Quantum Solitons on Quantum Chaos: Coherent Structures, Anyons, and Statistical Mechanics

Abstract

This paper is concerned with the exact evaluation of functional integrals for the partition function Z (free energy F = -β ^-1 ℓn Z, β ^-1 = temperature) for integrable models like the quantum and classical sine-Gordon (s-G) models in 1+1 dimensions.^1–12 These models have wide applications in physics and are generic (and important) in that sense. The classical s-G model in 1+1 dimensions

$${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi$$

((1))

(m > 0 is a “mass”) has soliton (kink, anti-kink and breather) solutions. In Refs 1–12 we have reported a general theory of ‘soliton statistical mechanics’ (soliton SM) in which the particle description can be seen in terms of ‘solitons’ and ‘phonons’. The situation concerning the phonons and breather solutions of models like the quantum and classical s-G models has proved unexpected and the latter part of this present report (the §4 on quantum and classical thermodynamic limits) is devoted to this problem and its actual solution.