Professor Fabian Essler: Eigenstate Thermalization and Conservation Laws.

How do isolated many-particle quantum systems relax and ultimately give rise to the laws of Statistical Mechanics is a question that has exercised theoretical physicists since the early days of Quantum Theory. Much of our current understanding is based on a set of ideas known as the Eigenstate Thermalization Hypothesis (ETH). The latter provides statistical information of properties of energy eigenstates of “generic” systems, viewed through the lens of “few-body” physical observables. After reviewing the basics of eigenstates thermalization I turn to the question what takes the role of the ETH for integrable many-particle quantum systems. These are characterized by the existence of a macroscopic number of conservation laws, which lead to a much richer structure of energy eigenstates at finite energy densities.