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A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation

Hannani, Amirali; Olla, Stefano (2021), A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation. https://basepub.dauphine.psl.eu/handle/123456789/22770

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Type
Document de travail / Working paper
Date
2021
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
32
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Author(s)
Hannani, Amirali
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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 onedimensional 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.
Subjects / Keywords
Non-linear Schrodinger equation; multiplicative noise; thermalization; soliton conjecture