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arXiv · 2406.17715

Scattering for the one dimensional Hartree Fock equation

Cyril Malézé
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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.

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Cyril Malézé. 2024-06-25. Scattering for the one dimensional Hartree Fock equation. https://arxiv.org/abs/2406.17715

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