Freezing of the optical--branch energy in a diatomic FPU chain

Alberto Mario Maiocchi

doi:10.1007/s00220-019-03381-z

paper

Freezing of the optical--branch energy in a diatomic FPU chain

arXiv:1808.09359 · doi:10.1007/s00220-019-03381-z

Abstract

We study the exchange of energy between the modes of the optical branch and those of the acoustic one in a diatomic chain of particles, with masses $m_{1}$ and $m_{2}$ . We prove that, at small temperature and provided $m_{1} ≫ m_{2}$ , for the majority of the initial data the energy of each branch is approximately constant for times of order $β^{S /2}$ , where $S = ⌊ m_{1} / m_{2} /2 ⌋$ and $β$ is the inverse temperature. The result is uniform in the thermodynamic limit.