On the derivation of Fourier's law for coupled anharmonic oscillators
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
69 pages
69 pages