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arXiv · 1811.03150

Stability of equilibria for a Hartree equation for random fields

Charles Collot·Anne-Sophie de Suzzoni
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Abstract

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.

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Charles Collot, Anne-Sophie de Suzzoni. 2018-11-07. Stability of equilibria for a Hartree equation for random fields. https://arxiv.org/abs/1811.03150

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