  We consider a heavy quantum particle with an internal degree of freedom
moving on the $d$-dimensional lattice $\bbZ^d$ (e.g., a heavy atom with
finitely many excited states). The particle is coupled to a thermal medium
(bath) consisting of free relativistic bosons through an interaction of
strength $\la$ linear in creation and annihilation operators. The mass of the
quantum particle is assumed to be of order $\la^{-2}$, and we assume that the
internal degree of freedom is coupled "effectively" to the thermal medium. We
prove that the motion of the quantum particle is diffusive in $d\geq 4$ and for
$\la$ small enough.
