Transverse quantum decoherence of a fast particle in a gas

TL;DR

This paper investigates how a fast quantum particle loses coherence in a gas, deriving a generalized master equation that captures both longitudinal and transverse decoherence effects, with specific estimates for alpha particles.

Contribution

It introduces a generalized Caldeira-Leggett master equation incorporating angular cross section variations, highlighting the dominance of transverse decoherence in forward scattering regimes.

Findings

Transverse decoherence dominates when differential cross section is forward-focused.

Coherence lengths relate to momentum covariance and follow a Heisenberg-type uncertainty.

For alpha particles, the coherence region forms an elongated ellipsoid along the motion direction.

Abstract

The decoherence of a fast quantum particle in a gas is studied by applying the Kramers-Moyal expansion to the quantum master equation for the reduced density matrix of the particle. This expansion leads to a general form of the Caldeira-Leggett master equation accounting for the angular variation of the differential cross section. The equation describes the decoherence in both the longitudinal and transverse directions with respect to the particle motion. It is shown that, when the differential cross section is concentrated in the forward direction, transverse decoherence dominates. The coherence region off the diagonal of the density matrix is characterized by coherence lengths, which can be deduced, for Gaussian states, from the momentum covariance matrix according to a Heisenberg-type uncertainty relation. Finally, the longitudinal-to-transverse ratio of the coherence lengths is estimated for an alpha particle of a few MeVs. This ratio indicates that the coherence region looks like an ellipsoid elongated in the direction of motion.