Far from equilibrium phenomena in quantum systems – FAMOUS

This project deals with a very active subject of research: the description of quantum out of equilibrium dynamics. We plan to study questions of fundamental interest as well as problems of practical importance with numerical and analytic methods. Some of the problems we shall address are: 1) Instantaneous quantum quenches. We plan to understand the generic relaxation processes taking place after instantaneous quenches, i.e. a sudden change of a parameter in the Hamiltonian of an isolated quantum system. We shall study the destruction and build up of correlations, the approach to an asymptotic state and the nature of this state. Motivated by experiments in cold atoms we shall concentrate on quantum quenches across the superfluid - Mott insulator phase boundary in the Bose-Hubbard (BHM) and related models. We shall later test the obtained insights on other models and also study the effect of quenched disorder. 2) Quenching rate dependence. We plan to understand the quenching rate dependence of the off-equilibrium dynamics in classical and quantum systems slowly quenched across a second order phase transition. For the classical system we shall treat systems coupled to a thermal bath as usually encountered experimentally. In quantum systems we shall be mainly interested in closed cases relevant to experiments in cold atomic gases and to applications such as quantum adiabatic computation and quantum annealing. We will study the same quantum models as in (1), in particular the pure and disordered BHM. (3) Quantum dynamical fluctuations and driven quantum systems. We shall first extend to the quantum realm some ideas and techniques that have been very useful to understand the out of equilibrium relaxation of classical systems. In particular, we shall focus on symmetries such as time reversal and their consequences on fluctuations in and out of equilibrium. Afterwards we shall analyse the driven dynamics of quantum models on completely connected or Bethe lattices. These networks are interesting not only because they often provide reasonable approximations to finite dimensional systems (as known in the classical limit) but also due to their relevance to optimisation problems in computer science. (4) Influence of the environment on quantum dynamics. We plan to study the effect of a small coupling to the environment on the physical situations considered above in the case of fast and slow quenches. Furthermore, we wish to better characterize the notion of effective temperature that arises in the out of equilibrium dynamics of (mean-field) glassy systems.