Statistical Mechanics of Lam\'e Solitons
Statistical Mechanics
2009-11-11 v2 Mathematical Physics
math.MP
Pattern Formation and Solitons
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.cond-mat/0504295,
title = {Statistical Mechanics of Lam\'e Solitons},
author = {Ioana Bena and Avinash Khare and Avadh Saxena},
journal= {arXiv preprint arXiv:cond-mat/0504295},
year = {2009}
}
Comments
29 pages, 5 figures, submitted to Physica Scripta