A Scattering Result Around a Non-Localised Equilibria for the Quintic Hartree Equation for Random Fields
Analysis of PDEs
2023-09-20 v1
Abstract
We consider a quintic Hartree equation for a random field, which describes the temporal evolution of a infinitely many fermions, considering a three body interaction. We show a scattering result around a non-localised equilibria of the equation, for high dimensions . The Hartree equation for random variables was introduced by Anne-Sophie de Suzzoni but only for a two body interaction, that leads to a cubic Hartree equation for random variables. Scattering results for the cubic Hartree equation have been shown by Charles Collot and Anne-Sophie de Suzzoni, and we extend those results to the quintic Hartree equation. We consider a large range of potentials that includes the Dirac delta.
Keywords
Cite
@article{arxiv.2309.10500,
title = {A Scattering Result Around a Non-Localised Equilibria for the Quintic Hartree Equation for Random Fields},
author = {Cyril Malézé},
journal= {arXiv preprint arXiv:2309.10500},
year = {2023}
}