Decoherence rates for Galilean covariant dynamics

TL;DR

This paper introduces a measure of decoherence for certain quantum states, derives spatial decoherence rates for specific Galilean covariant dynamics, and analyzes their convergence to classical probability distributions.

Contribution

It defines a decoherence measure for Gaussian states, characterizes relaxation to Gaussian states, and establishes convergence of quantum Wigner functions to classical distributions.

Findings

Decoherence measure aligns with Morikawa's index for Gaussian states.

Derived explicit spatial decoherence rates for three classes of Galilean covariant semigroups.

Proved convergence of quantum Wigner functions to classical probability distributions.

Abstract

We introduce a measure of decoherence for a class of density operators. For Gaussian density operators in dimension one it coincides with an index used by Morikawa (1990). Spatial decoherence rates are derived for three large classes of the Galilean covariant quantum semigroups introduced by Holevo. We also characterize the relaxation to a Gaussian state for these dynamics and give a theorem for the convergence of the Wigner function to the probability distribution of the classical analog of the process.