14/12/2022, 16:00 — 17:00 — Online
Amirali Hannani, KU Leuven
A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation
In this talk, first, I give a very brief introduction to the NLS (Nonlinear Schrödinger Equation) and its long-time behavior. Then I introduce a mass-conserving stochastic perturbation of the discrete nonlinear Schrödinger equation that models the action of a heat bath at a given temperature. Afterward, I sketch the fact that the corresponding canonical Gibbs distribution is the unique invariant measure. Finally, as an application, I discuss the one-dimensional cubic focusing case on the torus, where we prove that in the limit for large time, continuous approximation, and low temperature, the solution converges to the steady wave of the continuous equation that minimizes the energy for a given mass. This is based on the following joint work with prof. Stefano Olla (Universite Paris Dauphine-PSL, GSSI, IUF):
Hannani, A., Olla, S. A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation. Stoch PDE: Anal Comp (2022). https://doi.org/10.1007/s40072-022-00263-9
