Mathematical Physics Seminar (March 5th) – Prof. Benjamin Doyon (KCL) – Ballistic fluctuations, long-range correlations, and the diffusive scale in one-dimensional systems.

Evaluating fluctuations and correlations at large scales of space and time in quantum and classical many-body systems, in and out of equilibrium, is one of the most important problems of emergent physics. I will explain how basic hydrodynamic principles give access to exact results at the ballistic scale, solely from the data of the Euler-scale hydrodynamic equations of the many-body system. This includes the large-deviation theory for fluctuations of time-integrated currents, and the Euler scaling limits of multi-point correlation functions. A framework for this is “ballistic macroscopic fluctuation theory” (BMFT), an adaptation of the well-known macroscopic fluctuation theory that has been very successful for purely diffusive systems. In particular, we find from the BMFT that generically, long-range spatial correlations develop over time if the initial state of the many-body system is spatially inhomogeneous. I will explain how these long-range correlations affect in an important way the diffusive corrections to the hydrodynamic equation. I will give examples of integrable systems based on generalised hydrodynamics, where the new diffusive-scale equation becomes reversible, and present numerical confirmations of the results in the hard rod gas. This is based on works with G. Perfetto, T. Sasamoto and T. Yoshimura, and with F. Hübner, L. Biagetti, and J. De Nardis.