MATHEMATICAL PHYSICS WEBINAR
RUTGERS UNIVERSITY
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Satya N. Majumdar – Laboratoire de Physique Theorique et Modeles Statistique (LPTMS)
Wednesday, February 5th , 10:45AM EST
Correlated Resetting Gas
I will first discuss the equilibrium properties of a gas of $N$ interacting particles on a line. This will include, for example, the log-gas in random matrix theory (RMT) and the Riesz gas which is a generalization of the log-gas. I will then discuss some examples of stationary point processes that are out of equilibrium. As a simple example, I will introduce a model of $N$ independent Brownian particles that are subjected to simultaneous stochastic resetting with rate $r$. The simultaneous resetting generates an effective dynamical all-to-all attractions between particles that persist even at long times in its nonequilibrium stationary state (NESS). Despite the presence of strong correlations, many physical observables such as the average density, extreme statistics, order and gap/spacing statistics, full counting statistics etc. (the standard observables of interest in RMT) can be computed exactly in the NESS and they exhibit rich and interesting behaviors. The physical mechanism built in this simple model allows it to generalize and invent a whole class of solvable strongly correlated out of equilibrium point processes, some of which are experimentally realisable in optical trap systems.