The Hartree equation for infinite quantum systems
Journées équations aux dérivées partielles (2014), article no. 8, 18 p.

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.

DOI: 10.5802/jedp.111
Sabin, Julien 1

1 Laboratoire de Mathématiques d’Orsay UMR CNRS 8628 Université Paris-Sud 91405 Orsay, France
     author = {Sabin, Julien},
     title = {The {Hartree} equation for infinite quantum systems},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {8},
     pages = {1--18},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2014},
     doi = {10.5802/jedp.111},
     language = {en},
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Sabin, Julien. The Hartree equation for infinite quantum systems. Journées équations aux dérivées partielles (2014), article  no. 8, 18 p. doi : 10.5802/jedp.111.

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