Anomalous energy transport in the FPU–β chain

We consider the energy current correlation function for the FPU-β 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 with the system size N .