Wojciech De Roeck

Exponentially Slow Heating in Periodically Driven Many-Body Systems

We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that, for systems with local interactions, the energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including the decay of highly energetic excitations in cold atomic and solid-state systems.

Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems

We establish some general dynamical properties of quantum many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasiconserved extensive quantity

Stability and instability towards delocalization in many-body localization systems

{H}_{*}

Asymptotic Quantum Many-Body Localization from Thermal Disorder

, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well approximated by the evolution with the Hamiltonian

Quantum version of free-energy-irreversible-work relations

{H}_{*}

Theory of many-body localization in periodically driven systems

up to time

Scenario for delocalization in translation-invariant systems

{\ensuremath{\tau}}_{*}

Fluctuations of Quantum Currents and Unravelings of Master Equations

, which is exponentially large in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where

A rigorous theory of many-body prethermalization for periodically driven and closed quantum systems

{H}_{*}

LARGE DEVIATION GENERATING FUNCTION FOR CURRENTS IN THE PAULI-FIERZ MODEL

is ergodic, the driven system prethermalizes to a thermal state described by