Non-equilibrium Dynamics and Random Matrices

I will review some aspects of many-body Anderson localization. Many-body localized systems have a type of integrable Hamiltonian, with an extensive set of operators that are localized in real-space that each commute with the Hamiltonian. The eigenstates of the Hamiltonian within the localized phase may exhibit symmetry-breaking long-range order (or topological order), even in low dimensions and at high "temperature", where such order can not occur at thermal equilibrium.