Solving quantum master equations in phase space by continued-fraction methods

TL;DR

This paper introduces continued-fraction methods adapted from classical techniques to solve quantum master equations in phase space, enabling analysis of nonlinear quantum systems with environmental interactions.

Contribution

It develops a novel continued-fraction approach for quantum master equations in phase space, extending classical methods to quantum systems with dissipation and fluctuations.

Findings

Successfully applied to quantum Brownian motion in periodic potentials

Enables analysis of nonlinear quantum systems with environmental effects

Provides a new computational tool for quantum phase space dynamics

Abstract

Inspired on the continued-fraction technique to solve the classical Fokker--Planck equation, we develop continued-fraction methods to solve quantum master equations in phase space (Wigner representation of the density matrix). The approach allows to study several classes of nonlinear quantum systems subjected to environmental effects (fluctuations and dissipation), with the only limitations that the starting master equations may have. We illustrate the method with the canonical problem of quantum Brownian motion in periodic potentials.