2001/07/02 by Bassano Vacchini, B. Vacchini
Computer Science · Mathematics · Physics and Astronomy · #Brownian motion #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Covariance #Differential equation #Dynamic structure factor #Fokker–Planck equation #Lindblad equation #Master equation #Mathematical physics #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum statistical mechanics #Statistical physics #Statistics #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.1386409
published as J. Math. Phys. 42 (2001) 4291-4312 · 18 pages, revtex, no figures, to appear in J. Math. Phys
arxiv created 2001/07/02 · openalex publication_date 2001/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A recently proposed master equation in the Lindblad form is studied with respect to covariance properties and existence of a stationary solution. The master equation describes the interaction of a test particle with a quantum fluid, the so-called Rayleigh gas, and is characterized by the appearance of a two-point correlation function known as the dynamic structure factor, which reflects symmetry and statistical mechanics properties of the fluid. In the case of a free gas, all relevant physical parameters such as fugacity, ratio between the masses, momentum transfer, and energy transfer are put into evidence, giving an exact expansion of the dynamic structure factor. The limit in which these quantities are small is then considered. In particular, in the Brownian limit a Fokker–Planck equation is obtained in which the corrections due to quantum statistics can be explicitly evaluated and are given in terms of the Bose function g0(z) and the Fermi function f0(z).