The Hartree equation for infinite quantum systems

Julien Sabin[1]

  • [1] Laboratoire de Mathématiques d’Orsay UMR CNRS 8628 Université Paris-Sud 91405 Orsay, France

Journées Équations aux dérivées partielles (2014)

  • page 1-18
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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Sabin, Julien. "The Hartree equation for infinite quantum systems." Journées Équations aux dérivées partielles (2014): 1-18. <http://eudml.org/doc/275556>.

@article{Sabin2014,
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.},
affiliation = {Laboratoire de Mathématiques d’Orsay UMR CNRS 8628 Université Paris-Sud 91405 Orsay, France},
author = {Sabin, Julien},
journal = {Journées Équations aux dérivées partielles},
language = {eng},
pages = {1-18},
publisher = {Groupement de recherche 2434 du CNRS},
title = {The Hartree equation for infinite quantum systems},
url = {http://eudml.org/doc/275556},
year = {2014},
}

TY - JOUR
AU - Sabin, Julien
TI - The Hartree equation for infinite quantum systems
JO - Journées Équations aux dérivées partielles
PY - 2014
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 18
AB - 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.
LA - eng
UR - http://eudml.org/doc/275556
ER -

References

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