Abstract:
I will review the basic physical hypothesis on the microscopic dynamics of a quantum system which are made to justify its approximate treatment with the tools of statistical mechanics. In particular, I will focus on the modern treatment of the ergodic hypothesis, the Eigenstate Thermalisation Hypothesis (or ETH). The prominent failure mode in generic quantum systems is called Many-Body Localization (or MBL) and it is at the core of the current research on the foundations of statistical mechanics.