Master equation for quantum Brownian motion derived by stochastic methods

Abstract

The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz and Zhang, which was based on the direct computation of path integrals, or to that of Halliwell and Yu, based on the evolution of the Wigner function for a linear closed quantum system. We first show by using the influence functinal formalism that the reduced Wigner function for the open system coincides with a distribution function resulting from averaging both over the initial conditions and the stochastic source of a formal Langevin equation. The master equation for the reduced Wigner function can then be deduced as a Fokker-Planck equation obtained from the formal Langevin equation.

10 pages, RevTeX. To appear in the proceedings of the 5th Peyresq meeting

References in corpus (6)

• Stochastic semiclassical gravity
• Stochastic semiclassical fluctuations in Minkowski spacetime
• Hydrodynamic transport functions from quantum kinetic theory
• Spacelike Fluctuations of the Stress Tensor for de Sitter Vacuum
• Mode decomposition and renormalization in semiclassical gravity
• Semiclassical Cosmological Perturbations Generated during Inflation

Cited by in corpus (7)

• Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
• Thermalization in Quenched Open Quantum Cosmology
• Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
• NonMarkovian Abraham--Lorentz--Dirac Equation: Radiation Reaction without Pathology
• Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation-Dissipation Inequalities
• Quantum Thermodynamic Uncertainties in Nonequilibrium Systems from Robertson-Schrödinger Relations
• System plus reservoir approach to quantum Brownian motion of a rod-like particle