Kubo-Martin-Schwinger states of classical dynamical systems with infinite phase space

F. Rocca, M. Sirugue, D. Testard

F. Rocca, M. Sirugue, D. Testard

Zied Ammari, Antsa Ratsimanetrimanana

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.

Oleksandr Gamayun, Miłosz Panfil, Felipe Taha Sant’Ana

In this work we study the Kubo-Martin-Schwinger (KMS) relation in the Yang-Gaudin model of an interacting mobile impurity. We use the integrability of the model to compute the dynamic injection and ejection Green's functions at finite temperatures. We show that due to separability of the Hilbert space with an impurity, the ejection Green's functions in a canonical ensemble cannot be reduced to a single expectation value as per microcanonical picture. Instead, it involves a thermal average over contributions from different subspaces of the Hilbert space which, due to the integrability, are resolved using the so-called spin rapidity. It is then natural to consider the injection and ejection Green's functions within each subspace. By means of reformulating the original KMS condition as a Riemann-Hilbert problem, we analytically demonstrate that such Green's functions obey a refined analogous relation, which is finally corroborated by numerical evaluation.

Takehisa Fujita and Naohiro Kanda, Taku Matsui

We consider equilibrium states of weakly coupled anharmonic quantum oscillators on Z. We consider the Resolvent CCR Algebra introduced by D.Buchholtz and H.Grundling, and we show that the infinite volume limit of equilibrium states satisfies the KMS (Kubo-Martin-Schwinger) condition with good regularity(= locally Fock representation). Uniqueness of the KMS states is proven as well.

Natig M. Atakishiyev, S. M. Chumakov, Ana Leonor Rivera +1 more