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arXiv · 1805.10072

A large probability averaging Theorem for the defocousing NLS

Dario Bambusi·Alberto Maiocchi·Luca Turri
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Abstract

We consider the nonlinear Schroedinger equation on the one dimensional torus, with a defocousing polynomial nonlinearity and study the dynamics corresponding to initial data in a set of large measure with respect to the Gibbs measure. We prove that along the corresponding solutions the modulus of the Fourier coefficients is approximately constant for times of order $β^{2+ς}$, $β$ being the inverse of the temperature and $ς$ a positive number (we prove $ς= 1/10$). The proof is obtained by adapting to the context of Gibbs measure for PDEs some tools of Hamiltonian perturbation theory.

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Dario Bambusi, Alberto Maiocchi, Luca Turri. 2018-05-25. A large probability averaging Theorem for the defocousing NLS. https://doi.org/10.1088/1361-6544%2Fab17e8

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