Title
An extension of the Kac ring model
Author
Publication type
article
Publication
London ,
Subject
Physics
Source (journal)
Journal of physics: A: mathematical and general. - London, 1968 - 2006
Volume/pages
36(2003) :46 , p. 11547-11559
ISSN
0305-4470
ISI
000187213600004
Carrier
E
Target language
English (eng)
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 becomes very large, the magnetization satisfies an autonomous equation as a function of time with exponentially fast relaxation to the equilibrium magnetization as determined by the microcanonical ensemble. This is proved 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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