Statistical mechanics of the double-quadratic chain: Exact results and ideal-gas phenomenology for nonreflectionless solitary waves

The ideal-gas phenomenology of Currie and co-workers is extended to systems which bear solitary-wave excitations that are nontransparent to small oscillations. This extension enlarges the class of nonlinear systems which may be viewed at low temperatures as ideal gases of kinks and phonons. The authors treat the double-quadratic chain in detail, finding that the analysis can be carried quite far for this simple example system.