Diffusion of a massive quantum particle coupled to a quasi-free thermal medium

TL;DR

This paper proves that a heavy quantum particle with internal states exhibits diffusive motion when coupled to a thermal medium, in dimensions four and higher, under weak coupling conditions.

Contribution

It demonstrates diffusive behavior of a quantum particle with internal degrees of freedom in high dimensions, extending understanding of quantum diffusion in many-body systems.

Findings

Quantum particle exhibits diffusive motion in dimensions d≥4.

Diffusion occurs under weak coupling conditions.

Results apply to particles with internal degrees of freedom.

Abstract

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.