Title:

Nonequilibrium stronglycorrelated dynamics

We study nonequilibrium and stronglycorrelated dynamics in two contexts. We begin by analysing quantum manybody systems out of equilibrium through the lens of cold atomic impurities in Bose gases. Such highlyimbalanced mixtures provide a controlled arena for the study of interactions, dissipation, decoherence and transport in a manybody quantum environment. Specifically we investigate the oscillatory dynamics of a trapped and initially highlylocalised impurity interacting with a weaklyinteracting trapped quasi lowdimensional Bose gas. This relates to and goes beyond a recent experiment by the Inguscio group in Florence. We witness a delicate interplay between the selftrapping of the impurity and the inhomogeneity of the Bose gas, and describe the dissipation of the energy of the impurity through phononic excitations of the Bose gas. We then study the transport of a driven, periodicallytrapped impurity through a quasi onedimensional Bose gas. We show that placing the weaklyinteracting Bose gas in a separate periodic potential leads to a phononic excitation spectrum that closely mimics those in solid state systems. As a result we show that the impurityBose gas system exhibits phononinduced resonances in the impurity current that were predicted to occur in solids decades ago but never clearly observed. Following this, allowing the bosons to interact strongly, we predict the effect of different stronglycorrelated phases of the Bose gas on the motion of the impurity. We show that, by observing the impurity, properties of the excitation spectrum of the Bose gas, e.g., gap and bandwidth, may be inferred along with the filling of the bosonic lattice. In other words the impurity acts as a probe of its environment. To describe the dynamics of such a stronglycorrelated system we use the powerful and nearexact timeevolving block decimation (TEBD) method, which we describe in detail. The second part of this thesis then analyses, for the first time, the performance of this method when applied to simulate nonequilibrium classical stochastic processes. We study its efficacy for a wellunderstood model of transport, the totallyasymmetric exclusion process, and find it to be accurate. Next, motivated by the inefficiency of samplingbased numerical methods for high variance observables we adapt and apply TEBD to simulate a pathdependent observable whose variance increases exponentially with system size. Specifically we calculate the expected value of the exponential of the work done by a varying magnetic field on a onedimensional Ising model undergoing Glauber dynamics. We confirm using Jarzynski's equality that the TEBD method remains accurate and efficient. Therefore TEBD and related methods complement and challenge the usual Monte Carlobased simulators of nonequilibrium stochastic processes.
