Quantum Integrable Systems

Quantum Integrable Systems

by Asesh Roy Chowdhury

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Overview

The work of established quantum mechanics authors, this book logically introduces the subject, first, by establishing a background, then by moving to the quantum case and finally by presenting the latest research and applications.

Product Details

ISBN-13: 9781135439750
Publisher: CRC Press
Publication date: 01/28/2004
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 424
File size: 19 MB
Note: This product may take a few minutes to download.

Table of Contents

NONLINEAR SYSTEMS AND CLASSICAL IST
Introduction
Definition of Integrability
Lax Pair Technique
Inverse Scattering Transform
Hamiltonian Structure
COORDINATE BETHE ANSATZ
Introduction
Nonlinear Systems and the CBA
Fermionic System
Boundary Condition in Bethe Ansatz
Heisenberg Spin Chain
Spin of the Bethe Ansatz State
Other Integrable Models
YANG-BAXTER EQUATION
Introduction
General Description
Factorized Scattering
Baxter's Star Triangle Relation
Vertex Models
Reflection Equation Algebra
CONTINUOUS INTEGRABLE SYSTEMS
Introduction
Quantum Continuous Integrable Systems
Conserved Quantities
Nonultralocal systems and the YBE
Operator Product Expansion and YBE
Finite Boundary Conditions
Modified Classical Yang-Baxter Equation
ALGEBRAIC BETHE ANSATZ
Introduction
Discrete Self Trapping Model
Asymmetric XXZ Model in a Magnetic Field
Analytical Bethe Ansatz
Off-Shell Bethe Ansatz
Nested Bethe Ansatz
Fusion Procedure
Fusion Procedure for Open chains
Fusion Procedure for Transfer Matrices
Application of Fusion Procedure
INTEGRABLE LONG-RANGE MODELS
Introduction
Long-Range Models from the ABA
Symmetry Transformation
Calogero-Moser Models
SEPARATION OF VARIABLES
Introduction
Hamilton-Jacobi Equation
Sklyanin's Method for SoV
Goryachev-Chaplygin Top
Quantum Case and the Role of Lie Algebra
Bi-Hamiltonian Structure and SoV
SoV for GCM Model
SoV and Boundary Conditions
BÄCKLUND TRANSFORMATIONS
Introduction
Permutability Theorem
Bäcklund Transformations and Classical Inverse Scattering
Bäcklund Transformations from Riccati Equation
Darboux Bäcklund Transformations
The Exponential Lattice
Canonical Transformations
Group Property of Bäcklund Transformations
Recent Developments in Bäcklund Transformation Theory
Sklyanin's Formalism for Canonical Bäcklund
Transformations
Extended Phase Space Method
Quantization of Bäcklund Transformations
Method of Projection Operators
QUANTUM GLM EQUATION
Introduction
Quantum GLM Equation
Quantum Floquet Function
Exact Quantization
Quantum GLM Equation in a Continuous System
Bound States and an Alternative Approach
APPENDICES
Direct Product Calculus
Grassman Algebra
Bethe Ansatz Equation
AKNS Problem
BIBLIOGRAPHY
INDEX

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