%0 Journal Article
%T On the derivation of Fourier's law for coupled anharmonic oscillators
%A Jean Bricmont
%A Antti Kupiainen
%J Mathematics
%D 2006
%I arXiv
%X We study the Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice and subjected to a stochastic forcing mimicking heat baths of temperatures T_1 and T_2 on the hyperplanes at x_1=0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equlibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile.
%U http://arxiv.org/abs/math-ph/0605062v1