Quantum linear Boltzmann equation with finite intercollision time

TL;DR

This paper identifies issues in existing quantum linear Boltzmann equations related to momentum decoherence and introduces a new equation accounting for finite intercollision time to better model quantum gas dynamics.

Contribution

It proposes a novel quantum linear Boltzmann equation that incorporates finite intercollision time, addressing previous inconsistencies in modeling momentum decoherence.

Findings

Ideal collisions cause complete momentum decoherence

Finite intercollision time allows coherence to persist

New equation improves quantum gas modeling accuracy

Abstract

Inconsistencies are pointed out in the usual quantum versions of the classical linear Boltzmann equation constructed for a quantized test particle in a gas. These are related to the incorrect formal treatment of momentum decoherence. We prove that ideal collisions would result in complete momentum decoherence, the persistence of coherence is only due to the finite intercollision time. A corresponding novel quantum linear Boltzmann equation is proposed.