different method has been performed.
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.
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.
STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
闫振亚; 张鸿庆
2001-01-01
The homogeneous balance method was improved and applied to two systems of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations.
Matrix algorithms for solving (in)homogeneous bound state equations.
Blank, M; Krassnigg, A
2011-07-01
In the functional approach to quantum chromodynamics, the properties of hadronic bound states are accessible via covariant integral equations, e.g. the Bethe-Salpeter equation for mesons. In particular, one has to deal with linear, homogeneous integral equations which, in sophisticated model setups, use numerical representations of the solutions of other integral equations as part of their input. Analogously, inhomogeneous equations can be constructed to obtain off-shell information in addition to bound-state masses and other properties obtained from the covariant analogue to a wave function of the bound state. These can be solved very efficiently using well-known matrix algorithms for eigenvalues (in the homogeneous case) and the solution of linear systems (in the inhomogeneous case). We demonstrate this by solving the homogeneous and inhomogeneous Bethe-Salpeter equations and find, e.g. that for the calculation of the mass spectrum it is as efficient or even advantageous to use the inhomogeneous equation as compared to the homogeneous. This is valuable insight, in particular for the study of baryons in a three-quark setup and more involved systems.
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.
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.
Quantum Inverse Scattering Method with anyonic grading
Batchelor, M T; Guan, X-W; Links, J; Zhou, H-Q
2008-01-01
We formulate the Quantum Inverse Scattering Method for the case of anyonic grading. This provides a general framework for constructing integrable models describing interacting hard-core anyons. Through this method we reconstruct the known integrable model of hard core anyons associated with the XXX model, and as a new application we construct the anyonic $t-J$ model. The energy spectrum for each model is derived by means of a generalisation of the algebraic Bethe ansatz. The grading parameters implementing the anyonic signature give rise to sector-dependent phase factors in the Bethe ansatz equations.
The quantum inverse scattering method with anyonic grading
Batchelor, M. T.; Foerster, A.; Guan, X.-W.; Links, J.; Zhou, H.-Q.
2008-11-01
We formulate the quantum inverse scattering method for the case of anyonic grading. This provides a general framework for constructing integrable models describing interacting hard-core anyons. Through this method we reconstruct the known integrable model of hard core anyons associated with the XXX model, and as a new application we construct the anyonic t - J model. The energy spectrum for each model is derived by means of a generalization of the algebraic Bethe ansatz. The grading parameters implementing the anyonic signature give rise to sector-dependent phase factors in the Bethe ansatz equations.
Exact Solution for Perk－Schultz Model with Boundary Impurities *
Institute of Scientific and Technical Information of China (English)
LI Guang-Liang; YUE Rui-Hong; SHI Kang-Jie; HOU Bo-Yu
2001-01-01
The Perk-Schultz model with SUq(m｜n) spin boundary impurities is constructed by dressing the c-number reflecting K-matrix with the local L-matrix which acts non-trivially on an impurity Hilbert space. The eigenvalue of the transfer matrix and the corresponding Bethe ansatz equations with different c-number reflecting K-matrices are obtained by using the nested Bethe ansatz method (m ≠ n). When m ＝ 1,n ＝ 2, our results come back to that of supersymmetric t - J model with SUq(1｜2) spin boundary impurities.
Exact solution of the trigonometric SU(3 spin chain with generic off-diagonal boundary reflections
Directory of Open Access Journals (Sweden)
Guang-Liang Li
2016-09-01
Full Text Available 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.
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.
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.
Atomic-accuracy prediction of protein loop structures through an RNA-inspired Ansatz.
Directory of Open Access Journals (Sweden)
Rhiju Das
Full Text Available Consistently predicting biopolymer structure at atomic resolution from sequence alone remains a difficult problem, even for small sub-segments of large proteins. Such loop prediction challenges, which arise frequently in comparative modeling and protein design, can become intractable as loop lengths exceed 10 residues and if surrounding side-chain conformations are erased. Current approaches, such as the protein local optimization protocol or kinematic inversion closure (KIC Monte Carlo, involve stages that coarse-grain proteins, simplifying modeling but precluding a systematic search of all-atom configurations. This article introduces an alternative modeling strategy based on a 'stepwise ansatz', recently developed for RNA modeling, which posits that any realistic all-atom molecular conformation can be built up by residue-by-residue stepwise enumeration. When harnessed to a dynamic-programming-like recursion in the Rosetta framework, the resulting stepwise assembly (SWA protocol enables enumerative sampling of a 12 residue loop at a significant but achievable cost of thousands of CPU-hours. In a previously established benchmark, SWA recovers crystallographic conformations with sub-Angstrom accuracy for 19 of 20 loops, compared to 14 of 20 by KIC modeling with a comparable expenditure of computational power. Furthermore, SWA gives high accuracy results on an additional set of 15 loops highlighted in the biological literature for their irregularity or unusual length. Successes include cis-Pro touch turns, loops that pass through tunnels of other side-chains, and loops of lengths up to 24 residues. Remaining problem cases are traced to inaccuracies in the Rosetta all-atom energy function. In five additional blind tests, SWA achieves sub-Angstrom accuracy models, including the first such success in a protein/RNA binding interface, the YbxF/kink-turn interaction in the fourth 'RNA-puzzle' competition. These results establish all-atom enumeration as
Nuclear magnetic polarizability and the slope of the Thomas-Reiche-Kuhn-Levinger-Bethe sum rule
Gorchtein, Mikhail
2015-01-01
Thomas-Reiche-Kuhn-Levinger-Bethe sum rule that relates the strength of the photoexcitation of the giant dipole resonance in a nucleus to the number of elementary scatterers-protons within that nucleus by means of a subtracted forward dispersion relation. I extend this dispersion relation consideration to the case of virtual photons and show that the size of the magnetic polarizability of a nucleus, under the assumption of a separation between the nuclear and hadronic scales, may be related to the slope of the transverse virtual photoabsorption cross section integrated over the energy. I check this approximate sum rule for the deuteron where necessary data is available, discuss possible applications and connection with other sum rules postulated in the literature.
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.
Sandwiched trilayer of Bethe lattices in the form of spin-(1/2,1,1/2)
Energy Technology Data Exchange (ETDEWEB)
Albayrak, Erhan, E-mail: albayrak@erciyes.edu.t [Erciyes University, Department of Physics, 38039 Kayseri (Turkey); Aker, Aynur [Erciyes University, Department of Physics, 38039 Kayseri (Turkey)
2010-11-15
The sandwiched trilayer of Bethe lattices in the form of the spins with spin-(1/2,1,1/2) Ising model is studied in terms of the recursion relations with either ferromagnetic or antiferromagnetic type bilinear interactions between the nearest-neighbor (NN) spins. The ground-state (GS) phase diagrams are obtained and it was found that the model presents six different GS phase configurations. In order to obtain the phase diagrams, the thermal variations of the order-parameter, spin-spin correlation functions and free energy are analyzed and different topological phase diagrams are obtained. It was found that the system exhibits different critical behaviors such as, second- and first-order phase transitions, tricritical and bicritical points for the values of the coordination numbers q=3,4 and 6.
Comultiplication in ABCD algebra and scalar products of bethe wave functions
Mikhailov, A.
1994-07-01
The representation of scalar products of Bethe wave functions in terms of dual fields, proved by A. G. Izergin and V. E. Korepin in 1987, plays an important role in the theory of completely integrable models. The proof in [A. G. Izergin, Dokl. Akad. Nauk SSSR, 297, No. 2, 331 (1987)] and [V. E. Korepin, Commun. Math. Phys., 113, 177 190 (1978)] is based on the explicit expression for the “senior” coefficient, which was guessed in the Izergin paper and then proved to satisfy some recurrent relations, which determine it unambiguously. In this paper we present an alternative proof based on direct computation. It uses the operation of comultiplication in the ABCD-algebra.
La cerámica Khirbet Kerak (Beth Yerah, Israel y la etnicidad: un enfoque alternativo
Directory of Open Access Journals (Sweden)
Bernardo Gandulla
2007-07-01
Full Text Available
La cerámica Khirbet Kerak, descubierta en el sudoeste del Mar de Galilea en 1930 por W. F. Albright, ha sido desde entonces motivo de muchas controversias. Las razones de las discusiones en torno a este estilo radican en su carácter aparentemente intrusivo en Palestina, entre el 2800-2400 a.C., puesto que esta cerámica es típica en la Cultura Transcaucásica Temprana o Cultura Kura-Araxes y en Siria Septentrional, durante el Bronce Antiguo, siendo especialmente abundante en la etapa final de este período. Sin embargo los estudios realizados en Beth Shan (Chazan y McGovern, ver n. 17, muestran que los materiales Khirbet Kerak fueron de producción local lo que parece descartar su carácter intrusivo. Por tanto, desde nuestro punto de vista, el “fenómeno Khirbet Kerak” constituye así un hito de singular importancia en la conformación de las tradiciones culturales de Canaan a partir de un sustrato etnocultural común hurrita, en un eje de interacción cultural norte a sur desde la región del Lago Van, que habrá de proyectarse de distintas formas en la macrorregión alcanzando hasta los antiguos hebreos, en cuanto cananeos, como se reflejan en instituciones del derecho privado presentes en las narraciones del Génesis.
Palabras clave: Canaán - Bronce Antiguo - Beth Yerah - Khirbet Kerak - Hurritas
- Hebreos
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...
Flow Equations for N Point Functions and Bound States
Ellwanger, Ulrich
1994-01-01
We discuss the exact renormalization group or flow equation for the effective action and its decomposition into one particle irreducible N point functions. With the help of a truncated flow equation for the four point function we study the bound state problem for scalar fields. A combination of analytic and numerical methods is proposed, which is applied to the Wick-Cutkosky model and a QCD-motivated interaction. We present results for the bound state masses and the Bethe-Salpeter wave function. (Figs. 1-4 attached as separate uuencoded post-script files.)
Wittenbrink, Nils; Venghaus, Florian; Williams, David; Eisfeld, Wolfgang
2016-11-01
A new diabatization method is presented, which is suitable for the development of accurate high-dimensional coupled potential energy surfaces for use in quantum dynamics studies. The method is based on the simultaneous use of adiabatic wave function and energy data, respectively, and combines block-diagonalization and diabatization by ansatz approaches. It thus is called hybrid diabatization. The adiabatic wave functions of suitable ab initio calculations are projected onto a diabatic state space and the resulting vectors are orthonormalized like in standard block-diagonalization. A parametrized diabatic model Hamiltonian is set up as an ansatz for which the block-diagonalization data can be utilized to find the optimal model. Finally, the parameters are optimized with respect to the ab initio reference data such that the deviations between adiabatic energies and eigenvalues of the model as well as projected state vectors and eigenvectors of the model are minimized. This approach is particularly advantageous for problems with a complicated electronic structure where the diabatic state space must be of higher dimension than the number of calculated adiabatic states. This is an efficient way to handle problems with intruder states, which are very common for reactive systems. The use of wave function information also increases the information content for each data point without additional cost, which is beneficial in handling the undersampling problem for high-dimensional systems. The new method and its performance are demonstrated by application to three prototypical systems, ozone (O3), methyl iodide (CH3I), and propargyl (H2CCCH).
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.
Boundary Effects for One-Dimensional Bariev Model with Hard-Core Repulsion
Institute of Scientific and Technical Information of China (English)
LIXiao-Jun; YUERui-Hong
2004-01-01
For the Bariev 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.
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.
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.
Edison, John R; Monson, Peter A
2014-07-14
Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.
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.
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.
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.
Zen, Andrea; Coccia, Emanuele; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo
2014-03-11
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 multireference 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 multideterminant 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. In the orthogonally twisted ethylene, we find a degeneracy of π and π* molecular orbitals, as correctly predicted by multireference procedures, and our best estimates of the twisting barrier, using respectively the variational Monte Carlo (VMC) and the lattice regularized diffusion Monte Carlo (LRDMC) methods, are 71.9(1) and 70.2(2) kcal/mol, in very good agreement with the high-level MR-CISD+Q value, 69.2 kcal/mol. In the methylene we estimate an adiabatic triplet-singlet (X̃(3)B1-ã(1)A1) energy gap of 8.32(7) and 8.64(6) kcal/mol, using respectively VMC and LRDMC, consistently with the experimental-derived finding for Te, 9.363 kcal/mol. On the other hand, we show that the simple ansatz of a Jastrow correlated single determinant (JSD) wave function is unable to provide an accurate description of the electronic structure in these diradical molecules, both at variational level (VMC torsional barrier of C2H4 of 99.3(2) kcal/mol, triplet-singlet energy gap of CH2 of 13.45(10) kcal/mol) and, more remarkably, in the fixed-nodes projection schemes (LRDMC
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.
The mixed-spin ternary-alloy in the form of ABpC1- p on the Bethe lattice
Albayrak, Erhan
2011-04-01
The ABpC1-p type of mixed ferromagnetic-ferrimagnetic ternary-alloy with A (spin-3/2), B (spin-1) and C (spin-5/2) ions was studied on the Bethe lattice with the odd numbered shells containing only A ions, while the even numbered shells either containing B or C ions randomly. The phase diagrams were obtained on the (R=|JAC|/JAB,kTc/JAB) and (p, kTc/JAB) planes for given values of p and R, respectively, with the coordination numbers z=3, 4, 5 and 6. The explicit dependence of the phase diagrams on z and each shell of the Bethe lattice having only one type of ion lead to some differences when compared with the previous works. The model presents one or two compensation temperatures for appropriate values of the system parameters.
Sciarappa, Antonio
2016-10-01
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.
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...
Beth Lanham on Six Sigma in healthcare. Interview by Luc R. Pelletier.
Lamham, Beth
2003-01-01
Beth Lanham, BSN RN, is a Six Sigma Coordinator in the department of quality management, staff development and safety, at Froedtert Hospital in Milwaukee, WI. Ms. Lanham received her bachelor's degree from Otterbein College in Westerville, OH and has an extensive clinical and management background in critical care nursing. In April 2000, Ms. Lanham completed the Six Sigma Black Belt training program through the American Society for Quality. She is currently working as a Six Sigma Black Belt and is actively involved with numerous committees and projects aimed at reducing medical errors and enhancing patient safety. Ms. Lanham has presented Six Sigma initiatives at the International Quality Congress sponsored by the American Society for Quality, the University Healthcare Consortium National Conference, the International Quality and Productivity Center National Conference on Six Sigma for Healthcare Providers, and the American Hospital Association Patient Safety Leadership Fellowship Retreat. Six Sigma projects at Froedtert Hospital are aimed at reducing errors associated with patient controlled analgesia pumps, continuous intravenous infusions, narcotic sedation in postoperative patients, insulin therapy, and handling of laboratory specimens. Six Sigma has also been applied toward reducing falls on a rehabilitation unit.
An exact solution on the ferromagnetic face-cubic spin model on a Bethe lattice
Ohanyan, V. R.; Ananikyan, L. N.; Ananikian, N. S.
2007-04-01
The lattice spin model with Q-component discrete spin variables restricted to have orientations orthogonal to the faces of Q-dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The partition function of the model with dipole-dipole and quadrupole-quadrupole interaction for arbitrary planar graph is presented in terms of double graph expansions. The latter is calculated exactly in case of trees. The system of two recurrent relations (RR) which allows to calculate all thermodynamic characteristics of the model is obtained. The correspondence between thermodynamic phases and different types of fixed points of the RR is established. Using the technique of simple iterations the plots of the zero field magnetization and quadrupolar moment are obtained. Analyzing the regions of stability of different types of fixed points of the system of recurrent relations the phase diagrams of the model are plotted. For Q⩽2 the phase diagram of the model is found to have three tricritical points, whereas for Q>2 there are one triple and one tricritical points.
Fast and Accurate Electronic Excitations in Cyanines with the Many-Body Bethe-Salpeter Approach.
Boulanger, Paul; Jacquemin, Denis; Duchemin, Ivan; Blase, Xavier
2014-03-11
The accurate prediction of the optical signatures of cyanine derivatives remains an important challenge in theoretical chemistry. Indeed, up to now, only the most expensive quantum chemical methods (CAS-PT2, CC, DMC, etc.) yield consistent and accurate data, impeding the applications on real-life molecules. Here, we investigate the lowest lying singlet excitation energies of increasingly long cyanine dyes within the GW and Bethe-Salpeter Green's function many-body perturbation theory. Our results are in remarkable agreement with available coupled-cluster (exCC3) data, bringing these two single-reference perturbation techniques within a 0.05 eV maximum discrepancy. By comparison, available TD-DFT calculations with various semilocal, global, or range-separated hybrid functionals, overshoot the transition energies by a typical error of 0.3-0.6 eV. The obtained accuracy is achieved with a parameter-free formalism that offers similar accuracy for metallic or insulating, finite size or extended systems.
Heavy quarkonium potential from Bethe-Salpeter wave function on the lattice
Kawanai, Taichi
2013-01-01
We propose a novel method for the determination of the interquark potential together with quark "kinetic mass'' $m_Q$ from the equal-time $Q\\bar{Q}$ Bethe-Salpeter (BS) amplitude in lattice QCD. Our approach allows us to calculate spin-dependent $Q\\bar{Q}$ potentials, e.g. the spin-spin potential, as well. In order to investigate several systematic uncertainties on such $Q\\bar{Q}$ potentials, we carry out lattice QCD simulations using quenched gauge configurations generated with the single plaquette gauge action with three different lattice spacings, $a \\approx$ 0.093, 0.068 and 0.047 fm, and two different physical volumes, $L \\approx$ 2.2 and 3.0 fm. For heavy quarks, we employ the relativistic heavy quark (RHQ) action which can control large discretization errors introduced by large quark mass $m_Q$. The spin-independent central $Q\\bar{Q}$ potential for the charmonium system yields the "Coulomb plus linear'' behavior with good scaling and small volume dependence. We explore the quark mass dependence over th...
Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field
Institute of Scientific and Technical Information of China (English)
Khalid Bannora; Galal Ismail; Wafaa Hassan
2011-01-01
The thermodynamics and the phase diagram of random field Ising model (RFIM) on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field (B). A Gaussian distribution of random field (hi) with zero mean and variance = H2RF is considered. The free-energy (F), the magnetization (M) and the order parameter (q) are investigated for several values of coordination number (z). The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature TC = J/k and when HRF = 0 for finite z. The free-energy (F) values increase as T increases for different intensities of random field (HRF) and finite z. The internal energy (U) has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases. The ferromagnetic (FM)-paramagnetic (PM) phase boundary is clearly observed only when z →∞. While FM-PM-spin glass (SG) phase boundaries are present for finite z. The magnetic susceptibility (X) shows a sharp cusp at TC in a small random field for finite z and rounded different peaks on increasing HRF.
Effects of the projectile electronic structure on Bethe-Bloch stopping parameters for Ag
Energy Technology Data Exchange (ETDEWEB)
Moussa, D., E-mail: djamelmoussa@gmail.co [USTHB, Faculte de Physique, B.P. 32, 16111 Bab-Ezzouar, Algiers (Algeria); Damache, S. [Division de Physique, CRNA, 02 Bd. Frantz Fanon, B.P. 399 Alger-gare, Algiers (Algeria); Ouichaoui, S., E-mail: souichaoui@gmail.co [USTHB, Faculte de Physique, B.P. 32, 16111 Bab-Ezzouar, Algiers (Algeria)
2010-06-15
Energy losses of protons and alpha particles in silver have been accurately measured under the same experimental conditions over the velocity range E{sub lab}=(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 . 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.
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.
3-state Hamiltonians associated to solvable 33-vertex models
Crampé, N.; Frappat, L.; Ragoucy, E.; Vanicat, M.
2016-09-01
Using the nested coordinate Bethe ansatz, we study 3-state Hamiltonians with 33 non-vanishing entries, or 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they correspond to diffusing particles with two possible internal states which may be exchanged during the diffusion (transmutation). The first step of the nested coordinate Bethe ansatz is performed providing the eigenvalues in terms of rapidities. We give the constraints ensuring the consistency of the computations. These rapidities also satisfy Bethe equations involving 4 × 4 R-matrices, solutions of the Yang-Baxter equation which implies new constraints on the models. We solve them allowing us to list all the solvable 33-vertex models.
Equation-of-motion coupled cluster perturbation theory revisited
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe;
2014-01-01
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples......-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]...
Guner, Ozkan; Bekir, Ahmet; Unsal, Omer; Cevikel, Adem C.
2017-01-01
In this paper, we pay attention to the analytical method named, ansatz method for finding the exact solutions of the variable-coefficient modified KdV equation and variable coefficient diffusion-reaction equation. As a result the singular 1-soliton solution is obtained. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. This method can be extended to solve other variable coefficient nonlinear partial differential equations.
On the path integral representation of the Wigner function and the Barker-Murray ansatz
Sels, Dries; Brosens, Fons; Magnus, Wim
2012-01-01
The propagator of the Wigner function is constructed from the Wigner-Liouville equation as a phase space path integral over a new effective Lagrangian. In contrast to a paper by Barker and Murray (1983) [1], we show that the path integral can in general not be written as a linear superposition of classical phase space trajectories over a family of non-local forces. Instead, we adopt a saddle point expansion to show that the semiclassical Wigner function is a linear superposition of classical solutions for a different set of non-local time dependent forces. As shown by a simple example the specific form of the path integral makes the formulation ideal for Monte Carlo simulation.
Simple polynomial approximation to modified Bethe formula low-energy electron stopping powers data
Energy Technology Data Exchange (ETDEWEB)
Taborda, A., E-mail: ana.taborda@irsn.fr [Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PRP-HOM/SDI/LEDI, BP-17, 92262 Fontenay-aux-Roses (France); Desbrée, A. [Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PRP-HOM/SDI/LEDI, BP-17, 92262 Fontenay-aux-Roses (France); Reis, M.A. [C" 2TN, Campus Tecnológico e Nuclear, Instituto Superior Técnico, Universidade de Lisboa, EN10 km139.7, 2685-066 Bobadela LRS (Portugal)
2015-08-01
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.
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.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Directory of Open Access Journals (Sweden)
J. Strečka
2012-12-01
Full Text Available The spin-1/2 Ising-Heisenberg model on diamond-like decorated Bethe lattices is exactly solved in the presence of the longitudinal magnetic field by combining the decoration-iteration mapping transformation with the method of exact recursion relations. In particular, the ground state and low-temperature magnetization process of the ferrimagnetic version of the considered model is investigated in detail. Three different magnetization scenarios with up to two consecutive fractional magnetization plateaus were found, whereas the intermediate magnetization plateau may either correspond to the classical ferrimagnetic spin arrangement and/or the field-induced quantum ferrimagnetic spin ordering without any classical counterpart.
Energy Technology Data Exchange (ETDEWEB)
Radozycki, Tomasz [Cardinal Stefan Wyszynski University, Faculty of Mathematics and Natural Sciences, College of Sciences, Warsaw (Poland)
2015-09-15
The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in the two-dimensional massless quantum electrodynamics (the so-called Schwinger model) are considered. It is shown that while boosting a bound state (a 'meson') this amplitude is subject to approximate Lorentz contraction. The effect is exact for large separations of constituent particles ('quarks'), while for small distances the deviation is more significant. For this phenomenon to appear, the full function, i.e. with the inclusion of all instanton contributions, has to be considered. The amplitude in each separate topological sector does not exhibit such properties. (orig.)
Resurgent transseries & Dyson-Schwinger equations
Klaczynski, Lutz
2016-09-01
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 finding is that the flow of data between the different sectors of the transseries shows a pattern typical of resurgence, i.e. 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 when logarithmic monomials are included. We see our result as a harbinger of what future work might reveal about the transseries representations of observables in fully renormalised four-dimensional quantum field theories and adduce a tentative yet to our mind weighty argument as to why one should not expect otherwise. This paper is considerably self-contained. Readers with little prior knowledge are let in on the basic reasons why perturbative series in quantum field theory eventually require an upgrade to transseries. Furthermore, in order to acquaint the reader with the language utilised extensively in this work, we also provide a concise mathematical introduction to grid-based transseries.
Kakehashi, Yoshiro; Chandra, Sumal
2016-08-01
The ground-state properties of iron-group transition metals from Sc to Cu have been investigated on the basis of the first-principles momentum dependent local ansatz (MLA) theory. Correlation energy gain is found to show large values for Mn and Fe: 0.090 Ry (Mn) and 0.094 Ry (Fe). The Hund-rule coupling energies are found to be 3000 K (Fe), 1400 K (Co), and 300 K (Ni). It is suggested that these values can resolve the inconsistency in magnetic energy between the density functional theory and the first-principles dynamical coherent potential approximation theory at finite temperatures. Charge fluctuations are shown to be suppressed by the intra-orbital correlations and inter-orbital charge-charge correlations, so that they show nearly constant values from V to Fe: 1.57 (V and Cr), 1.52 (Mn), and 1.44 (Fe), which are roughly twice as large as those obtained by the d band model. The amplitudes of local moments are enhanced by the intra-orbital and inter-orbital spin-spin correlations and show large values for Mn and Fe: 2.87 (Mn) and 2.58 (Fe). These values are in good agreement with the experimental values estimated from the effective Bohr magneton number and the inner core photoemission data.
Gravastar Solutions with Continuous Pressures and Equation of State
De Benedictis, A; Ilijic, S; Kloster, S; Viswanathan, K S
2006-01-01
We study the gravitational vacuum star (gravastar) configuration as proposed by other authors in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure in previous papers is replaced by a continuous stress-energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial $p_r$ and tangential $p_t$ pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar. Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.
Solving Potential Scattering Equations without Partial Wave Decomposition
Energy Technology Data Exchange (ETDEWEB)
Caia, George; Pascalutsa, Vladimir; Wright, Louis E
2004-03-01
Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a partial-wave expansion. We illustrate this procedure for the Bethe-Salpeter equation for pion-nucleon scattering and give explicit details for the one-nucleon-exchange term in the potential. Finally, we show how this method can be applied to pion photoproduction from the nucleon with {pi}N rescattering being treated so as to maintain unitarity to first order in the electromagnetic coupling. The procedure for removing the azimuthal angle dependence becomes increasingly complex as the spin of the particles involved increases.
Zen, Andrea; Sorella, Sandro; Guidoni, Leonardo
2013-01-01
Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely: the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Throu...
Rebolini, Elisa
2015-01-01
We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of four small molecules: N2, CO2, H2CO, and C2H4. The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.
Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model
Rylands, Colin; Andrei, Natan
2016-09-01
A Luttinger liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a localized transmitting and reflecting impurity. We solve exactly the Hamiltonian by means of an incoming-outgoing scattering Bethe basis which properly incorporates all scattering processes. A related model, the weak-tunneling model, wherein the impurity is replaced by a tunnel junction, is solved by the same method. The consistency of the construction is established through a generalized Yang-Baxter relation. Periodic boundary conditions are imposed and the resulting Bethe ansatz equations are derived by means of the off-diagonal Bethe ansatz approach. We derive the spectrum of the model for all coupling constant regimes and calculate the impurity free energy. We discuss the low energy behavior of the systems for both repulsive and attractive interactions.
Wheeler, M
2013-01-01
We study the scalar product S_{l,m} between an on-shell and an off-shell Bethe state in models with SU(3)-invariance, where l and m denote the cardinalities of the two sets of Bethe roots. We construct recursion relations relating S_{l,m} to scalar products of smaller dimension, namely S_{l-1,m} and S_{l,m-1}. Solving these recursion relations we obtain new multiple integral expressions for S_{l,m}, whose integrands are (l+m) \\times (l+m) determinants, and closely related to the Slavnov determinant expression for the SU(2) scalar product.
Vitanov, Nikolay K.
2010-08-01
We search for traveling-wave solutions of the class of equations ∑p=1N1αp{∂pQ}/{∂tp}+∑q=1N2βq{∂qQ}/{∂xq}+∑m=1MμmQm=0 where αp,βq and μm are parameters. We obtain such solutions by the method of simplest equation for the cases when the simplest equation is the the equation of Bernoulli or the equation of Riccati. We modify the methodology of the simplest equation of Kudryashov as follows. Kudryashov uses the first step of the test for Painleve property in order to determine the size of the solution of the studied PDE. We divide the studied PDEs in two parts: part A which contains the derivatives, and part B which contains the rest of the equation. The application of the ansatz or the extended ansatz of Kudryashov, transforms part A and part B to two polynomials. We balance the highest powers of the polynomials for the parts A and B and, thus obtain a balance equation which depends on the kind of the used simplest equation. The balance equations are connected to nonlinear algebraic systems of relationships among the parameters of the equations and the parameters of the solution. On the basis of these systems, we obtain numerous solutions of the studied class of equations.
Feng, Sheng-Ya
2011-01-01
In this paper, we study a class of second order differential operators with quadratic potentials $L$ and its principal part $L_{S}$. Thanks to Hamiltonian formalism and a multiplier technique, we first obtain heat kernel of $L_{S}$, then we, by use of the action function and volume element, solve a matrix Riccati equations and a scalar differential equation which leads us to the heat kernel of $L$ via a probabilistic ansatz. As application, we finally recover and generalise several classical results on celebrated operators.
Numeric Solutions of Dirac-Gursey Spinor Field Equation Under External Gaussian White Noise
Aydogmus, Fatma
2016-06-01
In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.
A New Generalization of Extended Tanh-Function Method for Solving Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHENG Xue-Dong; CHEN Yong; LI Biao; ZHANG Hong-Qing
2003-01-01
Making use of a new generalized ansatze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations.As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extendedtanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain othernew and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profilesolitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.
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
Quasi-exactly solvable relativistic soft-core Coulomb models
Agboola, Davids
2013-01-01
By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials $V_q(r)=-Z/\\left(r^q+\\beta^q\\right)^{1/q}$, $Z>0$, $\\beta>0$, $q\\geq 1$. We consider cases $q=1$ and $q=2$ and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtain using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derive in terms of the roots of a set of Bethe ansatz equations.
Richardson-Gaudin integrability in the contraction limit of the quasispin
De Baerdemacker, Stijn
2012-01-01
Background: The reduced, level-independent, Bardeen-Cooper-Schrieffer Hamiltonian is exactly diagonalizable by means of a Bethe Ansatz wavefunction, provided the free variables in the Ansatz are the solutions of the set of Richardson-Gaudin equations. On the one side, the Bethe Ansatz is a simple product state of generalised pair operators. On the other hand, the Richardson-Gaudin equations are strongly coupled in a non-linear way, making them prone to singularities. Unfortunately, it is non-trivial to give a clear physical interpretation to the Richardson-Gaudin variables because no physical operator is directly related to the individual variables. Purpose: The purpose of this paper is to shed more light on the critical behavior of the Richardson-Gaudin equations, and how this is related to the product wave structure of the Bethe Ansatz. Method: A pseudo-deformation of the quasi-spin algebra is introduced, leading towards a Heisenberg-Weyl algebra in the contraction limit of the deformation parameter. This e...
Directory of Open Access Journals (Sweden)
Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Modeling the pion Generalized Parton Distribution
Mezrag, C
2015-01-01
We compute the pion Generalized Parton Distribution (GPD) in a valence dressed quarks approach. We model the Mellin moments of the GPD using Ans\\"atze for Green functions inspired by the numerical solutions of the Dyson-Schwinger Equations (DSE) and the Bethe-Salpeter Equation (BSE). Then, the GPD is reconstructed from its Mellin moment using the Double Distribution (DD) formalism. The agreement with available experimental data is very good.
Tricomi, FG
2013-01-01
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 diff
Spacetimes with a separable Klein-Gordon equation in higher dimensions
Kolar, Ivan
2015-01-01
We study spacetimes that lead to a separable Klein-Gordon equation in a general dimension. We introduce an ansatz for the metric in higher dimensions motivated by analogical work by Carter in four dimensions and find solutions of the Klein-Gordon equation. For such a metric we solve the Einstein equations and regain the Kerr-NUT-(A)dS spacetime as one of our results. Other solutions lead to the Einstein-K\\"ahler metric of a Euclidean signature. Next we investigate a warped geometry of two Klein-Gordon separable spaces with a properly chosen warped factor. We show that the resulting metric leads also to a separable Klein--Gordon equation and we find the corresponding solutions. Finally, we solve the Einstein equations for the warped geometry and obtain new solutions.
Modified Shallow Water Equations for significantly varying bottoms
Dutykh, Denys
2012-01-01
In the present study we propose an modified version of the nonlinear shallow water (Saint-Venant) equations for the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing the appropriate shallow water ansatz and imposing some constraints. Our derivation procedure does not explicitly involve any small parameter and is straightforward. The novel system is a non-dispersive, and non-hydrostatic extension of the classical Saint-Venant equations. We also propose a finite volume discretization of the obtained hyperbolic system. Several test-cases are presented to highlight the added value of the new model. Some implications to tsunami wave modelling are also discussed.
A Dynamical Principle For 3D-4D Interlinkage In Salpeter-like Equations
Mitra, A N
2001-01-01
The half-century old Markov-Yukawa Transversality Principle ($MYTP$) which provides a theoretical rationale for the covariant instantaneous approximation ($CIA$) that underlies all Salpeter- like equations, is generalized to a Covariant null-plane Ansatz ($CNPA$). A common characteristic of both formulations is an exact 3D-4D interlinkage of BS amplitudes which provides for a two-tier description, the 3D form for spectroscopy, and the 4D form for transition amplitudes as 4D loop integrals. Some basic applications of $MYTP$ on the covariant null plane (quark mass function, vacuum condensates, and decay constants) are given on the lines of earlier applications of the same under Covariant Instantaneity to such processes. PACS: 03.65.-w ; 03.65.Co ; 11.10.Qr ; 11.10.St Keywords: Markov-Yukawa Transversality Principle ($MYTP$); Salpeter-like eqs; Cov Instantaneity Ansatz ($CIA$); Cov null-plane Ansatz ($CNPA$); 3D-4D interlinkage; Vertex function; 4D loops
Jarvis, P D
2004-01-01
The labelling of states of irreducible representations of GL(3) in an O(3) basis is well known to require the addition of a single O(3)-invariant operator, to the standard diagonalisable set of Casimir operators in the subgroup chain GL(3) - O(3) - O(2). Moreover, this `missing label' operator must be a function of the two independent cubic and quartic invariants which can be constructed in terms of the angular momentum vector and the quadrupole tensor. It is pointed out that there is a unique (in a well-defined sense) combination of these which belongs to the O(3) invariant Bethe subalgebra of the twisted Yangian Y(GL(3);O(3)) in the enveloping algebra of GL(3).
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Chin, Alex W; Prior, Javier; Huelga, Susana F; Plenio, Martin B
2011-10-14
The sub-Ohmic spin-boson model possesses a quantum phase transition at zero temperature between a localized and a delocalized phase, whose properties have so far only been extracted by numerical approaches. Here we present an extension of the Silbey-Harris variational polaron ansatz which allows us to develop an analytical theory which correctly describes a continuous transition with mean-field exponents for 0
DEFF Research Database (Denmark)
Daryai-Hansen, Petra; Barfod, Sonja; Schwarz, Lena
2015-01-01
. The German language profile is presented from three perspectives: a language policy perspective, on which the language profile was developed; from the perspective of the teachers who design the language profile inspired by the CLIL approach; finally, from the students’ perspective. How do students experience...... Perspektive der Lehrkräfte, die inspiriert durch den CLIL-Ansatz das Sprachprofil didaktisch gestalten. Abschließend fokussieren wir auf die Perspektive der Studierenden: Wie erleben sie ihren Lernprozess? Welche Resultate erzielen sie ihrer Ansicht nach?...
Separation of variables for integrable spin-boson models
Amico, Luigi; Osterloh, Andreas; Wirth, Tobias
2010-01-01
We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang-Baxter algebra. The main deviation from the standard approach consists in a half infinite 'Sklyanin lattice' made of the eigenvalues of the operator zeros of the Bethe annihilation operator. By a separation of variables, functional TQ equations are obtained for this half infinite lattice. They provide valuable information about the spectrum of a given Hamiltonian model. We apply this procedure to integrable spin-boson models subject to both twisted and open boundary conditions. In the case of general twisted and certain open boundary conditions polynomial solutions to these TQ equations are found and we compute the spectrum of both the full transfer matrix and its quasi-classical limit. For generic open boundaries we present a two-parameter family of Bethe equations, derived from TQ equations that are compatible with polynomial solutions for Q. A connection of these parameters to the boundary fields is stil...
Baryon properties and glueballs from Poincare-covariant bound-state equations
Sanchis-Alepuz, Helios
2012-01-01
In this thesis the covariant Bethe-Salpeter equation formalism is used to study some properties of ground-state baryons. This formalism relies on the knowledge of the interaction kernel among quarks and of the full quark propagator. For the interaction kernel, which is in principle a sum of infinitely many diagrams, I use the Ladder truncation. It amounts to reduce the interaction to a flavor-blind quark-mass independent vector-vector interaction between two quarks, mediated by a dressed gluon. The irreducible three-body interactions are neglected. The full quark propagator is obtained as a solution of the quark Dyson-Schwinger equation which is truncated such that, together with the truncation in the interaction kernel, chiral symmetry is correctly implemented. It is called Rainbow truncation, and together with the truncated kernel equation it constitutes the Rainbow-Ladder truncation of the Bethe-Salpeter equation. Any truncation induces the introduction of a model to account for the properties of the full ...
Quantum transport equations for low-dimensional multiband electronic systems: I.
Kupčić, I; Rukelj, Z; Barišić, S
2013-04-10
A systematic method of calculating the dynamical conductivity tensor in a general multiband electronic model with strong boson-mediated electron-electron interactions is described. The theory is based on the exact semiclassical expression for the coupling between valence electrons and electromagnetic fields and on the self-consistent Bethe-Salpeter equations for the electron-hole propagators. The general diagrammatic perturbation expressions for the intraband and interband single-particle conductivity are determined. The relations between the intraband Bethe-Salpeter equation, the quantum transport equation and the ordinary transport equation are briefly discussed within the memory-function approximation. The effects of the Lorentz dipole-dipole interactions on the dynamical conductivity of low-dimensional spα models are described in the same approximation. Such formalism proves useful in studies of different (pseudo)gapped states of quasi-one-dimensional systems with the metal-to-insulator phase transitions and can be easily extended to underdoped two-dimensional high-Tc superconductors.
Zen, Andrea; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo
2013-10-08
Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely, the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudopotential, and the basis set for QMC calculations. We also introduce a new method for the computation of forces with finite variance on open systems and a new strategy for the definition of the atomic orbitals involved in the Jastrow-Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets.
Directory of Open Access Journals (Sweden)
Silvia Hartung
2015-11-01
Full Text Available Der Einsatz von E-Portfolios in Bildungsinstitutionen liegt klar im Trend. Damit die daran geknüpften Erwartungen auch erfüllt werden, ist neben einer technischen auch zwingend eine inhaltliche Einführung Lernender in die Ziele und Hintergründe der E-Portfolio-Arbeit notwendig. Der vorliegende Beitrag gibt einen Einblick in die (Weiter-Entwicklung des Online-Kurses «E-Portfolios: Einführung in die Dokumentation und Selbstbeurteilung von Lernprozessen». Besonderes Augenmerk legen wir in diesem Beitrag auf das «didaktische Herzstück» der Veranstaltung: den Rollenspiel-Ansatz. Wie gut hat diese Idee funktioniert? Eignet sich der Rollenspiel-Ansatz für die Einführung in die E-Portfolio-Arbeit? Wir beschreiben, wie der Online-Kurs entstanden ist und erläutern sein didaktisches Design. Daraufhin schildern wir unsere Erfahrungen mit der Pilotdurchführung und legen Ablauf und Ergebnisse der Evaluation dar. Schliesslich beschreiben wir die Anpassungen, die aufgrund der Evaluationsergebnisse am Kurskonzept vorgenommen wurden.
Satin, Seema
2015-01-01
We attempt to introduce an new approach towards study of certain interesting issues in classical gravity. This can be done for few confined, but interesting and meaningful physical situations, which can be modeled by a classical stochastic Einstein equation. The Einstein equation can be looked upon as an equation of motion, while introducing to it a classical stochastic source or classical fluctuations as driving source. This is analogous to the Langevin equation formalism, in Brownian motion studies. A justification for the validity of such an ansatz for classical gravity is given. The regime of validity of such an approach and the consequences and possible outcomes of this formulation are discussed. We also mention, further relevant directions and applications of the same,that act as motivation towards the new proposal. This field of study can be seen to emerge out of well established ideas and results in Brownian motion theory as well as the Stochastic Semiclassical Gravity (which is already an active area...
Levy-Bencheton, D; Terras, V
2015-01-01
We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanin's separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and eigenstates of the antiperiodic transfer matrix are completely characterized by a system of discrete equations. We prove the existence of different reformulations of this characterization in terms of functional equations of Baxter's type. We notably consider the homogeneous functional $T$-$Q$ equation which is the continuous analog of the aforementioned discrete system and show, in the case of a model with an even number of sites, that the complete spectrum and eigenstates of the antiperiodic transfer matrix can equivalently be described in terms of a particular class of its $Q$-solutions, hence leading to a complete system of Bethe equations. Finally, we compute the form factors of local operators for which we obtain determinant representations in finite volume.
Second Reference State and Complete Eigenstates of Open XYZ Chain
Institute of Scientific and Technical Information of China (English)
FENG Jun; CHEN Xi; HAO Kun; HOU Bo-Yu; SHI Kang-Jie; SUN Cheng-Yi; YANG Wen-Li
2011-01-01
The second reference state of the open XYZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz.
Quantum-mechanical derivation of the Davydov equations for multi-quanta states
Energy Technology Data Exchange (ETDEWEB)
Kerr, W.C.; Lomdahl, P.S.
1989-01-01
Our purpose here is to present a derivation of the Davydov equations which employs only quantum-mechanical techniques. The derivation here is more general than our previous treatment of this problem because we use an Ansatz which has present several quanta of the high frequency oscillator system rather than just one quantum. Since some steps of the calculation are the same as those in our paper which treats the single quantum case, reference will be made to that paper for some of the those details. 9 refs.
Strange star admitting Chaplygin equation of state in Finch-Skea spacetime
Bhar, Piyali
2015-10-01
In the present paper we propose a new model of an anisotropic strange star which admits the Chaplygin equation of state. The exterior spacetime is described by a Schwarzschild line element. The model is developed by assuming the Finch-Skea ansatz (Finch and Skea in Class. Quantum Gravity 6:467, 1989. We obtain the model parameters in closed form. Our model is free from a central singularity. Choosing some particular values for the parameter we show that our model corroborates the observational data of the strange star PSR J1614-2230 (Gangopadhyay et al. in Mon. Not. R. Astron. Soc. 431:3216, 2013.
Hadronic bound states in SU(2) from Dyson-Schwinger equations
Energy Technology Data Exchange (ETDEWEB)
Vujinovic, Milan [Karl-Franzens-Universitaet Graz, Institut fuer Physik, Graz (Austria); Williams, Richard [Justus-Liebig-Universitaet Giessen, Institut fuer Theoretische Physik, Giessen (Germany)
2015-03-01
By using the Dyson-Schwinger/Bethe-Salpeter formalism in Euclidean spacetime, we calculate the ground state spectrum of J ≤ 1 hadrons in an SU(2) gauge theory with two fundamental fermions. We show that the rainbow-ladder truncation, commonly employed in QCD studies, is unsuitable for a description of an SU(2) theory. This we remedy by truncating at the level of the quark-gluon vertex Dyson-Schwinger equation in a diagrammatic expansion. Results obtained within this novel approach show good agreement with lattice studies. These findings emphasize the need to use techniques more sophisticated than rainbow-ladder when investigating generic strongly interacting gauge theories. (orig.)
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations
Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping
2016-10-01
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such 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 the 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 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 very good 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 good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.
Energy Technology Data Exchange (ETDEWEB)
Abril, Isabel, E-mail: ias@ua.e [Departament de Fisica Aplicada, Universitat d' Alacant, Apartat 99, E-03080 Alacant (Spain); Denton, Cristian D.; Vera, Pablo de [Departament de Fisica Aplicada, Universitat d' Alacant, Apartat 99, E-03080 Alacant (Spain); Kyriakou, Ioanna; Emfietzoglou, Dimitris [Medical Physics Laboratory, University of Ioannina Medical School, Ioannina 451 10 (Greece); Garcia-Molina, Rafael [Departamento de Fisica - CIOyN, Universidad de Murcia, Apartado 4021, E-30080 Murcia (Spain)
2010-06-15
The irradiation of biological systems by energetic ion beams has multiple applications in medical physics and space radiation health, such as hadrontherapy for cancer treatment or protection of astronauts against space radiation. Therefore, for a better control and understanding of the effects of radiation damage in living tissues, it is necessary to advance an accurate description of the energy loss from the ion beam to the target. In the present work we use the dielectric formalism to calculate the probability for an energetic proton to produce electronic excitations in two targets of high biological interest, namely, liquid water and DNA. Also, the mean energy of the electronic excitations in these targets is found as a function of the incident proton energy. The electronic response of the target, characterized by its energy-loss function (ELF), is described by several models that fit the available experimental optical data (at zero momentum transfer), but use different approaches to obtain the Bethe surface, that is, to extend the ELF to any energy and momentum transferred.
Abril, Isabel; Denton, Cristian D.; de Vera, Pablo; Kyriakou, Ioanna; Emfietzoglou, Dimitris; Garcia-Molina, Rafael
2010-06-01
The irradiation of biological systems by energetic ion beams has multiple applications in medical physics and space radiation health, such as hadrontherapy for cancer treatment or protection of astronauts against space radiation. Therefore, for a better control and understanding of the effects of radiation damage in living tissues, it is necessary to advance an accurate description of the energy loss from the ion beam to the target. In the present work we use the dielectric formalism to calculate the probability for an energetic proton to produce electronic excitations in two targets of high biological interest, namely, liquid water and DNA. Also, the mean energy of the electronic excitations in these targets is found as a function of the incident proton energy. The electronic response of the target, characterized by its energy-loss function (ELF), is described by several models that fit the available experimental optical data (at zero momentum transfer), but use different approaches to obtain the Bethe surface, that is, to extend the ELF to any energy and momentum transferred.
Shapiro, Stuart
2017-01-01
Hans A. Bethe elucidated our understanding of the fundamental forces of Nature by exploring and explaining countless phenomena occurring in nuclear laboratories and in stars. With the dawn of gravitational wave astronomy we now can probe compact binary mergers - Nature's cosmic collision experiments - to deepen our understanding, especially where strong-field gravitation is involved. In addition to gravitational waves, some mergers are likely to generate observable electromagnetic and/or neutrino radiation, heralding a new era of multimessenger astronomy. Robust numerical algorithms now allow us to simulate these events in full general relativity on supercomputers. We will describe some recent magnetohydrodynamic simulations that show how binary black hole-neutron star and neutron star-neutron star mergers can launch jets, lending support to the idea that such mergers could be the engines that power short gamma-ray bursts. We will also show how the magnetorotational collapse of very massive stars to spinning black holes immersed in magnetized accretion disks can launch jets as well, reinforcing the belief that such ``collapsars'' are the progenitors of long gamma-ray bursts. Computer-generated movies highlighting some of these simulations will be shown. We gratefully acknowledge support from NSF Grants 1300903 and 1602536 and NASA Grant NNX13AH44G.
Bethe-Salpeter wave functions of $\\eta_c(2S)$ and $\\psi(2S)$ states from full lattice QCD
Nochi, Kazuki; Sasaki, Shoichi
2016-01-01
We discuss the internal structure of radially excited charmonium mesons based on the equal-time and Coulomb gauge Bethe-Salpeter (BS) amplitudes, which are obtained in lattice QCD. Our simulations are performed with a relativistic heavy-quark action for the charm quark on the 2+1 flavor PACS-CS gauge configurations at the lightest pion mass, $M_{\\pi}=156(7)$ MeV. The variational method is applied to the study of optimal charmonium operator for ground and first excited states of $S$-wave charmonia. We successfully calculate the BS wave functions of $\\eta_c(2S)$ and $\\psi(2S)$ states, as well as $\\eta_c(1S)$ and $J/\\psi$ states, and then estimate the root-mean-square radii of both the $1S$ and $2S$ charmonium states. We also examine whether a series of the BS wave functions from the ground state to excited states can be described by a single set of the spin-independent and spin-dependent interquark potentials with a unique quark mass. It is found that the quark kinetic mass and, both the central and spin-spin c...
Directory of Open Access Journals (Sweden)
Maksimova A.A.
2016-01-01
Full Text Available 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 knowledge, i.e., philosophy and psychology: the study of B.A. Beschorner has a lot in common with the principles of cultural-historical psychology, formulated by L. Vygotsky, M. Lisina and other national psychologists. Although B. A. Beschorner do not stick directly to cultural-historical and activity theory, her results correspond with the basic provisions of these theories. The analysis of B.A. Beschorner’s works confirms the commonality of her findings to those obtained in terms of the cultural-historical theory. It proves that scientific thoughts even going in independent ways, may lead to similar results, which ultimately demonstrates the validity of the findings and the versatility of approaches to the problem
Finite $\\epsilon_2$-corrections to the $\\mathcal{N}=2$ SYM prepotential
Bourgine, Jean-Emile
2015-01-01
We derive the first $\\epsilon_2$-correction to the instanton partition functions of $\\mathcal{N}=2$ Super Yang-Mills (SYM) in four dimensions in the Nekrasov-Shatashvili limit $\\epsilon_2\\rightarrow 0$. In the latter we recall the emergence of the famous Thermodynamic Bethe Ansatz-like equation which has been found by Mayer expansion techniques. Here we combine efficiently these to field theory arguments. In a nutshell, we find natural and resolutive the introduction of a new operator $\
A functional RG equation for the c-function
DEFF Research Database (Denmark)
Codello, A.; D'Odorico, G.; Pagani, C.
2014-01-01
After showing how to prove the integrated c-theorem within the functional RG framework based on the effective average action, we derive an exact RG flow equation for Zamolodchikov's c-function in two dimensions by relating it to the flow of the effective average action. In order to obtain a non......-trivial flow for the c-function, we will need to understand the general form of the effective average action away from criticality, where nonlocal invariants, with beta functions as coefficients, must be included in the ansatz to be consistent. Then we apply our construction to several examples: exact results......, local potential approximation and loop expansion. In each case we construct the relative approximate c-function and find it to be consistent with Zamolodchikov's c-theorem. Finally, we present a relation between the c-function and the (matter induced) beta function of Newton's constant, allowing us...
A detailed study of nonperturbative solutions of two-body Dirac equations
Energy Technology Data Exchange (ETDEWEB)
Crater, H.W.; Becker, R.L.; Wong, C.Y.; Van Alstine, P.
1992-12-01
In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a sixteen component wave function which contain Lorentz covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second order relativistic Schroedinger-like equation for a reduced eight component wave function determined by an effective interaction -- the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions.
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Midya, Bikashkali; Roychoudhury, Rajkumar
2010-01-01
Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second order linear differential operator with position depndent coefficients and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to remove bound state(s) and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation (PCT) to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is...
Solution of the 5D Einstein equations in a dilaton background model
de Paula, W; Forkel, H; Beyer, M
2008-01-01
We obtain an explicit solution of the 5d Einstein equations in a dilaton background model. We demonstrate that for each metric ansatz that only depends on the extra coordinate, it is possible to uniquely determine the dilaton field and its potential consistently with the 5d Einstein equation. In this holographic dual model of QCD, conformal symmetry of the Anti-de-Sitter metric near the 4d boundary is broken by a term that leads to an area law for the Wilson loop. We verify that confinement of the string modes dual to mesons follows from the metric background and the corresponding dilaton solution of the gravity-dilaton coupled equations. In addition, we show that the meson Regge trajectories constrain the metric and corresponding dilaton background within the area law requirement. We can also incorporate asymptotic freedom in the gravity background within the model.
The spectrum of tachyons in AdS/CFT
Bajnok, Zoltan; Hegedus, Arpad; Nepomechie, Rafael I; Palla, Laszlo; Sieg, Christoph; Suzuki, Ryo
2013-01-01
We analyze the spectrum of open strings stretched between a D-brane and an anti-D-brane in planar AdS/CFT using various tools. We focus on open strings ending on two giant gravitons with different orientation in $AdS_5 \\times S^5$ and study the spectrum of string excitations using the following approaches: open spin-chain, boundary asymptotic Bethe ansatz and boundary thermodynamic Bethe ansatz (BTBA). We find agreement between a perturbative high order diagrammatic calculation in ${\\cal N}=4$ SYM and the leading finite-size boundary Luscher correction. We study the ground state energy of the system at finite coupling by deriving and numerically solving a set of BTBA equations. While the numerics give reasonable results at small coupling, they break down at finite coupling when the total energy of the string gets close to zero, possibly indicating that the state turns tachyonic. The location of the breakdown is also predicted analytically.
Vacuum energy of the Bukhvostov-Lipatov model
Bazhanov, Vladimir V; Runov, Boris A
2016-01-01
Bukhvostov and Lipatov have shown that weakly interacting instantons and anti-instantons in the $O(3)$ non-linear sigma model in two dimensions are described by an exactly soluble model containing two coupled Dirac fermions. We propose an exact formula for the vacuum energy of the model for twisted boundary conditions, expressing it through a special solution of the classical sinh-Gordon equation. The formula perfectly matches predictions of the standard renormalized perturbation theory at weak couplings as well as the conformal perturbation theory at short distances. Our results also agree with the Bethe ansatz solution of the model. A complete proof the proposed expression for the vacuum energy based on a combination of the Bethe ansatz techniques and the classical inverse scattering transform method is presented in the second part of this work [40].
Uniform light-cone gauge for strings in AdS{sub 5} x S{sup 5}: solving su(1 vertical bar 1) sector
Energy Technology Data Exchange (ETDEWEB)
Arutyunov, Gleb [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands); Frolov, Sergey [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany)
2006-01-15
We introduce a uniform light-cone gauge for strings propagating in AdS{sub 5} x S{sup 5} space-time. We use the gauge to analyze strings from the su(1 vertical bar 1) sector, and show that the reduced model is described by a quadratic action for two complex fermions. Thus, the uniform light-cone gauge allows us to solve the model exactly. We analyze the near BMN spectrum of states from the su(1 vertical bar 1) sector and show that it correctly reproduces the 1/J corrections. We also compute the spectrum in the strong coupling limit, and derive the famous {lambda}{sup 1/4} asymptotics. We then show that the same string spectrum can be also derived by solving Bethe ansatz type equations, and discuss their relation to the quantum string Bethe ansatz for the su(1 vertical bar 1) sector.
Vacuum energy of the Bukhvostov-Lipatov model
Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Runov, Boris A.
2016-10-01
Bukhvostov and Lipatov have shown that weakly interacting instantons and anti-instantons in the O (3) non-linear sigma model in two dimensions are described by an exactly soluble model containing two coupled Dirac fermions. We propose an exact formula for the vacuum energy of the model for twisted boundary conditions, expressing it through a special solution of the classical sinh-Gordon equation. The formula perfectly matches predictions of the standard renormalized perturbation theory at weak couplings as well as the conformal perturbation theory at short distances. Our results also agree with the Bethe ansatz solution of the model. A complete proof the proposed expression for the vacuum energy based on a combination of the Bethe ansatz techniques and the classical inverse scattering transform method is presented in the second part of this work [42].
Institute of Scientific and Technical Information of China (English)
CHENYong; WANGQi; LIBiao
2004-01-01
Making use of a new and more general ansatz, we present the generalized algebraic method to uniformly construct a series of new and general travelling wave solution for nonlinear partial differential equations. As an application of the method, we choose a (1+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003) 17] and find other new and more general solutions at the same time, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrass doubly periodic wave solutions.
On the method of strained parameters for a KdV type of equation with exact dispersion property
Karjanto, N
2016-01-01
This paper provides an alternative methodology for analysis of three-wave interactions under the exact dispersion relation associated with gravity waves in fluid of intermediate depth. A Korteweg-de Vries type of equation with exact dispersion property is adopted as the governing equation for unidirectional wave packet evolution. Following the idea from Zakharov's seminal paper (Zakharov, V. E. (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. \\textit{Journal of Applied Mechanics and Technical Physics}, {\\bf 9}, 190--194), the equation is transformed from the spatial--temporal domain to the wavenumber--temporal domain. The solution of the transformed equation is sought using the perturbation theory, for which the ansatz is expressed in the form of a regular expansion in the increasing order of a small parameter. After implementing the na\\"{i}ve perturbation method, due to nonlinear mode generation and particular combinations of wavenumbers, the third-order solution contain...
Energy Technology Data Exchange (ETDEWEB)
Zheng Xuedong; Chen Yong; Zhang Hongqing
2003-05-12
Making use of a new generalized ansatzes, we present the generalized extended tanh-function method for constructing the exact solutions of nonlinear partial differential equations (NPDEs) in a unified way. Applying the generalized method, with the aid of MAPLE, we consider the Wu-Zhang equation (which describes (1+1)-dimensional dispersive long wave). As a result, we can successfully obtain the solitary wave solutions that can be found by the extended tanh-function method and the modified extended tanh-function method. More importantly, for the equation, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary wave solutions, bell-profile solitary wave solutions, periodic wave solutions, rational solutions, singular solutions and other new formal solutions. As an illustrative sample, the properties of some soliton solutions for Wu-Zhang equation are shown by some figures.
Energy Technology Data Exchange (ETDEWEB)
Airapetian, A. [Giessen Univ. (Germany). Physikalisches Inst.; Michigan Univ., Ann Arbor MI (United States). Randall Lab. of Physics; Akopov, N. [Yerevan Physics Institue (Armenia); Akopov, Z. [DESY, Hamburg (DE)](and others)
2009-09-15
Hard exclusive leptoproduction of real photons from an unpolarized proton target is studied in an effort to elucidate generalized parton distributions. The data accumulated during the years 1996-2005 with the HERMES spectrometer are analyzed to yield asymmetries with respect to the combined dependence of the cross section on beam helicity and charge, thereby revealing previously unseparated contributions from deeply virtual Compton scattering and its interference with the Bethe-Heitler process. The integrated luminosity is sufficient to show correlated dependences on two kinematic variables, and provides the most precise determination of the dependence on only the beam charge. (orig.)
Vladimirov, Igor; Jak, Eugene
2007-04-28
We study an interacting particle system on the simple cubic lattice satisfying the nearest neighbor exclusion (NNE) which forbids any two nearest sites to be simultaneously occupied. Under the constraint, we develop an edge-to-site reduction of the Bethe-Peierls entropy approximation of the cluster variation method. The resulting NNE-corrected Bragg-Williams approximation is applied to statistical mechanical modeling of a liquid silicate formed by silica and a univalent network modifier, for which we derive the molar Gibbs energy of mixing and enthalpy of mixing and compare the predictions with available thermodynamic data.
A Numerical Approach for the Solution of Schrödinger Equation With Pseudo-Gaussian Potentials
Directory of Open Access Journals (Sweden)
Iacob Theodor-Felix
2015-12-01
Full Text Available The Schrödinger equation with pseudo-Gaussian potential is investigated. The pseudo-Gaussian potential can be written as an infinite power series. Technically, by an ansatz to the wave-functions, exact solutions can be found by analytic approach [12]. However, to calculate the solutions for each state, a condition that will stop the series has to be introduced. In this way the calculated energy values may suffer modifications by imposing the convergence of series. Our presentation, based on numerical methods, is to compare the results with those obtained in the analytic case and to determine if the results are stable under different stopping conditions.
Glinka, Lukasz Andrzej
2015-01-01
In this paper, making use of the 't Hooft-Polyakov-Julia-Zee ansatz for the SU(2) Yang-Mills-Higgs gauge field theory, we present the straightforward generalization of the Bogomoln'yi equations and its several consequences. Particularly, this is shown that this idea is able to generate new types of non-abelian both dyons and magnetic monopoles and, moreover, that within the new model the scalar field can be described through the Coulomb potential, whereas, up to a constant, the non-abelian gauge field becomes the Wu-Yang monopole.
Time-periodic solutions of the Benjamin-Ono equation
Energy Technology Data Exchange (ETDEWEB)
Ambrose , D.M.; Wilkening, Jon
2008-04-01
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one of the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.
Krauskopf, Carl H., III
This unit for 10th grade students on "Macbeth" is intended for college bound students. It was developed as a part of a series by the Public Education Religion Studies Center at Wright State University. In the seven-week unit, students examine the Elizabethan cultural background of Shakespeare's "Macbeth," including the political, social and…
Dynamical mass generation in unquenched QED using the Dyson--Schwinger equations
Kizilersu, Ayse; Sizer, Tom; Williams, Anthony G; Williams, Richard
2014-01-01
We present a comprehensive numerical study of dynamical mass generation for unquenched QED in four dimensions, in the absence of four-fermion interactions, using the Dyson--Schwinger approach. We begin with an overview of previous investigations of criticality in the quenched approximation. To this we add an analysis using a new fermion-antifermion-boson interaction ansatz, the Kizilersu-Pennington (KP) vertex, developed for an unquenched treatment. After surveying criticality in previous unquenched studies, we investigate the performance of the KP vertex in dynamical mass generation using a renormalized fully unquenched system of equations. This we compare with the results for two hybrid vertices incorporating the Curtis--Pennington vertex in the fermion equation. We conclude that the KP vertex is as yet incomplete, and its relative gauge-variance is due to its lack of massive transverse components in its design.
An, Hongli; Fan, Engui; Zhu, Haixing
2015-01-01
The 2+1-dimensional compressible Euler equations are investigated here. A power-type elliptic vortex ansatz is introduced and thereby reduction obtains to an eight-dimensional nonlinear dynamical system. The latter is shown to have an underlying integral Ermakov-Ray-Reid structure of Hamiltonian type. It is of interest to notice that such an integrable Ermakov structure exists not only in the density representations but also in the velocity components. A class of typical elliptical vortex solutions termed pulsrodons corresponding to warm-core eddy theory is isolated and its behavior is simulated. In addition, a Lax pair formulation is constructed and the connection with stationary nonlinear cubic Schrödinger equations is established.
The neutron star in Cassiopeia A: equation of state, superfluidity, and Joule heating
Bonanno, A; Burgio, G F; Urpin, V
2013-01-01
The thermomagnetic evolution of the young neutron star in Cassiopea A is studied by considering fast neutrino emission processes. In particular, we consider neutron star models obtained from the equation of state computed in the framework of the Brueckner-Bethe-Goldstone many-body theory and variational methods, and models obtained with the Akmal-Pandharipande-Ravenhall equation of state. It is shown that it is possible to explain a fast cooling regime as the one observed in the neutron star in Cassiopea A if the Joule heating produced by dissipation of the small-scale magnetic field in the crust is taken into account. We thus argue that it is difficult to put severe constraints on the superfluid gap if the Joule heating is considered.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Uzunov, Ivan M.; Georgiev, Zhivko D.
2014-10-01
We study the dynamics of the localized pulsating solutions of generalized complex cubic- quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. At first using ansatz of the travelling wave, and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard - Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed material parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability.
Institute of Scientific and Technical Information of China (English)
DOU Fu-Quan; SUN Jian-An; DUAN Wen-Shan; SHI Yu-Ren; L(U) Ke-Pu; HONG Xue-Ren
2006-01-01
With the aid of computerized symbolic computation, the new modified Jacobi elliptic function expansion method for constructing exact periodic solutions of nonlinear mathematical physics equation is presented by a new general ansatz. The proposed method is more powerful than most of the existing methods. By use of the method, we not only can successfully recover the previously known formal solutions but also can construct new and more general formal solutions for some nonlinear evolution equations. We choose the (3+1)-dimensional Kadomtsev-Petviashvili equation to illustrate our method. As a result, twenty families of periodic solutions are obtained. Of course, more solitary wave solutions, shock wave solutions or triangular function formal solutions can be obtained at their limit condition.
Deguchi, Tetsuo; Ranjan Giri, Pulak
2016-04-01
Every solution of the Bethe-ansatz equations (BAEs) is characterized by a set of quantum numbers, by which we can evaluate it numerically. However, no general rule is known how to give quantum numbers for the physical solutions of BAE. For the spin-1/2 XXX chain we rigorously derive all the quantum numbers for the complete set of the Bethe-ansatz eigenvectors in the two down-spin sector with any chain length N. Here we obtain them both for real and complex solutions. We also show that all the solutions associated with them are distinct. Consequently, we prove the completeness of the Bethe ansatz and give an exact expression for the number of real solutions which correspond to collapsed bound-state solutions (i.e., two-string solutions) in the sector: 2[(N-1)/2-(N/π ){{tan}}-1(\\sqrt{N-1})] in terms of Gauss’ symbol. Moreover, we prove in the sector the scheme conjectured by Takahashi for solving BAE systematically. We also suggest that by applying the present method we can derive the quantum numbers for the spin-1/2 XXZ chain.
The boundary RSOS \\mathcal{M}(3,5) model
Deeb, Omar El
2015-01-01
We consider the critical non-unitary minimal model {\\cal M}(3,5) with integrable boundaries. We analyze the patterns of zeros of the eigenvalues of the transfer matrix and then determine the spectrum of the critical theory through the Thermodynamic Bethe Ansatz (TBA) equations. We derive these equations for all excitations by solving, the TBA functional equation satisfied by the transfer matrices of the associated A_{4} RSOS lattice model of Forrester and Baxter in Regime III, then determine their corresponding energies. The excitations are classified in terms of (m,n) systems.
Orbifolded Konishi from the mirror TBA
Energy Technology Data Exchange (ETDEWEB)
De Leeuw, Marius [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institute, Am Muehlenberg 1, 14476 Potsdam (Germany); Van Tongeren, Stijn J, E-mail: Marius.de.Leeuw@aei.mpg.de, E-mail: S.J.vanTongeren@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)
2011-08-12
Starting with a discussion of the general applicability of the simplified mirror thermodynamic Bethe ansatz (TBA) equations to simple deformations of the AdS{sub 5} x S{sup 5} superstring, we proceed to study a specific type of orbifold to which the undeformed simplified TBA equations directly apply. We then use this set of equations, as well as Luescher's approach, to determine the next-to-leading-order wrapping correction to the energy of what we call the orbifolded Konishi state and show that they perfectly agree. In addition we discuss wrapping corrections to the ground-state energy of the orbifolded model under consideration.
Dupuy, Nicolas; Bouaouli, Samira; Mauri, Francesco; Sorella, Sandro; Casula, Michele
2015-06-07
We study the ionization energy, electron affinity, and the π → π(∗) ((1)La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the (1)La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral (1)La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
Energy Technology Data Exchange (ETDEWEB)
Dupuy, Nicolas, E-mail: nicolas.dupuy@impmc.upmc.fr [Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05 (France); Bouaouli, Samira, E-mail: samira.bouaouli@lct.jussieu.fr [Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05 (France); Mauri, Francesco, E-mail: francesco.mauri@impmc.upmc.fr; Casula, Michele, E-mail: michele.casula@impmc.upmc.fr [CNRS and Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05 (France); Sorella, Sandro, E-mail: sorella@sissa.it [International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste (Italy)
2015-06-07
We study the ionization energy, electron affinity, and the π → π{sup ∗} ({sup 1}L{sub a}) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the {sup 1}L{sub a} excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral {sup 1}L{sub a} excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
Dupuy, Nicolas; Bouaouli, Samira; Mauri, Francesco; Sorella, Sandro; Casula, Michele
2015-06-01
We study the ionization energy, electron affinity, and the π → π∗ (1La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the 1La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral 1La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
Tucker, J. W.; Balcerzak, T.; Gzik, M.; Sukiennicki, A.
1998-09-01
The complete global phase diagram for a magnetic spin-1 bilayer, whose interactions are described by the Blume Emery Griffiths model (BEG), is studied by cluster variational theory within the pair approximation. The results obtained, are also the exact results pertaining to the BEG model on a Bethe lattice having coordination number, z=5. Useful analytic expressions are derived for trajectories in phase space containing the second-order (continuous) phase boundaries. The physical existence of these second-order boundaries, together with the location of the first-order phase boundaries, are determined from a Gibbs free energy analysis. Detailed comparison of the results with those of other workers on this, and closely related systems, is made.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software
Directory of Open Access Journals (Sweden)
L. L. Williams
2015-01-01
Full Text Available This paper calculates the Kaluza field equations with the aid of a computer package for tensor algebra, xAct. The xAct file is provided with this paper. We find that Thiry’s field equations are correct, but only under limited circumstances. The full five-dimensional field equations under the cylinder condition are provided here, and we see that most of the other references miss at least some terms from them. We go on to establish the remarkable Kaluza Lagrangian, and verify that the field equations calculated from it match those calculated with xAct, thereby demonstrating self-consistency of these results. Many of these results can be found scattered throughout the literature, and we provide some pointers for historical purposes. But our intent is to provide a definitive exposition of the field equations of the classical, five-dimensional metric ansatz of Kaluza, along with the computer algebra data file to verify them, and then to recover the unique Lagrangian for the theory. In common terms, the Kaluza theory is an “ω=0” scalar field theory, but with unique electrodynamic couplings.
Accounting for the analytical properties of the quark propagator from Dyson-Schwinger equation
Dorkin, S M; Kampfer, B
2014-01-01
An approach based on combined solutions of the Bethe-Salpeter (BS) and Dyson-Schwinger (DS) equations within the ladder-rainbow approximation in the presence of singularities is proposed to describe the meson spectrum as quark antiquark bound states. We consistently implement into the BS equation the quark propagator functions from the DS equation, with and without pole-like singularities, and show that, by knowing the precise positions of the poles and their residues, one is able to develop reliable methods of obtaining finite interaction BS kernels and to solve the BS equation numerically. We show that, for bound states with masses $M 1 $ GeV, however, the propagator functions reveal pole-like structures. Consequently, for each type of mesons (unflavored, strange and charmed) we analyze the relevant intervals of $M$ where the pole-like singularities of the corresponding quark propagator influence the solution of the BS equation and develop a framework within which they can be consistently accounted for. The...
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
EvangelosChaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.
Quantum integrable systems. Quantitative methods in biology
Feverati, Giovanni
2011-01-01
Quantum integrable systems have very strong mathematical properties that allow an exact description of their energetic spectrum. From the Bethe equations, I formulate the Baxter "T-Q" relation, that is the starting point of two complementary approaches based on nonlinear integral equations. The first one is known as thermodynamic Bethe ansatz, the second one as Kl\\"umper-Batchelor-Pearce-Destri- de Vega. I show the steps toward the derivation of the equations for some of the models concerned. I study the infrared and ultraviolet limits and discuss the numerical approach. Higher rank integrals of motion can be obtained, so gaining some control on the eigenvectors. After, I discuss the Hubbard model in relation to the N = 4 supersymmetric gauge theory. The Hubbard model describes hopping electrons on a lattice. In the second part, I present an evolutionary model based on Turing machines. The goal is to describe aspects of the real biological evolution, or Darwinism, by letting evolve populations of algorithms. ...
Energy Technology Data Exchange (ETDEWEB)
Chen, Yong [Ningbo Univ., Ningbo (China). Department of Mathematics; Shanghai Jiao-Tong Univ., Shangai (China). Department of Physics; Chinese Academy of sciences, Beijing (China). Key Laboratory of Mathematics Mechanization
2005-03-01
A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion.
Analytic self-similar solutions of the Oberbeck-Boussinesq equations
Barna, I. F.; Mátyás, L.
2015-09-01
In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtoniain Navier-Stokes --- with Boussinesq approximation --- and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field has a strongly damped oscillating behavior which is an interesting feature.
Analytic self-similar solutions of the Oberbeck-Boussinesq equations
Barna, I F
2015-01-01
In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtoniain Navier-Stokes --- with Boussinesq approximation --- and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field has a strongly damped oscillating behavior which is an interesting feature.
Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Aydogmus, F., E-mail: fatma.aydogmus@gmail.com [Istanbul University, Department of Physics, Faculty of Science (Turkey)
2015-02-15
The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the “Heisenberg dream.” In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented.
A cosmological model in Weyl-Cartan spacetime; 1, Field equations and solutions
Puetzfeld, D
2001-01-01
In this first article of a series on alternative cosmological models we present an extended version of a cosmological model in Weyl-Cartan spacetime. The new model can be viewed as a generalization of a model developed earlier jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e. torsion $T^{\\alpha}$ and nonmetricity $Q_{\\alpha \\beta}$, are proportional to the Weyl 1-form. The hypermomentum $\\Delta_{\\alpha \\beta}$ depends on our ansatz for the nonmetricity and vice versa. We derive the explicit form of the field equations for different cases and provide solutions for a broad class of parameters. We demonstrate that it is possible to construct models in which the non-Riemannian quantities die out with time. We show how our model fits into the more general framework of metric-affine gravity (MAG).
A cosmological model in Weyl-Cartan spacetime: I. Field equations and solutions
Puetzfeld, Dirk
2002-06-01
In this first paper of a series on alternative cosmological models we present an extended version of a cosmological model in Weyl-Cartan spacetime. The new model can be viewed as a generalization of a model developed earlier jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e. torsion Tα and nonmetricity Qαβ, are proportional to the Weyl 1-form. The hypermomentum Δαβ depends on our ansatz for the nonmetricity and vice versa. We derive the explicit form of the field equations for different cases and provide solutions for a broad class of parameters. We demonstrate that it is possible to construct models in which the non-Riemannian quantities die out with time. We show how our model fits into the more general framework of metric-affine gravity (MAG).
A cosmological model in Weyl-Cartan spacetime: I. Field equations and solutions
Energy Technology Data Exchange (ETDEWEB)
Puetzfeld, Dirk [Institute for Theoretical Physics, University of Cologne, 50923 Cologne (Germany)
2002-06-21
In this first paper of a series on alternative cosmological models we present an extended version of a cosmological model in Weyl-Cartan spacetime. The new model can be viewed as a generalization of a model developed earlier jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e. torsion T{sup {alpha}} and nonmetricity Q{sub {alpha}}{sub {beta}}, are proportional to the Weyl 1-form. The hypermomentum {delta}{sub {alpha}}{sub {beta}} depends on our ansatz for the nonmetricity and vice versa. We derive the explicit form of the field equations for different cases and provide solutions for a broad class of parameters. We demonstrate that it is possible to construct models in which the non-Riemannian quantities die out with time. We show how our model fits into the more general framework of metric-affine gravity (MAG)
On solving the Schrödinger equation for a complex deictic potential in one dimension
Indian Academy of Sciences (India)
Ram Mehar Singh
2014-09-01
Making use of an ansatz for the eigenfunction, we investigate closed-form solutions of the Schrödinger equation for an even power complex deictic potential and its variant in one dimension. For this purpose, extended complex phase-space approach is utilized and nature of the eigenvalue and the corresponding eigenfunction is determined by the analyticity property of the eigenfunction. The imaginary part of the energy eigenvalue exists only if the potential parameters are complex, whereas it reduces to zero for real coupling parameters and the result coincides with those derived from the invariance of Hamiltonian under $\\mathcal{PT}$ operations. Thus, a non-Hermitian Hamiltonian possesses real eigenvalue, if it is $\\mathcal{PT}$-symmetric.
Equation of state for isospin asymmetric nuclear matter using Lane potential
Basu, D N; Samanta, C
2006-01-01
A variational method of obtaining equation of state (EOS) for symmetric nuclear matter from a density dependent M3Y interaction supplemented by a zero-range potential is described. The energy per nucleon is minimized to obtain the ground state of symmetric nuclear matter. The saturation energy per nucleon used for nuclear matter calculations is determined from the co-efficient of the volume term of Bethe-Weizs\\"acker mass formula which is evaluated by fitting the recent experimental and estimated atomic mass excesses from Audi-Wapstra-Thibault atomic mass table by minimizing the mean square deviation. The constants of density dependence of the effective interaction are obtained by reproducing the saturation energy per nucleon and the saturation density of spin and isospin symmetric cold infinite nuclear matter. The EOS of symmetric nuclear matter, thus obtained, provide reasonably good estimate of nuclear incompressibility. Once the consants of density dependence are determined, EOS for asymmetric nuclear mat...
Indian Academy of Sciences (India)
George F R Ellis
2007-07-01
The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.
Pethick, C. J.
2011-04-01
The talk will touch on a number of themes in the application of many-body theory to neutron stars and stellar collapse. One of these will be the composition and equation of state of nuclear matter. Specific topics will include nuclei in neutron stars, superfluidity and superconductivity of nuclear matter, and inhomogeneous phases of nuclear matter. A second major theme will be neutrino processes in dense matter: neutrino emission is the most powerful cooling mechanism for young neutron stars, and rates of neutrino processes are a key ingredient in simulations of stellar collapse.
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Winding vacuum energies in a deformed O(4) sigma model
Bazhanov, Vladimir V; Lukyanov, Sergei L
2014-01-01
We consider the problem of calculating the Casimir energies in the winding sectors of Fateev's SS-model, which is an integrable two-parameter deformation of the O(4) non-linear sigma model in two dimensions. This problem lies beyond the scope of all traditional methods of integrable quantum field theory including the thermodynamic Bethe ansatz and non-linear integral equations. Here we propose a solution based on a remarkable correspondence between classical and quantum integrable systems and express the winding energies in terms of certain solutions of the classical sinh-Gordon equation.
Winding vacuum energies in a deformed O(4) sigma model
Energy Technology Data Exchange (ETDEWEB)
Bazhanov, Vladimir V. [Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200 (Australia); Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200 (Australia); Kotousov, Gleb A. [Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200 (Australia); Lukyanov, Sergei L., E-mail: sergei@physics.rutgers.edu [NHETC, Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855-0849 (United States); L.D. Landau Institute for Theoretical Physics, Chernogolovka 142432 (Russian Federation)
2014-12-15
We consider the problem of calculating the Casimir energies in the winding sectors of Fateev's SS-model, which is an integrable two-parameter deformation of the O(4) non-linear sigma model in two dimensions. This problem lies beyond the scope of all traditional methods of integrable quantum field theory including the thermodynamic Bethe ansatz and non-linear integral equations. Here we propose a solution based on a remarkable correspondence between classical and quantum integrable systems and express the winding energies in terms of certain solutions of the classical sinh-Gordon equation.
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.; Teschner, J.
2010-06-15
We give a direct derivation of a proposal of Nekrasov-Shatashvili concerning the quantization conditions of the Toda chain. The quantization conditions are formulated in terms of solutions to a nonlinear integral equation similar to the ones coming from the thermodynamic Bethe ansatz. This is equivalent to extremizing a certain function called Yang's potential. It is shown that the Nekrasov-Shatashvili formulation of the quantization conditions follows from the solution theory of the Baxter equation, suggesting that this way of formulating the quantization conditions should indeed be applicable to large classes of quantized algebraically integrable models. (orig.)
Quantum mass correction for the twisted kink
Pawellek, Michael
2008-01-01
We present an analytic result for the 1-loop quantum mass correction in semiclassical quantization for the twisted \\phi^4 kink on S^1 without explicit knowledge of the fluctuation spectrum. For this purpose we use the contour integral representation of the spectral zeta function. By solving the Bethe ansatz equations for the n=2 Lame equation we obtain an analytic expression for the corresponding spectral discriminant. We discuss the renormalization issues of this model. An energetically preferred size for the compact space is finally obtained.
Fioravanti, D; Fioravanti, Davide; Rossi, Marco
2001-01-01
A generalization of the Yang-Baxter algebra is found in quantizing the monodromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang-Baxter equation still ensures that the transfer matrix generates operators in involution which form the Cartan sub-algebra of the braided quantum group. Representations diagonalizing these operators are described through relying on an easy generalization of Algebraic Bethe Ansatz techniques. The conjecture that this monodromy matrix algebra leads, {\\it in the cylinder continuum limit}, to a Perturbed Minimal Conformal Field Theory description is analysed and supported.
Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Jianping Zhao
2012-01-01
Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
Evangelos Chaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.
Directory of Open Access Journals (Sweden)
Karim Fathi
2010-07-01
really integrated Peace and Conflict Researcher should be familiar with epistemological and heuristic contexts, but also metatheoretical and theoretical contexts as well. Abstract - Deutsch Angesichts immer komplexerer Konflikte in der Friedens- und Konfliktforschung (Friedens- und Konfliktforschung sind Metatheorien von Nöten, die diese unübersichtliche Vielfalt unterschiedlicher Methoden zu integrieren vermögen. Im Rahmen des vorliegenden Papers soll hierzu ein konzeptioneller Vorschlag skizziert werden, indem zwei holistische und bekannte Ansätze der mediativen Konfliktbearbeitung in einem integrativen Kontext diskutiert werden:- Der Konfliktmanagement-Ansatz nach Prof. Dr. Friedrich Glasl (2004.- Die Transcend-Methode nach Prof. Dr. Johan Galtung (2000. Den theoretischen Rahmen, auf den sich die Überlegungen dieser Arbeit stützen, liefert der Integrale Ansatz (IA von Ken Wilber (2001 – eine viel diskutierte philosophische „Theorie von Allem“, die im Rahmen der Friedens- und Konfliktforschung jedoch noch weitgehend unberücksichtigt geblieben ist. Daher ist es im Rahmen der Arbeit von weiterem Interesse den IA auf seinen Mehrwert für eine integrierte Friedens- und Konfliktforschung zu untersuchen.Die Untersuchung verlief wie folgt: 1. Vorstellung der in der Untersuchung berücksichtigten Ansätze: a. Der Konfliktmanagement-Ansatz von Glasl unterscheidet eine Vielzahl von Kategorien und Ansatzmomenten, die ein komplexes Interventionsspektrum ergeben. Sehr wichtig ist hierbei unter anderem die Berücksichtigung von Eskalationsstufen, die eine Unterscheidung zwischen perzeptions- (niedrige Eskalation, gefühls- (mittlere Eskalation und verhaltensorientierten (hohe Eskalation Maßnahmen ermöglichen. b. Die Konflikttransformation nach Galtung zeichnet sich unter anderem durch dreigeteilte Schematisierungen aus, die ein komplexes Verständnis von Gewalt (direkt, kulturell, strukturell, Konflikt (Verhalten, Annahmen, Widerspruch und Frieden (Gewaltlosigkeit
Rojas, E; El-Bennich, B; Oliveira, O; Frederico, T
2013-01-01
We investigate the dressed quark-gluon vertex combining two established non-perturbative approaches to QCD: the Dyson-Schwinger equation (DSE) for the quark propagator and lattice-regularized simulations for the quark, gluon and ghost propagators. The vertex is modeled using a generalized Ball-Chiu ansatz parameterized by a single form factor $\\tilde X_0$ which effectively represents the quark-ghost scattering kernel. The solution space of the DSE inversion for $\\tilde X_0$ is highly degenerate, which can be dealt with by a numerical regularization scheme. We consider two possibilities: (i) linear regularization and (ii) the Maximum Entropy Method. These two numerical approaches yield compatible $\\tilde X_0$ functions for the range of momenta where lattice data is available and feature a strong enhancement of the generalized Ball-Chiu vertex for momenta below 1 GeV. Our ansatz for the quark-gluon vertex is then used to solve the quark DSE which yields a mass function in good agreement with lattice simulations...
Planck constant as spectral parameter in integrable systems and KZB equations
Levin, A.; Olshanetsky, M.; Zotov, A.
2014-10-01
We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.
Xu, Ling; Cheng, Xuan; Dai, Chao-Qing
2015-12-01
Although the mapping method based on Riccati equation was proposed to obtain variable separation solutions many years ago, two important problems have not been studied: i) the equivalence of variable separation solutions by means of the mapping method based on Riccati equation with the radical sign combined ansatz; and ii) lack of physical meanings for some localized structures constructed by variable separation solutions. In this paper, we re-study the (2+1)-dimensional Boiti-Leon-Pempinelli equation via the mapping method based on Riccati equation and prove that nine types of variable separation solutions are actually equivalent to each other. Moreover, we also re-study localized structures constructed by variable separation solutions. Results indicate that some localized structures reported in the literature are lacking real values due to the appearance of the divergent and un-physical phenomenon for the initial field. Therefore, we must be careful with the initial field to avoid the appearance of some un-physical or even divergent structures in it when we construct localized structures for the potential field.
Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation
Directory of Open Access Journals (Sweden)
Ivan M. Uzunov
2014-01-01
Full Text Available We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE in the presence of intrapulse Raman scattering (IRS. We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability. We apply the Melnikov method also to the equation of Duffing-Van der Pol oscillator used for the investigation of the influence of the IRS on the bandwidth limited amplification. We prove the existence and stability of a limit cycle that arises in a neighborhood of a homoclinic trajectory of the corresponding unperturbed system. The condition of existence of the limit cycle derived here coincides with the relation between the critical value of velocity and the amplitude of the solitary wave solution (Uzunov, 2011.
Niccoli, G
2014-01-01
Generic inhomogeneous integrable XXZ chains with arbitrary spins are studied by means of the quantum separation of variables (SOV) method. Within this framework, a complete description of the spectrum (eigenvalues and eigenstates) of the antiperiodic transfer matrix is derived in terms of discrete systems of equations involving the inhomogeneity parameters of the model. We show here that one can reformulate this discrete SOV characterization of the spectrum in terms of functional T-Q equations of Baxter's type, hence proving the completeness of the solutions to the associated systems of Bethe-type equations. More precisely, we consider here two such reformulations. The first one is given in terms of Q-solutions, in the form of trigonometric polynomials of a given degree $N_s$, of a one-parameter family of T-Q functional equations with an extra inhomogeneous term. The second one is given in terms of Q-solutions, again in the form of trigonometric polynomials of degree $N_s$ but with double period, of Baxter's ...
Sharma, A
1997-01-01
A qqq BSE formalism based on an input 4-fermion Lagrangian of "current" u,d quarks, is employed for the construction of a relativistic qqq-wave function) via the BSE. Chiral invariance is ensured by the vector character of the gluonic propagator in the infrared regime, while the `constituent' masses are the low momentum limits of the dynamicalmass function generated by standard DB{\\chi}. The Covariant Instantaneity Ansatz (CIA) gives an exact 3D reduction of the BSE for baryon spectroscopy, while the reconstructed 4D form identifies the baryon quark vertex function reconstructed through a reversal of steps offered by the CIA structure. It is employed for the quark loop integrals for the neutron - proton mass difference which receives contributions from two sources : i) the strong SU(2) effect arising from the $u-d$ mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference works out at 1.28 MeV (vs. 1.29 expt), with only two free parameters characterizing the in...
Mitra, A N
1999-01-01
A qqq BSE formalism based on DB{\\chi}S of an input 4-fermion Lagrangian of `current' u,d quarks interacting pairwise via gluon-exchange-propagator in its self-energy via quark-loop integrals. To that end the baryon-qqq vertex function is derived under Covariant Instantaneity Ansatz (CIA), using Green's function techniques. This is a 3-body extension of an earlier q{\\bar q} (2-body) result on the exact 3D-4D interconnection for the respective BS wave functions under 3D kernel support, precalibrated to both q{\\bar q} and qqq spectra plus other observables. The quark loop integrals for the neutron (n) - proton (p) mass difference receive contributions from : i) the strong SU(2) effect arising from the d-u mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference comes dominantly from d-u effect (+1.71 Mev), which is mildly offset by e.m.effect (-0.44), subject to gauge corrections. To that end, a general method for QED gauge corrections to an arbitrary momentum de...
Wang, L. M.; Li, Chun; Yan, Z.-C.; Drake, G. W. F.
2017-03-01
Isotope shifts and total transition frequencies are calculated for the 2 2S-3 2S transition of the lithium isotopes 6Li, 7Li, 8Li, 9Li, and the halo nucleus 11Li. The accuracy is improved for previously calculated relativistic and quantum electrodynamic corrections, and in particular a disagreement for the Bethe logarithm is resolved for the ground 2S state. Our previous result is confirmed for the 2 2P state. We use the pseudostate expansion method to perform the sum over virtual intermediate states. Results for the second-order relativistic recoil term of order α2(μ/M ) 2 Ry are shown to make a significant contribution relative to the theoretical uncertainty, but because of accidental cancellations the final result for the isotope shift is nearly unchanged. However, the spin-orbit term makes an unexpectedly large contribution to the splitting isotope shift (SIS) for the 2 1/2 2P -2 3/2 2P fine structure, increasing the theoretical value for the 6Li-7Li isotopes to 0.556 31 (7 )±0.001 MHz. A comparison is made with high-precision measurements and other calculations for the SIS and for the total 2 2S-3 2S transition frequency.
Energy Technology Data Exchange (ETDEWEB)
Messite, J.; Fannick, N.L.
1978-07-01
In response to a request from a representative of the nursing staff, an investigation was made of possible methadone exposures at the Cumberland Outpatient Department of Beth Israel Hospital, Brooklyn, New York, a methadone-dispensing clinic. The distribution room measured 12 feet in all dimensions and was enclosed on three sides. Methadone had previously been received in prepackaged doses, but more recently the nurses had to count the contents of each 100-count bottle of methadone hydrochloride and separate tablets or diskets into individual doses. Nurses involved in dispensing the medication reported intermittent sleepiness, itching of the face, nose, and eyes, and dryness of skin on the hands and face. Urine studies indicated no detectable methadone or methadone metabolites at a limit of 1 microgram per milliliter. There is no evidence of methadone absorption; however, they recommend that skin contact with the tablets and diskets be kept to a minimum by use of instruments for moving the pills on the counting tray, frequent clean up of dust, and periodic hand washing.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Fractional Chemotaxis Diffusion Equations
Langlands, T A M
2010-01-01
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.
Oscillator construction of su(n|m) Q-operators
Energy Technology Data Exchange (ETDEWEB)
Frassek, Rouven, E-mail: rfrassek@physik.hu-berlin.de [Institut fuer Mathematik und Institut fuer Physik, Humboldt-Universitaet zu Berlin, Johann von Neumann-Haus, Rudower Chaussee 25, 12489 Berlin (Germany); Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Potsdam (Germany); Lukowski, Tomasz, E-mail: lukowski@mathematik.hu-berlin.de [Institut fuer Mathematik und Institut fuer Physik, Humboldt-Universitaet zu Berlin, Johann von Neumann-Haus, Rudower Chaussee 25, 12489 Berlin (Germany); Meneghelli, Carlo, E-mail: carlo@aei.mpg.de [Institut fuer Mathematik und Institut fuer Physik, Humboldt-Universitaet zu Berlin, Johann von Neumann-Haus, Rudower Chaussee 25, 12489 Berlin (Germany); Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Potsdam (Germany); Staudacher, Matthias, E-mail: matthias@aei.mpg.de [Institut fuer Mathematik und Institut fuer Physik, Humboldt-Universitaet zu Berlin, Johann von Neumann-Haus, Rudower Chaussee 25, 12489 Berlin (Germany); Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Potsdam (Germany)
2011-09-01
We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded Yang-Baxter equation, leading to an amalgam of bosonic and fermionic oscillator algebras. Our approach is fully algebraic, and leads to the exact solution of the associated compact spin chains while avoiding Bethe ansatz techniques. It furthermore elucidates the algebraic and combinatorial structures underlying the system of nested Bethe equations. Finally, our construction naturally reproduces the representation, due to Z. Tsuboi, of the hierarchy of Baxter Q-operators in terms of hypercubic Hasse diagrams.
Developmental Partial Differential Equations
Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto
2015-01-01
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...