Dynamics and Equilibrium States of Infinite Systems of Lattice Bosons

Explore the mathematical dynamics of infinite systems of lattice bosons through this 33-minute conference talk. Discover how the dynamics of these systems with infinitely many degrees of freedom defines a group of automorphisms on a C∗–algebra introduced by Buchholz, which extends the resolvent algebra of local field operators. Learn about the derivation of Lieb–Robinson type propagation bounds for states with uniform bounds on moments of local particle number. Understand how these bounds demonstrate that the dynamics of local observables generates a strongly continuous unitary group in the GNS representation. Examine how accumulation points of finite-volume Gibbs states satisfy the KMS condition with respect to this group, establishing the existence of KMS states. The presentation covers joint research with Jonas Lampart and Marius Lemm, delivered during the thematic meeting "Emergent phenomena in many-body quantum systems" at the Centre International de Rencontres Mathématiques in Marseille, France.