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Article Dans Une Revue Stochastics and Partial Differential Equations: Analysis and Computations Année : 2022

A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation

Résumé

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.
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Dates et versions

hal-03333707 , version 1 (03-09-2021)

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Domaine public

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Amirali Hannani, Stefano Olla. A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation. Stochastics and Partial Differential Equations: Analysis and Computations, 2022, 95, ⟨10.1007/s40072-022-00263-9⟩. ⟨hal-03333707⟩
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