Journal Club Benjamin Doyon (King's College London)
Join here (you need Microsoft Teams). Typical systems of many particles in strong interaction have extremely complex behaviours which are hard to study in detail. But when the system is very large, simplicity resurfaces: typically just a few degrees of freedom are relevant, which follow new, simple laws. Understanding what the emergent behaviours are from the underlying microscopic interactions is one of the foremost problems in modern science. A very powerful set of ideas and tools at our disposal is hydrodynamics. Although the Navier-Stokes and related equations have been studied for a very long time, we are now starting to uncover the full potential of the fundamental principles of hydrodynamics. In particular, in a recent breakthrough it was understood how to apply these principles to quantum and classical integrable models, where infinitely many conserved currents exist, giving ``generalised hydrodynamics”. I will overview the fundamental principles of hydrodynamics and their adaptation to integrable systems, with simple examples such as the quantum Lieb-Liniger model, the classical Toda model, and the soliton gases. I will discuss a recent cold-atom experiment that confirmed generalised hydrodynamics, and, if time permits, show some of the exact results that can be obtained with this formalism, such as exact nonequilibrium steady states and exact asymptotic of correlation functions at large space-time separations.