Stability of equilibria for a Hartree equation for random fields
Analysis of PDEs
2018-11-09 v1
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 . 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.
Cite
@article{arxiv.1811.03150,
title = {Stability of equilibria for a Hartree equation for random fields},
author = {Charles Collot and Anne-Sophie de Suzzoni},
journal= {arXiv preprint arXiv:1811.03150},
year = {2018}
}