Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Birkhoff normal form in low regularity for the nonlinear quantum harmonic oscillator

Résumé

Given small initial solutions of the nonlinear quantum harmonic oscillator on $\mathbb{R}$, we are interested in their long time behavior in the energy space which is an adapted Sobolev space. We perturbate the linear part by $V$ taken as multiplicative potentials, in a way that the linear frequencies satisfy a non-resonance condition. More precisely, we prove that for almost all potentials $V$, the low modes of the solution are almost preserved for very long times.

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Dates et versions

hal-03868272 , version 2 (29-06-2023)
hal-03868272 , version 1 (29-03-2024)

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Charbella Abou Khalil. Birkhoff normal form in low regularity for the nonlinear quantum harmonic oscillator. 2023. ⟨hal-03868272v2⟩
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