An extension of the Kac ring model

Details An extension of the Kac ring model An extension of the Kac ring model

2003-07-18

arxiv.org/abs/cond-mat/0307460v3

Physics

Condensed Matter

Statistical Mechanics

15 pages, v2 -> v3: minor typographic correction

Scientific paper

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.

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