My research focuses on the study of quantum systems out of equilibrium, more specifically, the question whether a quantum system starting from an arbitrary initial state would evolve in such a way as to exhibit stationary behaviour at large times and whether this would be described by a thermal or some other statistical ensemble. Such a generalised thermal ensemble has been conjectured to apply to the case of one dimensional systems possessing an infinite number of local conserved quantities (integrable systems) and one of the main goals of my work is to investigate the validity of this conjecture.