# A quantum Boltzmann equation for intrinsic decoherence in a dilute gas

## TL;DR

This paper derives a quantum Boltzmann equation to describe how weak long-range coherence in a dilute quantum gas decays due to collisions, linking decoherence to the classical Boltzmann framework.

## Contribution

It provides a detailed quantum mechanical derivation of the Boltzmann equation accounting for intrinsic decoherence effects in dilute gases.

## Key findings

- Decay rate of long-range coherence is related to the Boltzmann loss term.
- Collisions suppress quantum coherence in dilute gases.
- Conditions under which quantum gases obey Boltzmann dynamics are identified.

## Abstract

We use a careful treatment of time-dependent wave-mechanical scattering to determine the conditions under which a dilute, non-degenerate quantum gas can obey a Boltzmann equation. If the gas possesses weak long-range coherence, such as may occur when a gas is quantum mechanically throttled by tunnelling through a barrier, collisions within the gas will suppress this long range coherence. We calculate its decay rate and find it to be related to the Boltzmann equation's loss term.