On the convergence to statistical equilibrium for harmonic crystals

We consider the dynamics of a harmonic crystal in d dimensions with n components, d,n arbitrary, d,ngreater than or equal to1, and study the distribution mu(t) of the solution at time t is an element of R. The initial measure mu(0) has a translation-invariant correlation matrix, zero mean, and finite mean energy density. It also satisfies a Rosenblatt-resp. Ibragimov-Linnik type mixing condition. The main result is the convergence of mu(t) to a Gaussian measure as t-->infinity. The proof is based on the long time asymptotics of the Green's function and on Bernstein's room-corridors'' method. (C) 2003 American Institute of Physics.