The quench action approach to out-of-equilibrium quantum integrable models

In this PhD thesis quantum quenches to 1D quantum integrable models are studied by means of the quench action approach. Using the large-system-size scaling of overlaps between the initial state and Bethe states as basic input, this method gives an exact description in the thermodynamic limit of the time evolution and equilibrium of local observables after a quench. The method and its conditions are derived rigorously, after which implementations to interaction quenches from the BEC state of 1D free bosons to the Lieb-Liniger model and from the Néel state to the spin-1/2 XXZ chain are discussed in full detail. In both cases the root densities of the stationary state are determined via generalized thermodynamic Bethe Ansatz equations and solved analytically. For the Néel quench this is supplemented with a comparison to the prediction of a generalized Gibbs ensemble based on all local conserved charges. A surprising discrepancy between the predictions of the two methods is found, whereas the quench action result is shown to be consistent with numerical results. Furthermore, the quench action approach is employed to study instantaneous Bragg pulses in the Tonks-Girardeau gas and using a Fermi-Bose mapping pulses in a harmonic trap are also considered. Our results show a clear separation of timescales between rapid and trap-insensitive relaxation immediately after the pulse, followed by slow in-trap periodic behavior.