Symmetries and quantum pumping

We explore the role of symmetries in quantum systems, which are driven out of equilibrium, for example, by laser pumping. The proposal investigates, on the one hand, systems with macroscopically many conservation laws. This includes integrable quantum systems (e.g., spin-chains) and models, where strong disorder leads to (many-body) localization. On the other hand, it studies symmetry-protected resonances manifest in towers of equidistant eigenstates in the energy spectrum. The guiding principle of the proposal is that weak driving can have a substantial effect if it pumps into a degree of freedom that is approximately protected by some symmetry or, equivalently, a conservation law. An everyday example is a greenhouse, which can be heated up to high temperatures by weak sunlight because the energy within the greenhouse is approximately conserved. The proposal employs this principle in different quantum setups and investigates when a weak driving can bring a system far from equilibrium, because of underlying approximate symmetries. The central aim of the proposed program is to connect theoretically fascinating idealized models to realistic experiments of driven quantum matter and thus pave the way for the observation of new phenomena, inaccessible to equilibrium states. A weak driving is used to revive exceptional features inherited from the symmetries even when these are only approximately realized, as is typically the case in nature and experiments. The proposal considers different setups and non-equilibrium protocols that stabilize nonequilibrium (steady) states with remarkable properties: integrability based heat- or spin pumps, many-body localization-based switches and exotic superconductivity in driven systems. While parts of the proposal explore new symmetry-based phenomena and their potential for technological applications, a complementary part develops efficient descriptions of driven quantum systems in the presence of symmetries and thus pushes the frontiers of non-equilibrium physics.