---
OA_type: closed access
_id: '2742'
abstract:
- lang: eng
  text: We consider a system of N weakly interacting fermions with a real analytic
    pair interaction. We prove that for a general class of initial data there exists
    a fixed time T such that the difference between the one particle density matrix
    of this system and the solution of the nonlinear Hartree equation is of order
    N−1 for any time t⩽T.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Alexander
  full_name: Elgart, Alexander
  last_name: Elgart
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Benjamin
  full_name: Schlein, Benjamin
  last_name: Schlein
- first_name: Horng
  full_name: Yau, Horng
  last_name: Yau
citation:
  ama: Elgart A, Erdös L, Schlein B, Yau H. Nonlinear Hartree equation as the mean
    field limit of weakly coupled fermions. <i>Journal de Mathématiques Pures et Appliquées</i>.
    2004;83(10):1241-1273. doi:<a href="https://doi.org/10.1016/j.matpur.2004.03.006">10.1016/j.matpur.2004.03.006</a>
  apa: Elgart, A., Erdös, L., Schlein, B., &#38; Yau, H. (2004). Nonlinear Hartree
    equation as the mean field limit of weakly coupled fermions. <i>Journal de Mathématiques
    Pures et Appliquées</i>. Elsevier. <a href="https://doi.org/10.1016/j.matpur.2004.03.006">https://doi.org/10.1016/j.matpur.2004.03.006</a>
  chicago: Elgart, Alexander, László Erdös, Benjamin Schlein, and Horng Yau. “Nonlinear
    Hartree Equation as the Mean Field Limit of Weakly Coupled Fermions.” <i>Journal
    de Mathématiques Pures et Appliquées</i>. Elsevier, 2004. <a href="https://doi.org/10.1016/j.matpur.2004.03.006">https://doi.org/10.1016/j.matpur.2004.03.006</a>.
  ieee: A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Nonlinear Hartree equation as
    the mean field limit of weakly coupled fermions,” <i>Journal de Mathématiques
    Pures et Appliquées</i>, vol. 83, no. 10. Elsevier, pp. 1241–1273, 2004.
  ista: Elgart A, Erdös L, Schlein B, Yau H. 2004. Nonlinear Hartree equation as the
    mean field limit of weakly coupled fermions. Journal de Mathématiques Pures et
    Appliquées. 83(10), 1241–1273.
  mla: Elgart, Alexander, et al. “Nonlinear Hartree Equation as the Mean Field Limit
    of Weakly Coupled Fermions.” <i>Journal de Mathématiques Pures et Appliquées</i>,
    vol. 83, no. 10, Elsevier, 2004, pp. 1241–73, doi:<a href="https://doi.org/10.1016/j.matpur.2004.03.006">10.1016/j.matpur.2004.03.006</a>.
  short: A. Elgart, L. Erdös, B. Schlein, H. Yau, Journal de Mathématiques Pures et
    Appliquées 83 (2004) 1241–1273.
date_created: 2018-12-11T11:59:22Z
date_published: 2004-10-01T00:00:00Z
date_updated: 2026-09-22T13:05:18Z
day: '01'
doi: 10.1016/j.matpur.2004.03.006
extern: '1'
external_id:
  arxiv:
  - '0311043'
fulldoi: https://doi.org/10.1016/j.matpur.2004.03.006
intvolume: '        83'
issue: '10'
language:
- iso: eng
month: '10'
oa_version: None
page: 1241 - 1273
publication: Journal de Mathématiques Pures et Appliquées
publication_identifier:
  eissn:
  - 1776-3371
  issn:
  - 0021-7824
publication_status: published
publisher: Elsevier
publist_id: '4150'
status: public
title: Nonlinear Hartree equation as the mean field limit of weakly coupled fermions
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 83
year: '2004'
...