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A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation

Hannani, Amirali; Olla, Stefano (2022), A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation, Stochastics and Partial Differential Equations: Analysis and Computations, p. 32. 10.1007/s40072-022-00263-9

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Stochastics and Partial Differential Equations: Analysis and Computations
Publisher
Springer
Pages
32
Publication identifier
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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
Discrete Nonlinear Schrödinger Equation; Thermalization; Large Deviations; Hypoelliptic diffusions; Solitary waves