The Moyal Equation for open quantum systems

Abstract

We generalize the Moyal equation, which describes the dynamics of quantum observables in phase space, to quantum systems coupled to a reservoir. It is shown that phase space observables become functionals of fluctuating noise forces introduced by the coupling to the reservoir. For Markovian reservoirs, the Moyal equation turns into a functional differential equation in which the reservoir's effect can be described by a single parameter.

arXiv comment7 pages

References in corpus (5)

• Decoherence, einselection, and the quantum origins of the classical
• Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics
• Symplectic evolution of Wigner functions in markovian open systems
• Exact positivity of the Wigner and P-functions of a Markovian open system
• Uniform cross phase modulation for nonclassical radiation pulses

Cited by in corpus (3)

• Simulation methods for open quantum many-body systems
• Negativity-Mutual Information conversion and coherence in two-coupled harmonic oscillators
• A Phase-space Formulation of the Belavkin-Kushner-Stratonovich Filtering Equation for Nonlinear Quantum Stochastic Systems