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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 d4d\geq 4. 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}
}