Ergodicity of quantum cellular automata

Autor(en): Richter, S
Werner, RF
Stichwörter: approach to equilibrium; cellular automata; interacting particle systems; oscillation norm; Physics; Physics, Mathematical; quantum spin systems
Erscheinungsdatum: 1996
Herausgeber: PLENUM PUBL CORP
Journal: JOURNAL OF STATISTICAL PHYSICS
Volumen: 82
Ausgabe: 3-4
Startseite: 963
Seitenende: 998
Zusammenfassung: 
We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analoges of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique invariant state. Intuitively, ergodicity obtains if the local transition operators exhibit sufficiently large disorder. The ergodicity criteria also imply bounds for the exponential decay of correlations in the unique invariant state. The main technical tool is a quantum version of oscillation norms, defined in the classical case as the sum over all sites of the variations of an observable with respect to local spin flips.
ISSN: 00224715
DOI: 10.1007/BF02179798

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