Abstract

In equilibrium, the concept of universality has been largely exploited to understand phase transitions and their collective behavior. However, much less is known about universal properties in the far-from equilibrium dynamics of strongly interacting quantum matter. In this talk, we will discuss some universal aspects of non-equilibrium quantum dynamics focussing on transport. The simplest approach to the problem is to posit a dichotomy between ergodic and non-ergodic dynamics. In the former case, fast relaxation to a local equilibrium is followed by slow diffusion of globally conserved quantities according to the laws of hydrodynamics. By contrast, transport can be absent in systems with a large number of emergent local conservation laws, as exemplified by many-body localization in strongly disordered quantum systems. Recent investigations, however, suggest considerable refinements for this classification. In this talk, we will discuss that in systems, which conserve the dipole moment of an associated global charge, transport becomes subdiffusive. Such dipole conserving systems are relevant for fracton phases of quantum matter, that are characterized by excitations with restricted mobility. We explain these findings by analytically constructing a general hydrodynamic model, yielding an accurate description of the scaling form of charge correlation functions. We will furthermore discuss experimentally relevant signatures of such higher-moment conserving systems.