Numerical extraction of sound velocities of energy transfer based on solitons in Fermi-Pasta-Ulam chains

According to the Boltzmann distribution assumption of solitons, in thermal equilibrium, there is the most probable soliton whose average kinetic energy per site equals the thermal energy k(B)T. Based on the momentum excitation method, the soliton can be numerically excited in the static Fermi-Pasta-Ulam (FPU) chains. By associating the excited soliton with the corresponding most probable soliton, the temperature dependence of the velocity of solitons in thermal equilibrium can be numerically evaluated. The results agree very well with the temperature dependence of the sound velocity of energy transfer. This confirms that solitons are promising candidates for energy carriers in FPU chains. Moreover, the validity of the Boltzmann distribution assumption of solitons in FPU chains is also confirmed. This work sheds light on how to numerically (even experimentally) investigate solitons in thermal equilibrium.