In recent years, a lot of attention has been devoted to non-equilibrium quantum dynamics and to the structure of dissipation in closed as well as open quantum systems. By today’s technology, it is now possible to study experimentally well-designed closed ultracold or nanoscale systems, and investigate fundamental processes such as thermalization, the formation of non-equilibrium steady states, or entanglement generation. This motivates theorists to reconsider many of the basic notions of quantum statistical physics. To give an example, it is now well understood that heat production in a closed quantum system is of statistical nature, even if the final state is pure.
Here we propose to study these fundamental issues in driven nano-systems and non-equilibrium models. In particular, we propose first to focus on the generic time evolution of the heat distribution, P_t(Q), and its dependence on the symmetries of the underlying Hamiltonians (universality classes). We believe that similar to other properties such as the universal level statistics, P_t(Q) displays a universal structure in certain limits which, however, may depend on the structure of avoided level crossings. A numerical and analytical determination of this universal distribution will be a major goal of the PhD student. As a continuation of this work, the PhD student shall explore the role of quantum geometry and topology, and the role of interactions.
This research will be carried out in close collaboration with Prof. Gergely Zaránd.
Excellent grades in most theoretical physics courses.