A quantum spin system with random interactions I

We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of evolution groups {τt(ω)}ω∈/Ω of the spin system. The notion of ergodicity of a measure preserving group of automorphisms of the probability space Ω, is used to prove the almost...

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Bibliographic Details
Published inProceedings of the Indian Academy of Sciences. Mathematical sciences Vol. 110; no. 4; pp. 347 - 356
Main Author Barreto, Stephen Dias
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.11.2000
Subjects
Automorphisms
Spin glasses
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Summary:We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of evolution groups {τt(ω)}ω∈/Ω of the spin system. The notion of ergodicity of a measure preserving group of automorphisms of the probability space Ω, is used to prove the almost sure independence of the Arveson spectrum Sp(τ(ω)) of τt(ε). As a consequence, for any family of (τ(ω),β) — KMS states {ρ(ω)}, the spectrum of the generator of the group of unitaries which implement τ(ω) in the GNS representation is also almost surely independent of ω.
ISSN:0253-4142
0973-7685
DOI:10.1007/BF02829530