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

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.

7 pages, 3 figures

References in corpus (2)

• Phase space dynamics of overdamped quantum systems
• Dynamics of Dissipative Quantum Systems--from Path Integrals to Master Equations

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• A "Square-root" Method for the Density Matrix and its Applications to Lindblad Operators
• Spin relaxation in phase space
• Two-particle Wigner functions in a one-dimensional Calogero-Sutherland potential