An extension of the Kac ring model
Statistical Mechanics
2007-05-23 v3
Abstract
We introduce a unitary dynamics for quantum spins which is an extension of a model introduced by Mark Kac to clarify the phenomenon of relaxation to equilibrium. When the number of spins gets very large, the magnetization satisfies an autonomous equation as function of time with exponentially fast relaxation to the equilibrium magnetization as determined by the microcanonical ensemble. This is proven as a law of large numbers with respect to a class of initial data. The corresponding Gibbs-von Neumann entropy is also computed and its monotonicity in time discussed.
Keywords
Cite
@article{arxiv.cond-mat/0307460,
title = {An extension of the Kac ring model},
author = {W. De Roeck and T. Jacobs and C. Maes and K. Netocny},
journal= {arXiv preprint arXiv:cond-mat/0307460},
year = {2007}
}
Comments
15 pages, v2 -> v3: minor typographic correction