A quantum spin system with random interactions I |
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Authors: | Stephen Dias Barreto |
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Affiliation: | (1) Indian Statistical Institute, Stat. Math. Unit, 560 059 Bangalore, India;(2) Department of Mathematics, Goa University, Sub P.O. Goa University, Taleigao Plateau, 403 206 Goa |
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Abstract: | 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. |
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Keywords: | Spin system quasi-local random dynamics evolution independent Arveson KMS |
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