Monitoring derivation of the quantum linear Boltzmann equation

TL;DR

This paper derives a quantum master equation for a particle in an ideal gas using a monitoring approach, capturing quantum effects non-perturbatively and unifying decoherence, dissipation, and classical limits.

Contribution

It introduces a non-perturbative Lindblad master equation for quantum gas dynamics derived via the monitoring approach, unifying quantum and classical descriptions.

Findings

The equation accounts for quantum scattering effects.

It reduces to classical linear Boltzmann equation for diagonal states.

The framework unifies decoherence and dissipation processes.

Abstract

We show how the effective equation of motion for a distinguished quantum particle in an ideal gas environment can be obtained by means of the monitoring approach introduced in [EPL 77, 50007 (2007)]. The resulting Lindblad master equation accounts for the quantum effects of the scattering dynamics in a non-perturbative fashion and it describes decoherence and dissipation in a unified framework. It incorporates various established equations as limiting cases and reduces to the classical linear Boltzmann equation once the state is diagonal in momentum.