Localization for random coupled harmonic oscillators on ${\mathbb{Z}}^d$

Abstract

In this paper we consider the localization properties of coupled harmonic oscillators in random media. Each of these oscillators is restricted to the lattice ${\mathbb{Z}}^d$. We show that for most states and an arbitrary choice of the random media, the long time localization for the coupled system holds in a time scale larger than the polynomial one.

17 pages, comments welcome