Extra QLunch: Zied Ammari

Speaker: Zied Ammari, Université de Rennes

Title: The Kubo-Martin-Schwinger condition for  Hamiltonian systems: Bose-Hubbard model

Abstract: The Kubo-Martin-Schwinger (KMS) condition is a fundamental property of statistical mechanics which characterize  the equilibrium of finite/infinite Quantum and Classical mechanical systems. The classical condition was introduced in the seventies by G.~Gallavotti and E.~Verboven as an alternative to the Dobrushin-Lanford-Ruelle (DLR) equation. In this talk, I will recall  this concept for the Bose-Hubbard model on finite graphs. Later, I will extend it to nonlinear Hamiltonian PDEs and speculate on its relevance. In particular, I will show that Gibbs measures are the unique KMS equilibrium states for such systems and  discuss some potential applications.