Stability of equilibria for a Hartree equation for random fields

@article{Collot2018StabilityOE,
  title={Stability of equilibria for a Hartree equation for random fields},
  author={Charles Collot and Anne-Sophie de Suzzoni},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
We consider a Hartree equation for a random variable, which describes the temporal evolution of infinitely many Fermions. On the Euclidean space, this equation possesses equilibria which are not localised. We show their stability through a scattering result, with respect to localised perturbations in the defocusing case in high dimensions $d\geq 4$. This provides an analogue of the results of Lewin and Sabin \cite{LS2}, and of Chen, Hong and Pavlovi\'c \cite{CHP2} for the Hartree equation on… 
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