Anomalous energy transport in the FPU-beta chain

Abstract

We consider the energy current correlation function for the FPU-beta lattice. For small non-linearity one can rely on kinetic theory. The issue reduces then to a spectral analysis of the linearized collision operator. We prove thereby that, on the basis of kinetic theory, the energy current correlations decay in time as t^(-3/5). It follows that the thermal conductivity is anomalous, increasing as N^(2/5) with the system size N.