Abstract

This talk will review a number of integrability-based results on the dynamics of quantum spin chains and interacting atomic gases. In equilibrium, space- and time-dependent correlations will be reviewed, together with corresponding experimental observations. Integrability will also be used to describe the dynamics of (quasi)solitonic excitations and their scattering properties. For more generic out-of-equilibrium situations, a number of recent developments will be explained, including the Quench Action method for explicitly calculating the relaxation of observables after a quantum quench. The exact solution to the Néel-to-XXZ quench using the QA will be presented, together with recent results on the necessity to include quasilocal charges in the Generalized Gibbs Ensemble in order to properly describe post-quench steady-state properties.