A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation

Springer Science and Business Media LLC - Tập 11 - Trang 1379-1415 - 2022
Amirali Hannani1, Stefano Olla1,2,3
1CEREMADE, UMR CNRS Université Paris-Dauphine, PSL Research University, Paris, France
2Institut Universitaire de France, Paris, France
3GSSI, L’Aquila, Italy

Tóm tắt

We introduce a mass conserving stochastic perturbation of the discrete nonlinear Schrödinger equation that models the action of a heat bath at a given temperature. We prove that the corresponding canonical Gibbs distribution is the unique invariant measure. In the one-dimensional cubic focusing case on the torus, 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.

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