Title: Prethermalization and quasi-conserved quantities in Many-Body quantum systems with time-dependent Hamiltonians
Abstract: Understanding thermalization, i.e. the relaxation of a physical system to thermal equilibrium, is a central problem in statistical
physics. It is now well established that the presence of non-trivial quasi-conserved quantities can significantly slow down this process, leading to long-lived quasi-stationary states known as prethermal states. The approach to such states is referred to as
prethermalization.
In many-body quantum systems, external driving provides a powerful mechanism to engineer and control prethermal states. In the absence of many-body localization, general
theoretical arguments predict that time-dependent perturbations ultimately drive the system toward a featureless infinite-temperature Gibbs state. However, both rigorous results and experiments show that, under fast periodic driving, fermionic quantum lattice
systems can exhibit exponentially long-lived prethermal regimes, largely independent of the regularity of the drive.
The situation becomes even richer for quasi-periodic driving, i.e., when the system is driven by a superposition of incommensurate frequencies. In this case, the regularity
of the driving plays a crucial role in determining the lifetime of the prethermal regime.
In this talk, I will review the problem and survey recent rigorous results, focusing in particular on the case of finitely differentiable drivings. In this setting, the
prethermal state persists for polynomially long times in the driving frequency. I will also explain how to determine the optimal exponents governing this behavior. The analysis combines techniques from Hamiltonian perturbation theory adapted to quantum lattice
systems, cluster expansions, and Lieb–Robinson bounds.
This is joint work with Beatrice Langella.