[PDE & Applications seminar] Zachary Adams: A quasi-stationary approach to metastability for weakly interacting particle systems

19 October 2023 16:00 till 17:00 - Location: Snijderszaal 36.LB 01.010 EEMCS | Add to my calendar

We consider systems of N particles moving as Brownian motions interacting via an attractive potential. For instance, the Glauber dynamics associated with the classical mean-field O(2) spin system of statistical mechanics. In the large particle limit, the empirical measure of such systems is known to converge to a nonlocal parabolic PDE of McKean-Vlasov type. While the McKean-Vlasov system is known to possess no non-trivial stationary solutions, numerical experiments demonstrate the existence of an almost-synchronized state that persists over a long time scale. In this talk, we characterize this almost-synchronized state and the time scale on which it persists using methods involving sub-Markov semigroups, quasi-stationary distributions, and the spectral theory of Schrödinger operators. Control on the time scale in terms of the noise amplitude and particle number are obtained. This is joint work with Maximilian Engel (FU Berlin) and Rishabh Gvalani (Max Planck Institute for Mathematics in the Sciences).