Seminar Analysis: Julien Sabin (University of Cergy-Pontoise)
A Fermi gas occupying the whole euclidian space is an example of a translation-invariant quantum system with an infinite number of particles. We study its stability properties under the time-dependent nonlinear Hartree equation. If this system is slightly perturbed at the initial time, we show in particular that it returns to the translation-invariant state for large times. This is an instance of nonlinear dispersion for infinite quantum systems, which was recently studied by Frank, Lewin, Lieb and Seiringer in the linear case. This a joint work with Mathieu Lewin (CNRS/Cergy). I will also mention some recent work on Strichartz estimates for systems of orthonormal functions, joint with Rupert Frank (Caltech).
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