Distribution functions and excitation spectra of Toda systems at intermediate temperatures

The thermodynamic functions, the distribution of stochastic forces and energy, and the spectra of nonlinear excitations of 1D Toda systems embedded into a heat bath are studied. In a transition region of temperature, where the specific heat at constant length is about 34kBT, the systems show very specific properties that can be attributed to the interaction between solitary waves. A first one is the energy localisation at special sites in non-uniform Toda systems corresponding to multiple elastic collisions. Furthermore, we show that a finite-size Toda ring with weak thermal coupling develops in this temperature range a broadband coloured noise spectrum with an 1/f tail at low frequencies.