BETHE ANSATZ FOR NON-COMPACT GROUPS: THE PAIRING MODELS FOR BOSONS

2003 ◽  
Vol 17 (26) ◽  
pp. 1353-1363
Author(s):  
A. A. OVCHINNIKOV
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Inverse Scattering Method ◽  
Compact Groups ◽  
Scattering Method ◽  
Helium Nanodroplets ◽  
New Class ◽  
Quasiclassical Limit ◽  
Exactly Solvable ◽  
Solvable Pairing

We discuss the construction of the exactly solvable pairing models for bosons in the framework of the Quantum Inverse Scattering method. It is stressed that this class of models naturally appears in the quasiclassical limit of the algebraic Bethe ansatz transfer matrix. We propose the new pairing Hamiltonians for bosons, depending on the additional parameters. It is pointed out that the new class of the pairing models can be obtained from the fundamental transfer-matrix. The possible new application of the pairing models for confined bosons in the physics of helium nanodroplets is pointed out.

scholarly journals Integrable extended Hubbard models with boundary Kondo impurities

2001 ◽  
Vol 64 (3) ◽  
pp. 445-467
Author(s):  
Anthony J. Bracken ◽  
Xiang-Yu Ge ◽  
Mark D. Gould ◽  
Huan-Qiang Zhou
Keyword(s):  
Hilbert Space ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Magnetic Moments ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Ansatz Method ◽  
One Dimensional ◽  
Hubbard Models ◽  
Kondo Impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

scholarly journals EXACTLY SOLVABLE PAIRING MODEL USING AN EXTENSION OF THE RICHARDSON–GAUDIN APPROACH

2005 ◽  
Vol 14 (01) ◽  
pp. 47-55 ◽  
Author(s):  
A. B. BALANTEKIN ◽  
T. DERELI ◽  
Y. PEHLIVAN
Keyword(s):  
Energy Eigenstates ◽  
Energy Eigenvalues ◽  
New Class ◽  
Exactly Solvable ◽  
Sutherland Model ◽  
Pairing Model ◽  
Analytical Expressions ◽  
Solvable Pairing

We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and the first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero–Sutherland model is suggested.

scholarly journals QUASI-EXACTLY SOLVABLE DEFORMATIONS OF GAUDIN MODELS AND "QUASI-GAUDIN ALGEBRAS"

1998 ◽  
Vol 13 (04) ◽  
pp. 281-292 ◽  
Author(s):  
A. G. USHVERIDZE
Keyword(s):  
Bethe Ansatz ◽  
Complete Integrability ◽  
Integrable Models ◽  
Exact Solvability ◽  
New Class ◽  
Algebraic Bethe Ansatz ◽  
Exactly Solvable ◽  
Algebraic Deformation ◽  
Bethe Ansatz Solution ◽  
Gaudin Models

A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic Bethe ansatz solution only for some limited parts of the spectrum. An underlying algebra responsible for both the phenomena of complete integrability and quasi-exact solvability is constructed. We call it "quasi-Gaudin algebra" and demonstrate that it is a special non-Lie-algebraic deformation of the ordinary Gaudin algebra.

scholarly journals INTRODUCTION TO QUANTUM INTEGRABILITY

2010 ◽  
Vol 25 (17) ◽  
pp. 3307-3351 ◽  
Author(s):  
ANASTASIA DOIKOU ◽  
STEFANO EVANGELISTI ◽  
GIOVANNI FEVERATI ◽  
NIKOS KARAISKOS
Keyword(s):  
Boundary Conditions ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Quantum Groups ◽  
Braid Group ◽  
Short Review ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Quantum Integrability ◽  
Basic Concepts

In this paper, we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang–Baxter and boundary Yang–Baxter equations depending on the choice of boundary conditions. The relation between the aforementioned equations and the braid group is briefly discussed. A short review on quantum groups as well as the quantum inverse scattering method (algebraic Bethe ansatz) is also presented.

scholarly journals The Generalized Tavis—Cummings Model with Cavity Damping

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2124
Author(s):  
Nikolai Bogoliubov ◽  
Andrei Rybin
Keyword(s):  
Quantum Dynamics ◽  
Symmetric Functions ◽  
Annihilation Operator ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Determinant Representation ◽  
Exactly Solvable ◽  
Bethe Equations ◽  
Cavity Damping ◽  
Photon Annihilation

In this Communication, we consider a generalised Tavis–Cummings model when the damping process is taken into account. We show that the quantum dynamics governed by a non-Hermitian Hamiltonian is exactly solvable using the Quantum Inverse Scattering Method, and the Algebraic Bethe Ansatz. The leakage of photons is described by a Lindblad-type master equation. The non-Hermitian Hamiltonian is diagonalised by state vectors, which are elementary symmetric functions parametrised by the solutions of the Bethe equations. The time evolution of the photon annihilation operator is defined via a corresponding determinant representation.

scholarly journals Boundary two-parameter eight-state supersymmetric fermion model and Bethe ansatz solution

1999 ◽  
Vol 59 (3) ◽  
pp. 375-390 ◽  
Author(s):  
Anthony J. Bracken ◽  
Xiang-Yu Ge ◽  
Yao-Zhong Zhang ◽  
Huan-Qiang Zhou
Keyword(s):  
Boundary Conditions ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Fermion Model ◽  
Quantum Inverse ◽  
Boundary Terms ◽  
Bethe Ansatz Solution ◽  
Two Parameter

The recently introduced two-parameter eight-state Uq [gl(3|1)] supersymmetric fermion model is extended to include boundary terms. Nine classes of boundary conditions are constructed, all of which are shown to be integrable via the graded boundary quantum inverse scattering method. The boundary systems are solved by using the coordinate Bethe ansatz and the Bethe ansatz equations are given for all nine cases.

scholarly journals COMBINATORIAL BETHE ANSATZ AND GENERALIZED PERIODIC BOX-BALL SYSTEM

2008 ◽  
Vol 20 (05) ◽  
pp. 493-527 ◽  
Author(s):  
ATSUO KUNIBA ◽  
REIHO SAKAMOTO
Keyword(s):  
Energy Distribution ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Theta Function ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Local Energy ◽  
Initial Value ◽  
Rigged Configurations ◽  
Higher Spin

We reformulate the Kerov–Kirillov–Reshetikhin (KKR) map in the combinatorial Bethe ansatz from paths to rigged configurations by introducing local energy distribution in crystal base theory. Combined with an earlier result on the inverse map, it completes the crystal interpretation of the KKR bijection for [Formula: see text]. As an application, we solve an integrable cellular automaton, a higher spin generalization of the periodic box-ball system, by an inverse scattering method and obtain the solution of the initial value problem in terms of the ultradiscrete Riemann theta function.

Various Approaches to Spectral Problems for Integrable Systems in the QISM

1997 ◽  
Vol 12 (01) ◽  
pp. 79-87 ◽  
Author(s):  
I. V. Komarov
Keyword(s):  
Functional Equation ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Integrable Systems ◽  
Separation Of Variables ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Integrals Of Motion ◽  
Quantum Inverse ◽  
Spectral Problems

Algebraic Bethe Ansatz, separation of variables and Baxter's method of functional equation are three main approaches to finding spectrum of commuting integrals of motion in the frame of quantum inverse scattering method. Their connections are discussed.

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