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Multiple Time Analyticity of a Quantum Statistical State Satisfying the KMS Boundary Condition

1968; Kyoto University; Volume: 4; Issue: 2 Linguagem: Inglês

10.2977/prims/1195194880

1663-4926

Huzihiro Araki,

Statistical Mechanics and Entropy

A multiple time expectation ^(ABjC^)---^^)) in a stationary state <p satisfying the KMS boundary condition is studied.It is found to be holomorphic in a simplicial tube domain 0<Im ^<Im jf 2 <---<Im t n <fi, continuous and bounded in the closure and the expectation of cyclic permutation of operators are obtained as its values on various distinguished boundaries of the domain.§ 1. IntroductionThe Gibbs ensemble in quantum statistical mechanics satisfies the Kubo-Martin-Schwinger (KMS) boundary condition and a general property of such a state has been discussed by several authors [1], [2], [3], [4].In this paper we shall study the analyticity of (p(AB l (t^"-B n (t^i) in t^--t H .The main theorem is Theorem 3. 1 and 3. 3 of section 3.In passing, it is shown by the analytic!ty method that the center of the representing algebra is time translation invariant.It is also pointed out that the KMS boundary condition holds for the weak closure, which will be used in § 2. The KMS Boundary Condition and AnalyticityWe shall discuss an analyticity tube domain for single time expectation function in this section.We also give a proof that the center of the representative algebra is elementwise time translation invariant.