Exploring aspects of nonequilibrium physics with quantum impurity problems
Doctor of Philosophy
Traditionally the study of quantum mechanical ensembles was focused on the exploration of their equilibrium properties: the program has consisted of the classification of the quantum mechanical states of matter, and the identification of the striking phase transitions between them. On the other hand, questions about the out of equilibrium properties of quantum ensembles have largely remained academic until fairly recently. Particularly, the rapid technological progress in the field of atomic physics has enabled experimental demonstrations of nontrivial out of equilibrium phenomena which moreover are describable in terms of relatively simple theoretical models with a few parameters. Thus the time is ripe for a theoretical exploration of nonequilibrium physics. To this end, quantum impurity models offer a natural and simple starting point for studying nonequilibrium phenomena in the context of ultracold atoms, and pave the way toward the study of more complicated systems. I will discuss how the impurity-bath model offers a clean, simple realization of rich phenomenology including the dynamics of polaron formation as well as the orthogonality catastrophe, and can be engineered using dilute mixtures of cold atomic gases. Moreover I will demonstrate how impurity models are also embedded in the more complicated physics of the response of a one-dimensional system to an external perturbation, or a sudden local parameter change. Lastly, I will describe the approach to equilibrium of a more complicated system, the one dimensional Bose gas, following a sudden parameter change, and discuss some of the important questions which arise in this connection: does a quantum mechanical system thermalize? What is the appropriate asymptotic description of a nonequilibrium state? Does such a system retain a memory of its initial state?
Nonequilbrium physics; Impurity models