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.

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.

Profile modifications at critical density of laser-produced plasmas

1978 ◽  
Vol 19 (3) ◽  
pp. 387-403 ◽  
Author(s):  
P. K. Shukla ◽  
K. H. Spatschek
Keyword(s):  
Inverse Scattering ◽  
Ponderomotive Force ◽  
Critical Density ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Initial Value ◽  
Plasma Inhomogeneity ◽  
Langmuir Waves ◽  
Profile Modification ◽  
Self Consistent

Profile modification by the ponderomotive force of the mode-converted Langmuir waves at critical density of a laser-irradiated plasma is investigated. A nonlinear Schrödinger equation governing the interaction of Langmuir waves with slow plasma motion is obtained taking into account the plasma inhomogeneity, dissipation, and a driver. The initial value problem is solved by means of the inverse scattering method. The soliton formation and self-consistent density steepemng at the critical layer are investigated.

On Nonlinear Equations Amenable to the Inverse Scattering Method

1975 ◽  
Vol 53 (1) ◽  
pp. 58-61 ◽  
Author(s):  
J. G. Kingston ◽  
C. Rogers
Keyword(s):  
Inverse Scattering ◽  
Initial Value Problem ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Inverse Scattering Method ◽  
Nonlinear Evolution Equations ◽  
Scattering Method ◽  
Initial Value ◽  
Physical Importance ◽  
Extensive Class

The inverse scattering method can be used to solve the initial value problem for various nonlinear evolution equations of physical importance. Here an extensive class of equations for which the technique is available is delimited.

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 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.

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.

Sign in / Sign up

Export Citation Format

Share Document