Diffusive behavior from a quantum master equation

TL;DR

This paper demonstrates that a broad class of translation invariant quantum Markov processes exhibit diffusive behavior in the long-term, extending classical central limit theorems to quantum systems with scattering and relaxation dynamics.

Contribution

It introduces a general quantum Markov evolution model with local scattering and proves diffusion in the long-time limit, generalizing classical results to quantum particles.

Findings

Quantum Markov evolutions lead to diffusion over time.

Long-term momentum relaxation occurs exponentially fast.

Results extend classical diffusion theorems to quantum systems.

Abstract

We study a general class of translation invariant quantum Markov evolutions for a particle on $\bbZ^d$. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and exponentially fast relaxation of the momentum distribution. It is shown that the particle position diffuses in the long time limit. This generalizes standard results about central limit theorems for classical (non-quantum) Markov processes.