Diffusion of a Massive Quantum Particle Coupled to a Quasi-Free Thermal Medium

We consider a heavy quantum particle with an internal degree of freedom moving on the d-dimensional lattice Z(d) (e.g., a heavy atom with finitely many internal states). The particle is coupled to a thermal medium (bath) consisting of free relativistic bosons (photons or Goldstone modes) through an interaction of strength lambda linear in creation and annihilation operators. The mass of the quantum particle is assumed to be of order lambda(-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 >= 4 and for lambda small enough.