(MA3) In this Major Activity, we go beyond equilibrium properties of quantum many-body systems and investigate their dynamical evolution. Theoretically, nonequilibrium quantum dynamics is difficult because standard fieldtheoretic many-body techniques apply only to systems in equilibrium, where temperature is a well-defined concept. Quantum dynamics are notoriously difficult to simulate, even for small multiparticle systems. We hope to get a glimpse at the behavior of real material systems, but even an understanding of the dynamics of simple entangled systems would be a landmark accomplishment. This direction is closely related to the development, application, and verification of quantum information hardware because a quantum processor is necessarily operating out-of-equilibrium.

We will study shortterm quench dynamics through the propagation of entanglement, longtime nonequilibrum dynamics as it relates to thermalization, and investigate dynamics in stochastic gauge fields and quantum systems with SU(N) symmetry. The manybody interacting systems we will use in this MA include cold atomic and ionic systems, as well as superconducting qubits with more than 30 elements. The exploration of multiple physical platforms will help to establish whether there is universal dynamical behavior.