From interacting particles to equilibrium statistical ensembles

We argue that a particle language provides a conceptually simple framework for the description of anomalous equilibration in isolated quantum systems. We address this paradigm in the context of integrable models, which are those where particles scatter completely elastically and are stable against decay. In particular, we demonstrate that a complete description of equilibrium ensembles for interacting integrable models requires a formulation built from the mode occupation numbers of the underlying particle content, mirroring the case of noninteracting particles. This yields an intuitive physical interpretation of generalized Gibbs ensembles, and reconciles them with the microcanonical ensemble. We explain how previous attempts to identify an appropriate ensemble overlooked an essential piece of information, and provide explicit examples in the context of quantum quenches.