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Pré-Publication, Document De Travail Année : 2022

Stability of equilibria for a Hartree equation for random fields

Résumé

We consider a Hartree equation for a random variable, which describes the temporal evolution of infinitely many Fermions. On the Euclidean space, this equation possesses equilibria which are not localised. We show their stability through a scattering result, with respect to localised perturbations in the defocusing case in high dimensions $d\geq 4$. This provides an analogue of the results of Lewin and Sabin \cite{LS2}, and of Chen, Hong and Pavlovi\'c \cite{CHP2} for the Hartree equation on operators. The proof relies on dispersive techniques used for the study of scattering for the nonlinear Schr\"odinger and Gross-Pitaevskii equations.

Dates et versions

hal-03916576 , version 1 (30-12-2022)

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Charles Collot, Anne-Sophie de Suzzoni. Stability of equilibria for a Hartree equation for random fields. 2022. ⟨hal-03916576⟩
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