Mean field equations for the quantum dynamics of many particles

Patrick Gérard

Séminaire Bourbaki (2003-2004)

  • Volume: 46, page 147-164
  • ISSN: 0303-1179

Abstract

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The purpose of this talk is to describe how the Schrödinger evolution for the quantum N –body problem is approximated, as N tends to infinity, in a suitable regime, by a nonlinear evolution in three space dimensions. We shall discuss the case of bosons, which leads to the Schrödinger–Poisson equation, and the case of fermions, with its connections to the Hartree-Fock system.

How to cite

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Gérard, Patrick. "Équations de champ moyen pour la dynamique quantique d’un grand nombre de particules." Séminaire Bourbaki 46 (2003-2004): 147-164. <http://eudml.org/doc/252123>.

@article{Gérard2003-2004,
abstract = {L’objet de cet exposé est de montrer comment l’évolution de Schrödinger pour le problème à $N$ corps quantique est approchée, lorsque $N$ tend vers l’infini, dans un régime convenable, par une évolution non-linéaire en dimension trois d’espace. On traitera le cas des bosons, qui conduit à l’équation de Schrödinger-Poisson, et celui des fermions, qui débouche sur le système de Hartree-Fock.},
author = {Gérard, Patrick},
journal = {Séminaire Bourbaki},
keywords = {quantum $N$-body problem; mean field equations; Hartree equation; Schrödinger–Poisson equation; Hartree-Fock system; Slater determinants; BBGKY hierarchy},
language = {fre},
pages = {147-164},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Équations de champ moyen pour la dynamique quantique d’un grand nombre de particules},
url = {http://eudml.org/doc/252123},
volume = {46},
year = {2003-2004},
}

TY - JOUR
AU - Gérard, Patrick
TI - Équations de champ moyen pour la dynamique quantique d’un grand nombre de particules
JO - Séminaire Bourbaki
PY - 2003-2004
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 46
SP - 147
EP - 164
AB - L’objet de cet exposé est de montrer comment l’évolution de Schrödinger pour le problème à $N$ corps quantique est approchée, lorsque $N$ tend vers l’infini, dans un régime convenable, par une évolution non-linéaire en dimension trois d’espace. On traitera le cas des bosons, qui conduit à l’équation de Schrödinger-Poisson, et celui des fermions, qui débouche sur le système de Hartree-Fock.
LA - fre
KW - quantum $N$-body problem; mean field equations; Hartree equation; Schrödinger–Poisson equation; Hartree-Fock system; Slater determinants; BBGKY hierarchy
UR - http://eudml.org/doc/252123
ER -

References

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