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

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.