Phase space dynamics of overdamped quantum systems

TL;DR

This paper derives a Fokker-Planck type equation for the phase space dynamics of overdamped quantum systems, incorporating quantum fluctuations and valid across temperature regimes, validated against exact harmonic data.

Contribution

It introduces an exact path integral-based approach to describe quantum dissipative systems' phase space evolution, extending classical Fokker-Planck equations to quantum regimes.

Findings

Derived a Fokker-Planck type equation for quantum systems

Validated the approach against exact harmonic data

Demonstrated applicability across temperature ranges

Abstract

The phase space dynamics of dissipative quantum systems in strongly condensed phase is considered. Based on the exact path integral approach it is shown that the Wigner transform of the reduced density matrix obeys a time evolution equation of Fokker-Planck type valid from high down to very low temperatures. The effect of quantum fluctuations is discussed and the accuracy of these findings is tested against exact data for a harmonic system.