The Kubo–Martin–Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and Verboven, proposed an analogue to the KMS condition for infinite classical mechanical systems and highlighted its relationship with the Kirkwood–Salzburg equations and with the Gibbs equilibrium measures. In this paper, we prove that in a certain limiting regime of high temperature the classical KMS condition can be derived from the quantum condition in the simple case of the Bose–Hubbard dynamical system on a finite graph. The main ingredients of the proof are Golden–Thompson inequality, Bogoliubov inequality and semiclassical analysis.

中文翻译：

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KMS 边界条件的高温收敛：有限图上的 Bose-Hubbard 模型

Kubo-Martin-Schwinger (KMS) 条件是量子统计力学中广泛研究的基本性质，它表征了量子系统的热平衡状态。在 70 年代，Gallavotti 和 Verboven 提出了无限经典机械系统的 KMS 条件的类似物，并强调了它与 Kirkwood-Salzburg 方程和 Gibbs 平衡测量的关系。在本文中，我们证明了在一定的高温极限状态下，经典的 KMS 条件可以从有限图上 Bose-Hubbard 动力系统的简单情况下的量子条件推导出来。证明的主要成分是 Golden-Thompson 不等式、Bogoliubov 不等式和半经典分析。