Scaling approach to quantum non-equilibrium dynamics of many-body systems

Understanding non-equilibrium quantum dynamics of many-body systems is one of the most challenging problems in modern theoretical physics. While numerous approximate and exact solutions exist for systems in equilibrium, examples of non-equilibrium dynamics of many-body systems, which allow reliable theoretical analysis, are few and far between. In this paper we discuss a broad class of time-dependent interacting systems subject to external linear and parabolic potentials, for which the many-body Schr\"{o}dinger equation can be solved using a scaling transformation. We demonstrate that scaling solutions exist for both local and nonlocal interactions and derive appropriate self-consistency equations. We apply this approach to several specific experimentally relevant examples of interacting bosons in one and two dimensions. As an intriguing result we find that weakly and strongly interacting Bose-gases expanding from a parabolic trap can exhibit very similar dynamics.