High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph
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 mecha...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1363 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1363 |
| Access Level: | acceso abierto |
| Palabra clave: | Bose-Hubbard Golden-Thompson and Bogoliubov inequalities KMS property semiclassical analysis Wigner measures |
| Sumario: | 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. |
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