Quantum Matter Seminar

It is expected that a generic closed many-body system prepared in a well-behaved initial state will eventually thermalize, i.e. approach a Gibbs state. This property, while compatible with and even demanded by the physical intuition, is much stronger than ergodicity or mixing and is difficult to justify mathematically. Similarly, a generic many-body system subject to a periodic drive (a Floquet system) is expected to heat up and approach the state of maximal entropy. In this talk I will describe an infinite set of many-body Floquet systems of algebraic origin, both classical and quantum, for which thermalization of very general initial states can be studied analytically as well as numerically. In the classical case, these are many-body analogs of Arnold's cat map. Quantum models are obtained by quantizing the classical ones. In the classical case, one can show that a large class of initial states, including all Gibbs states of all uniformly differentiable local Hamiltonians, thermalize, provided a mild condition is satisfied (essentially, the absence of Many-Body Localization). In the quantum case, the results are similar but less complete, because the mechanism of thermalization is different. The talk is based on https://arxiv.org/abs/2601.00511 and https://arxiv.org/abs/2603.13631