Thermalisation and many-body localisation in ultracold quantum matter

In this thesis we investigate the aspects of many-body localisation (MBL) in the Ising and XY-model at infinite temperature and conclude that an MBL phase exists in both models. Additionally, we transform a non-hermitian PT-symmetric Hamiltonian into a hermitian MBL Hamiltonian. Furthermore, we explore a PT-symmetric Aubry-Andre model with quasi-disorder that exhibits a large PT-unbroken regime with a robust Anderson localised sub-regime. Lastly, we study the momentum behaviour of interacting quantum gases which are subject to periodic driving by simulating two bosons in a shaken box. We find that the behaviour of the momentum tail is dependent on the interaction.