Thermalization in quantum systems

Statistical mechanics underlies our understanding of the behaviour of large collections of particles and other types of degrees of freedom in almost every branch of science. Fundamental to the structure of statistical mechanics is the existence of a microcanonical ensemble (i.e. a completely isolated system). While such an ensemble can be defined for both classical and quantum systems, the precise description of the states it contains (i.e. microstates) is very different for the two classes of systems. As a consequence, the way in which each type of system evolves towards equilibrium starting from an initial state is also different. Further, the notion of equilibration of subsystems of an isolated system (aka thermalization), which is fundamental to the derivation of other ensembles starting from the microcanonical ensemble, is distinct for classical and quantum systems. In this talk, I will discuss this distinction and highlight the important role played by the Hilbert space structure of quantum mechanics in the process of thermalization. I will focus on a quantum phenomenon called Many-Body Localization, which has been extensively studied over the last decade and is responsible for the existence for the only known class of systems which do not generically thermalize. The role of randomness and quasiperiodicity in the physics of these systems will be discussed.