• A quantum spin system with random interactions I

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      https://www.ias.ac.in/article/fulltext/pmsc/110/04/0347-0356

    • Keywords

       

      Spin; system; quasi-local; random; dynamics; evolution; independent; Arveson; KMS

    • 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.

    • Author Affiliations

       

      Stephen Dias Barreto1 2

      1. Indian Statistical Institute, Stat. Math. Unit, Bangalore - 560 059, India
      2. Department of Mathematics, Goa University, Sub P.O. Goa University, Taleigao Plateau, Goa - 403 206
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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