Statistical mechanics teaches us how the equilibrium physics of many-body quantum systems emerges through the simple concept of thermal ensembles; the external world acts as a heat bath that fixes the temperature. For closed quantum systems, however, it is far from obvious how macroscopic equilibrium could emerge from the underlying microscopic dynamics. In particular, how do the mixed-state ensembles of statistical mechanics arise from the unitary time evolution of pure states? In the last two decades, such fundamental questions have been under intensive research and many aspects of the problem have been identified and understood. The notions of thermalization have even been generalized to integrable models, where ergodicity is broken due to the presence of an extensive set of conserved quantities, which have to be incorporated in the proper statistical ensembles. Although integrable systems are non-generic, it turns out that their special relaxation features survive on intermediate time scales even when the system is slightly perturbed away from integrability. Moreover, the presence of disorder can lead to a complete breakdown of ergodicity even in generic interacting systems. This phenomenon is known as many-body localization.
The dynamics of integrable systems does not only give rise to generalized thermal ensembles but can support persistent currents which do not decay with time, preventing thermalization and leading to the formation of nonequilibrium steady states (NESS). This requires the presence of macroscopic inhomogeneities in the initial state, which undergo ballistic broadening under the dynamics. In the project entitled “Quantum fronts and entanglement driven by inhomogeneities” we shall study some key features of the far-from-equilibrium dynamics of various integrable models, which is by far less understood than the relaxation from homogenous initial states. There are many fundamental questions unanswered which we shall address. First, can the form of the NESS for integrable systems be predicted by considering only some main characteristics of the nonequilibrium initial condition? Second, can one observe universal features in the relaxation towards the NESS, i.e. in the propagation of fronts induced by the inhomogeneity? Third, what are the main characteristics of entanglement generation in the front and what is the asymptotic entanglement structure in the NESS? Fourth, how robust are all the above features against perturbing the system away from integrability? Finally, how is the transport obstructed as a consequence of many-body localization? We will attack these questions using a number of different analytical (Bethe Ansatz, conformal field theory) and numerical (matrix product states) methods, for well-known spin chain models that are most relevant for current cold-atom experiments.