Statistical mechanics of Lamé solitons

Ioana Bena, Avinash Khare, Avadh Saxena
2006 Physica Scripta  
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
more » ... hermodynamics" of the soliton lattice solutions is also addressed. Moreover, in appropriate limits our results reduce to that of the sine-Gordon problem.
doi:10.1088/0031-8949/73/6/005 fatcat:j6y7xa42brhh7lfqx4a3xjxrty