Diffusion for a quantum particle coupled to phonons in $d\geq 3$

TL;DR

This paper proves diffusion behavior for a quantum particle interacting with a bosonic field in three or more dimensions, using a fully Hamiltonian model with initial thermal randomness, extending previous results by removing restrictive assumptions.

Contribution

It establishes diffusion for a quantum particle coupled to bosons in higher dimensions without restrictive assumptions, advancing the theoretical understanding of quantum diffusion.

Findings

Diffusion proven for quantum particles in $d ext{ } extgreater= 3$

Model is fully Hamiltonian with thermal initial states

Extends previous work by removing restrictive assumptions

Abstract

We prove diffusion for a quantum particle coupled to a field of bosons (phonons or photons). The importance of this result lies in the fact that our model is fully Hamiltonian and randomness enters only via the initial (thermal) state of the bosons. This model is closely related to the one considered in [De Roeck, Fr\"ohlich 2011], but various restrictive assumptions of the latter have been eliminated. In particular, depending on the dispersion relation of the bosons, the present result holds in dimension $d \geq 3$.