A ballistic motion disrupted by quantum reflections

TL;DR

This paper models a quantum particle in a periodic potential interacting with a gas, showing that quantum reflections cause a transition from ballistic to diffusive motion in a specific limiting regime.

Contribution

It provides a homogenization theorem demonstrating how quantum reflections induce diffusive behavior in a quantum test particle under combined periodic potential and gas interactions.

Findings

Particle exhibits ballistic motion without both forces.

Quantum reflections cause diffusive behavior.

Diffusion arises near reciprocal lattice points.

Abstract

I study a Lindblad dynamics modeling a quantum test particle in a Dirac comb that collides with particles from a background gas. The main result is a homogenization theorem in an adiabatic limiting regime involving large initial momentum for the test particle. Over the time interval considered, the particle would exhibit essentially ballistic motion if either the singular periodic potential or the kicks from the gas were removed. However, the particle behaves diffusively when both sources of forcing are present. The conversion of the motion from ballistic to diffusive is generated by occasional quantum reflections that result when the test particle's momentum is driven through a collision near to an element of the half-spaced reciprocal lattice of the Dirac comb.