Statistical Mechanics of Lamé Solitons

Details Statistical Mechanics of Lamé Solitons Statistical Mechanics of Lamé Solitons

2005-04-12

arxiv.org/abs/cond-mat/0504295v2

Physica Scripta 73, pp. 545-555 (2006)

Physics

Condensed Matter

Statistical Mechanics

29 pages, 5 figures, submitted to Physica Scripta

Scientific paper

10.1088/0031-8949/73/6/005

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.

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