Statistical Mechanics of Lam\'e Solitons

TL;DR

This paper investigates the statistical mechanics of Lamé solitons using transfer matrix methods, analyzing their thermodynamics at various temperatures and connecting to sine-Gordon results in certain limits.

Contribution

It provides an analytical approach to the partition function of Lamé solitons and explores their finite-temperature thermodynamics and zero-temperature behavior.

Findings

Analytical evaluation of the partition function for specific temperatures.

Approximate thermodynamics using ideal kink gas phenomenology.

Reduction to sine-Gordon results in certain limits.

Abstract

We study the exact statistical mechanics of Lam\'e solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schr\"odinger equation with the periodic Lam\'e potential. Since the latter is a quasi-exactly solvable system, an analytical evaluation of the partition function can be done only for a few temperatures. We also study approximately the finite temperature thermodynamics using the ideal kink gas phenomenology. The zero-temperature "thermodynamics" of the soliton lattice solutions is also addressed. Moreover, in appropriate limits our results reduce to that of the sine-Gordon problem.