Onset of Fokker-Planck dynamics within a closed finite spin system
Fachbereich Physik, Universität Osnabrück - Barbarastrasse 7, D-49069 Osnabrück, Germany, EU
Received: 14 November 2012
Accepted: 2 January 2013
Relaxation according to Fokker-Planck equations is a standard scenario in classical statistical mechanics. It is, however, not obvious how such a Fokker-Planck dynamics may emerge within a closed, finite quantum system. We present an analysis of a system comprising sixteen spins in which spatial inhomogeneities of the magnetization relax approximately in accord with a standard Fokker-Planck equation for a Brownian particle in a parabolic potential. While a single, specfic example is addressed in detail, arguments which indicate that the above findings may hold for a wider range of systems are given.
PACS: 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 05.30.-d – Quantum statistical mechanics / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
© EPLA, 2013