  We consider the dynamics of a field coupled to a harmonic crystal with $n$
components in dimension $d$, $d,n\ge 1$. The crystal and the dynamics are
translation-invariant with respect to the subgroup $\Z^d$ of $\R^d$. The
initial data is a random function with a finite mean density of energy which
also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition.
Moreover, initial correlation functions are translation-invariant with respect
to the discrete subgroup $\Z^d$. We study the distribution $\mu_t$ of the
solution at time $t\in\R$. The main result is the convergence of $\mu_t$ to a
Gaussian measure as $t\to\infty$, where $\mu_\infty$ is translation-invariant
with respect to the subgroup $\Z^d$.
