Scattering for the one dimensional Hartree Fock equation

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.