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Title:
The hydrodynamics of many-body integrable systems
Speaker:
Abstract:
Hydrodynamics is a powerful theory for the emergent behaviours at large scales of space-time inmany-body systems. The theory says that only few degrees of freedom are sufficient in order todescribe what is observed at such scales, and it provides equations for the dynamics of thesedegrees of freedom. Think of the simple water waves emerging from the motion and interaction of amyriad of water molecules. It is strongly based on the presence of microscopic conservation laws inthe many-body model, such as conservation of energy, momentum and mass. But the standardequations of hydrodynamics fail to describe one-dimensional integrable systems, including theultracold atomic gases observed in experiments. Integrable systems admit an extensive number ofconservation laws, which must be taken into account in the emergent hydrodynamic theory. Recentlythis theory, dubbed ``generalised hydrodynamics”, has been developed. In this talk, I will reviewfundamental aspects of hydrodynamics and the main idea and equations of generalisedhydrodynamics. I will discuss recent cold-atom experiments that confirm the theory, and, as timepermits, some results that can be obtained with this formalism such as nonequilibrium steady states,asymptotic of correlation functions, a generalisation of the Luttinger liquid theory, and somemathematically rigorous aspects.
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