A Quantum Spin System with Random Interactions I

Proceedings Mathematical Sciences

Stephen Dias Barreto¹ 

[1] Stat. Math. Unit, Indian Statistical Institute, Bangalore 0 0, India$$

关键词: Spin;    system;    quasi-local;    random;    dynamics;    evolution;    independent;    Arveson;    KMS.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of evolution groups ${mathcal{T}_t(𝜔)}_{𝜔in𝛺}$ 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 $mathrm{Sp}(mathcal{T}(𝜔))$ of $mathcal{T}_t(𝜔)$. As a consequence, for any family of $(mathcal{T}(𝜔), 𝛽)$-KMS states {ρ(𝜔)}, the spectrum of the generator of the group of unitaries which implement $mathcal{T}(𝜔)$ in the GNS representation is also almost surely independent of 𝜔.

【 授权许可】

Unknown