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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.
@incollection{JEDP_2014____A8_0,
author = {Sabin, Julien},
title = {The {Hartree} equation for infinite quantum systems},
booktitle = {},
series = {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},
url = {http://geodesic.mathdoc.fr/articles/10.5802/jedp.111/}
}
TY - JOUR AU - Sabin, Julien TI - The Hartree equation for infinite quantum systems JO - Journées équations aux dérivées partielles PY - 2014 SP - 1 EP - 18 PB - Groupement de recherche 2434 du CNRS UR - http://geodesic.mathdoc.fr/articles/10.5802/jedp.111/ DO - 10.5802/jedp.111 LA - en ID - JEDP_2014____A8_0 ER -
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. http://geodesic.mathdoc.fr/articles/10.5802/jedp.111/
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