Scattering for the one dimensional Hartree Fock equation
Analysis of PDEs
2025-03-11 v3
Abstract
We consider the Hartree-Fock equation in 1D, for a small and localised initial data and a finite measure potential. We show that there is no long range scattering due to a nonlinear cancellation between the direct term and the exchange term for plane waves. We employ the framework of space-time resonances that enables us to single out precisely this cancellation and to obtain scattering to linear waves as a consequence.
Cite
@article{arxiv.2406.17715,
title = {Scattering for the one dimensional Hartree Fock equation},
author = {Cyril Malézé},
journal= {arXiv preprint arXiv:2406.17715},
year = {2025}
}