Stability of equilibria for a Hartree equation for random fields

2018/11/07 by Collot, Charles, de Suzzoni, Anne-Sophie · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.03150

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≥ 4. This provides an analogue of the results of Lewin and Sabin \citeLS2, and of Chen, Hong and Pavlović \citeCHP2 for the Hartree equation on operators. The proof relies on dispersive techniques used for the study of scattering for the nonlinear Schrödinger and Gross-Pitaevskii equations.

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