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Julien Sabin
The Hartree equation for infinite quantum systems
Journées équations aux dérivées partielles (2014), Exp. No. 8, 18 p., doi: 10.5802/jedp.111
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Résumé - Abstract

We review some recent results obtained with Mathieu Lewin [21] concerning the nonlinear Hartree equation for density matrices of infinite trace, describing the time evolution of quantum systems with infinitely many particles. Our main result is the asymptotic stability of a large class of translation-invariant density matrices which are stationary solutions to the Hartree equation. We also mention some related result obtained in collaboration with Rupert Frank [13] about Strichartz estimates for orthonormal systems.


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