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Statistical Mechanics of Lamé Solitons

Ioana Bena·Avinash Khare·Avadh Saxena
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Abstract

We study the exact statistical mechanics of Lamé solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schrödinger equation with the periodic Lamé 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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Ioana Bena, Avinash Khare, Avadh Saxena. 2006-05-09. Statistical Mechanics of Lamé Solitons. https://doi.org/10.1088/0031-8949%2F73%2F6%2F005

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