Ali Zahra

Mardi 23 Septembre 2025, 14h00, salle E4.13b

Ali Zahra

Laboratoire de Physique et Chimie Théoriques, University of Lorraine, Nancy.

Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions

We study the symmetric Dyson exclusion process (SDEP)--a lattice gas with exclusion and long-range, Coulomb–type interactions that emerge both as the maximal-activity limit of the symmetric exclusion process and as a discrete version of Dyson's Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, we map the stochastic generator of the SDEP onto the spin-1/2 XX quantum chain, which in turn admits a free-fermion representation. At macroscopic scales we conjecture that the SDEP displays ballistic (Eulerian) scaling with a conservation law featuring a current that is a genuinely non-local functional of the density. This non-local one-component description is equivalent to a local two-components “complex Hopf’’ system for finite particle density. Closed evolution formulas allow us to solve the melting of single- and double-block initial states, producing limit shapes and arctic curves that agree with large-scale Monte-Carlo simulations. The model thus offers a tractable example of emergent non-local hydrodynamics driven by long-range interactions. Joint work with Jerome Dubail and Gunter Schutz [ arXiv:2508.09879 ]

Lien teams: https://teams.microsoft.com/l/meetup-join/19%3aac3d3339d1c740e0a3b81b94e49808c1%40thread.tacv2/1698658652943?context=%7b%22Tid%22%3a%22b8c19512-2aed-471d-a8d1-9b06e7da786a%22%2c%22Oid%22%3a%222ea0eb78-4abd-439c-8240-cc89774321a2%22%7d