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Construction of a Gibbs measure for the zonal Dirac equation
Anne-Sophie de Suzzoni, Cyril Malézé
We propose a framework to construct Gibbs measures for the Dirac equation. We consider the Dirac equation on the sphere with a "Hartree-type" nonlinearity. We consider a zonal mode…
Scattering for the one dimensional Hartree Fock equation
Cyril Malézé
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 nonlinea…
Stability of homogeneous equilibria of the Hartree-Fock equation, for its equivalent formulation for random fields
Charles Collot, Elena Danesi, Anne-Sophie de Suzzoni +1
The Hartree-Fock equation admits homogeneous states that model infinitely many particles at equilibrium. We prove their asymptotic stability in large dimensions, under assumptions…
A Scattering Result Around a Non-Localised Equilibria for the Quintic Hartree Equation for Random Fields
Cyril Malézé
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 sca…