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.
@article{JEDP_2014____A8_0,
author = {Sabin, Julien},
title = {The Hartree equation for infinite quantum systems},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
year = {2014},
pages = {1-18},
doi = {10.5802/jedp.111},
language = {en},
url = {http://dml.mathdoc.fr/item/JEDP_2014____A8_0}
}
Sabin, Julien. The Hartree equation for infinite quantum systems. Journées équations aux dérivées partielles, (2014), pp. 1-18. doi : 10.5802/jedp.111. http://gdmltest.u-ga.fr/item/JEDP_2014____A8_0/
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