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Title
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An extension of the Kac ring model
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Author
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Abstract
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| 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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Language
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English
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Source (journal)
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Journal of physics: A: mathematical and general. - London, 1968 - 2006
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Publication
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London
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2003
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ISSN
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0305-4470
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Volume/pages
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36
:46
(2003)
, p. 11547-11559
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ISI
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000187213600004
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