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

2023/09/19 by Cyril Malézé, Malézé, Cyril
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2309.10500

openalex publication_date 2023/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥ 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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