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...
Saved in:
Published in | Proceedings of the Indian Academy of Sciences. Mathematical sciences Vol. 110; no. 4; pp. 347 - 356 |
---|---|
Main Author | |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Springer Nature B.V
01.11.2000
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 |