The Equations of Generalised Hydrodynamics and Their Unusual Diffusive Corrections - Lecture 1

In this lecture from the Harvard CMSA program on Classical, quantum, and probabilistic integrable systems, Professor Benjamin Doyon from King's College London explores the hydrodynamics of one-dimensional many-body integrable models. Discover the equations of generalized hydrodynamics at the Euler scale, which depend only on the asymptotic state content and two-body scattering shift of the model. Learn about their properties including Hamiltonian structure, exact solutions, and absence of shocks. Examine why integrable models, as "linearly degenerate systems," don't display the superdiffusion typical in generic one-dimensional models with state-dependent currents. Understand how diffusive corrections to Euler equations aren't given by a standard derivative expansion but are instead governed by long-range correlations from Euler-scale fluctuation theory. Follow the arguments supporting the conjecture that integrable systems show no emergent stochasticity at all scales of hydrodynamics once long-range correlations are accounted for.