Adding decoherence to the Wigner equation

TL;DR

This paper derives a generalized Wigner equation incorporating decoherence effects from single-collision mechanisms, unifying known models and analyzing their impact on macroscopic dynamics and long-term behavior.

Contribution

It introduces a new, general decoherence term into the Wigner equation, encompassing existing models like the Wigner-Fokker-Planck equation, and studies its effects on macroscopic and asymptotic properties.

Findings

The generalized Wigner equation includes well-known decoherence models as special cases.

Decoherence influences the dynamics of density, current, and energy in quantum systems.

Adding a Caldeira-Legget friction term yields physically expected long-time asymptotics.

Abstract

Starting from the detailed description of the single-collision decoherence mechanism proposed by Adami, Hauray and Negulescu, we derive a Wigner equation endowed with a decoherence term of a fairly general form. This equation is shown to contain well known decoherence models, such as the Wigner-Fokker-Planck equation, as particular cases. The effect of the decoherence mechanism on the dynamics of the macroscopic moments (density, current, energy) is illustrated by deriving the corresponding set of balance laws. The issue of large-time asymptotics of our model is addressed in the particular, although physically relevant, case of gaussian solutions. It is shown that the addition of a Caldeira-Legget friction term provides the asymptotic behaviour that one expects on the basis of physical considerations.