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arXiv · 2309.10500

A Scattering Result Around a Non-Localised Equilibria for the Quintic Hartree Equation for Random Fields

Cyril Malézé
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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 $d\geq 4$. 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.

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Cyril Malézé. 2023-09-19. A Scattering Result Around a Non-Localised Equilibria for the Quintic Hartree Equation for Random Fields. https://arxiv.org/abs/2309.10500

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