Quantum Fokker-Planck models: the Lindblad and Wigner approaches

TL;DR

This paper bridges the quantum dynamical semigroup and Wigner function approaches to quantum open systems, analyzing stationary states and long-term behavior in systems with harmonic confinement and perturbations.

Contribution

It introduces new results connecting two key approaches to quantum open systems, especially for systems with harmonic potentials and sub-quadratic perturbations.

Findings

Analysis of stationary states in quantum Fokker-Planck models

Long-time asymptotics for systems with harmonic confinement

Application to systems with large sub-quadratic perturbations

Abstract

In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck equation. Our new results apply to open quantum systems in a harmonic confinement potential, perturbed by a (large) sub-quadratic term.