Benjamin Doyon – King’s College London
Wednesday, July 2nd , 2025
Zoom opens: 10:30AM DST
Seminar begins: 10:45AM DST
The anomalous hydrodynamic theory of integrable models at the diffusive order
The hydrodynamic theory for one-dimensional many-body integrable systems accounts for its extensive number of conserved quantities. At the Euler scale it is based on local relaxation to generalised Gibbs ensembles. Beyond the Euler scale, there are diffusive corrections, sub-leading in the inverse variation scale. Usually, within the framework of fluctuating hydrodynamics, a noise term is added representing the discarded ``fast’’ degrees of freedom, which leads to such effects. By Einstein’s relation, the hydrodynamic equation has second-derivative diffusive terms. But in one dimension, there are anomalies. I will explain how in integrable systems, the first sub-leading corrections are controlled, via a cumulant expansion, by long-range correlations that naturally appear out of equilibrium. The hydrodynamics is a coupled system of equations for average densities and their two-point correlations, without second-derivative terms. At the root of this is the fact that the fluctuating hydrodynamics is of a very special form: currents are not affected by any hydrodynamic noise, and the absence of shock production at the Euler scale guarantees that nonlinearities are tamed. I will argue that at all orders in the hydrodynamic expansion, currents do not have noise: all fluctuations come from deterministic Euler transport of initial fluctuations. I will give the example of the hard rods, thus showing that the previously assumed diffusive-scale equation is incorrect, with good numerical evidence.