Statistical mechanics is a central pillar of modern science. At its core is the idea of ergodicity, which allows for a simple description of an interacting quantum system in terms of a few properties like energy density, without keeping track of the entire wavefunction. But what if a quantum system fails to equilibrate?
In this talk, I will describe the phenomenon of many-body localization, wherein interacting particles in disordered landscapes fail to be ergodic. I will discuss recent controversies and show that a theory based on rare resonanaces, as opposed to rare regions, explains emperical numerical and experimental observations. I will then turn to physical consequences of non-ergodicity in strongly driven systems and describe topological energy pumps. These pumps may form the basis for on-chip, magnetic-field free, non-reciprocal devices in superconducting qubit architectures.