Interactions and Disorder in Novel Condensed Matter Systems

Despite almost a century of exploration, we continue to discover new systems where quantum mechanics, strong interactions and disorder combine in novel ways. These systems test the capabilities of our strongest theoretical tools. In this thesis I discuss work on three of these systems: bilayer graphene, disordered conductors and cold atom systems. In bilayer graphene I show that the large number of degenerate bands leads to a plethora of possible spontaneous symmetry breaking ground state. In disordered conductors I discuss how quantum interference can lead to arbitrarily long lived responses, so called memory eects. I also consider whether a novel spontaneous symmetry breaking state can be created in cold atomic gasses using nonequilibrium perturbations.