Finite-Temperature Excitations of the Classical Toda Chain

The finite-temperature excitation spectrum of the classical Toda lattice is obtained by numerical solution of the Bethe Ansatz. Bethe-Ansatz thermodynamics agrees exactly with known transfer-integral results. A soliton-phonon phenomenology is developed and its validity assessed with the Bethe-Ansatz spectrum as an exact standard. The phenomenology's intrinsic limitations become evident in a transition region, where a distinction between phonon and (nontopological) soliton is impossible.