02/04/2025, 17:00 — 18:00 — Online
Guido Mazzuca, Tulane University, USA
Generalized Hydrodynamics for the Volterra lattice
While the mathematical foundations of Generalized Hydrodynamics (GHD) are still incomplete, the theory has proven to be a powerful tool for obtaining accurate approximations of correlation functions in various integrable models. Notably, H. Spohn applied GHD to compute the correlation function of the Toda lattice. In this talk, we focus on the Volterra lattice, another integrable system. We introduce its Generalized Gibbs Ensemble (GGE) and establish a connection with the Anti-symmetric β-ensemble, a well-known random matrix model. This link enables us to explicitly determine the density of states for the Volterra lattice in terms of the corresponding quantity in the random matrix model. Using this result, we apply GHD to derive a linear approximation of the correlation function for the Volterra lattice. This talk is based on the following paper: G. M., Generalized Hydrodynamics for the Volterra Lattice: Ballistic and Nonballistic Behavior of Correlation Functions. J. Phys. A: Math. Theor. DOI: 10.1088/1751-8121/ad742b
