Soliton Statistical Mechanics: Statistical Mechanics of the Quantum and Classical Integrable Models

Abstract

It is shown how the Bethe Ansatz (BA) analysis for the quantum statistical mechanics of the Nonlinear Schrodinger Model generalises to the other quantum integrable models and to the classical statistical mechanics of the classical integrable models. The bose-fermi equivalence of these models plays a fundamental role even at classical level. Two methods for calculating the quantum or classical free energies are developed: one generalises the BA method the other uses functional integral methods. The familiar classical action-angle variables of the integrable models developed for the real line R are used throughout, but the crucial importance of periodic boundary conditions is recognized and these are imposed. Connections with the quantum inverse method for quantum integrable systems are established. The R-matrix and the Yang-Baxter relation play a fundamental role in the theory. The lectures draw together the quantum BA method, the quantum inverse method, and the generalised BA and functional integral methods introduced more recently.