Bound-state effects on the statistical mechanics of solitons in double-sine-Gordon systems

The bound states of the spectrum of the small oscillations in the neighborhood of soliton solutions may give nontrivial contribution to the partition function when their frequencies tend to zero. We investigate the case of the double-sine-Gordon system, where the soliton solution degenerates into a pair of sine-Gordon kinks at infinite distance with a change of the symmetry of the potentials and a corresponding slowing down for the frequency of the bound state. The latter is found to be the restoring symmetry mode, and some suggestions for its treatment are given.