Energy Carriers in the Fermi-Pasta-UlamβLattice: Solitons or Phonons?

Abstract

We investigate anomalous energy transport processes in the Fermi-Pasta-Ulam $\beta${} lattice, in particular, the maximum sound velocity of the relevant weakly damped energy carriers. That velocity is numerically resolved by measuring the propagating fronts of the correlation functions of energy-momentum fluctuations at different times. We use fixed boundary conditions and stochastic heat baths. The numerical results are compared with the theoretical predictions of the sound velocities for solitons and effective (renormalized) phonons, respectively. Excellent agreement has been found for the prediction of effective long wavelength phonons, giving strong evidence that the energy carriers should be effective phonons rather than solitons.