2007/06/29 by Bassano Vacchini, Klaus Hornberger · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boltzmann equation #Brownian dynamics #Brownian motion #Classical limit #Classical mechanics #Fokker–Planck equation #Limit (mathematics) #Lindblad equation #Master equation #Mathematical analysis #Mathematical physics #Mathematics #Partial differential equation #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum master equation #Quantum mechanics #Quantum potential #Relaxation (psychology) #quant-ph
paper · pdf · doi:10.1140/epjst/e2007-00362-9
published as Eur. Phys. J. Special Topics 151, 59-72 (2007) · 15 pages; to appear in Eur. Phys. J. Special Topics (2007)
arxiv created 2007/06/29 · openalex publication_date 2007/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show how the quantum analog of the Fokker-Planck equation for describing Brownian motion can be obtained as the diffusive limit of the quantum linear Boltzmann equation. The latter describes the quantum dynamics of a tracer particle in a dilute, ideal gas by means of a translation-covariant master equation. We discuss the type of approximations required to obtain the generalized form of the Caldeira-Leggett master equation, along with their physical justification. Microscopic expressions for the diffusion and relaxation coefficients are obtained by analyzing the limiting form of the equation in both the Schroedinger and the Heisenberg picture.