**Exploring the hydrodynamic limit of many-body quantum systems**

Andy Lucas

The emergence of hydrodynamics in complicated microscopic many-body models has been a problem of interest in physics for more than a century. In this talk, I will describe two of the diverse lessons that the classical theory of hydrodynamics can teach us about interacting quantum systems. Firstly, I will describe the electrical and thermal conductivity of a fluid of electrons in a metal. Hydrodynamic effects can lead to parametric violations of textbook results such as the Wiedemann-Franz law. I will provide possible hydrodynamic origins for some puzzling transport mysteries in solid-state physics. Secondly, I will derive the constraints relating hydrodynamic phenomena to the spreading of quantum information and chaos. By studying exotic quantum systems, including those holographically dual to a black hole, we find a number of non-trivial theories where bounds relating quantum chaos and classical diffusion are saturated. This provides simple experimental constraints on quantum chaos, a theory whose predictions have otherwise proven difficult to measure.