Semiclassical Ehrenfest paths in open quantum systems

TL;DR

This paper develops a phase-space approach to analyze semiclassical Ehrenfest trajectories in open quantum systems, explicitly deriving the Fokker-Planck equation for Gaussian mixtures and interpreting classical emergence.

Contribution

It introduces a phase-space framework that explicitly separates coherent and irreversible effects in open quantum dynamics, enhancing understanding of classical trajectory emergence.

Findings

Derived explicit Fokker-Planck equation for Gaussian mixture evolution.

Embedded generalized Ehrenfest theorem into phase-space to analyze observable expectations.

Provided a transparent interpretation of classical trajectories in open quantum systems.

Abstract

We study the semiclassical Ehrenfest trajectories in open quantum systems. We first derive in explicit form the Fokker-Planck equation that governs the time evolution of the mixing measure for a Gaussian mixture. Then, we embed the generalized Ehrenfest theorem recently obtained for open quantum systems into this phase-space picture to study the time evolution of the expectations of observable with respect to the Gaussian mixture. We show how the coherent and irreversible contributions are microscopically separated. Our work provides a transparent phase-space interpretation of the emergence of classical trajectories in open quantum dynamics.