Theoretical Methods in the Non-Equilibrium Quantum Mechanics of Many Bodies

A toolbox of theoretical methods pertinent to the study of non-equilibrium many-body quantum mechanics is presented with an eye to specific applications in cold atoms systems and solids. We discuss the generalization from unitary quantum mechanics to the non-unitary framework of open quantum systems. Theoretical techniques include the Keldysh close-time-path integral and its associated correlation functions, the quantum kinetic equation, and numerical integration of equations of motion both unitary and non-unitary. We explore how the relaxation of the assumption of equilibrium yields a whole new array of sometimes counterintuitive effects. We treat such examples as the non-equilibrium enhancement of BCS superfluidity by driving, bistability and coherent population transfer in Feshbach coupled fermions, and the dynamic stimulation of quantum coherence in bosons confined to a lattice. These systems are considered with an eye to enhancing some useful quantum properties and making them available in wider parameter regimes