On the Long Time Behavior of the Quantum Fokker-Planck equation

2002/04/16 by Christof Sparber, C. Sparber, J. A. Carrillo +9 · 3 citations
Mathematics · Physics and Astronomy · #35K15 #46N55 #47N50 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #math-ph #math.AP #math.MP #msc:35K15 #msc:46N55 #msc:47N50

paper · pdf · doi:10.48550/arxiv.math-ph/0204032

arxiv created 2002/04/16 · openalex publication_date 2002/04/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the long time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type scattering operator, subject to confining potentials of harmonic oscillator type. We establish the conditions under which there exists a thermal equilibrium state and prove exponential decay towards it, using (classical) entropy-methods. Additionally, we give precise dispersion estimates in the cases were no equilibrium state exists.

Cited by

• Frozen Gaussian sampling algorithms for simulating Markovian open quantum systems in the semiclassical regime
• Quantum Stochastic Gradient Descent in its continuous-time limit based on the Wigner formulation of Open Quantum Systems
• A time-splitting Fourier pseudospectral method for the Wigner(-Poisson)-Fokker-Planck equations

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