---
_id: '2745'
abstract:
- lang: eng
text: 'We consider the dynamics of N boson systems interacting through a pair potential
N -1 V a (x i -x j ) where V a (x)=a -3 V(x/a). We denote the solution to the
N-particle Schrödinger equation by Ψ N, t . Recall that the Gross-Pitaevskii (GP)
equation is a nonlinear Schrödinger equation and the GP hierarchy is an infinite
BBGKY hierarchy of equations so that if u t solves the GP equation, then the family
of k-particle density matrices [InlineMediaObject not available: see fulltext.]
solves the GP hierarchy. Under the assumption that a = Nε for 0 < ε < 3/5,
we prove that as N→∞ the limit points of the k-particle density matrices of Ψ
N, t are solutions of the GP hierarchy with the coupling constant in the nonlinear
term of the GP equation given by ∫ V (x)dx. The uniqueness of the solutions of
this hierarchy remains an open question.'
author:
- first_name: Alexander
full_name: Elgart, Alexander
last_name: Elgart
- first_name: László
full_name: László Erdös
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-Tzer
last_name: Yau
citation:
ama: Elgart A, Erdös L, Schlein B, Yau H. Gross-Pitaevskii equation as the mean
field limit of weakly coupled bosons. *Archive for Rational Mechanics and Analysis*.
2006;179(2):265-283. doi:10.1007/s00205-005-0388-z
apa: Elgart, A., Erdös, L., Schlein, B., & Yau, H. (2006). Gross-Pitaevskii
equation as the mean field limit of weakly coupled bosons. *Archive for Rational
Mechanics and Analysis*, *179*(2), 265–283. https://doi.org/10.1007/s00205-005-0388-z
chicago: 'Elgart, Alexander, László Erdös, Benjamin Schlein, and Horng Yau. “Gross-Pitaevskii
Equation as the Mean Field Limit of Weakly Coupled Bosons.” *Archive for Rational
Mechanics and Analysis* 179, no. 2 (2006): 265–83. https://doi.org/10.1007/s00205-005-0388-z.'
ieee: A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Gross-Pitaevskii equation as
the mean field limit of weakly coupled bosons,” *Archive for Rational Mechanics
and Analysis*, vol. 179, no. 2, pp. 265–283, 2006.
ista: Elgart A, Erdös L, Schlein B, Yau H. 2006. Gross-Pitaevskii equation as the
mean field limit of weakly coupled bosons. Archive for Rational Mechanics and
Analysis. 179(2), 265–283.
mla: Elgart, Alexander, et al. “Gross-Pitaevskii Equation as the Mean Field Limit
of Weakly Coupled Bosons.” *Archive for Rational Mechanics and Analysis*,
vol. 179, no. 2, Springer, 2006, pp. 265–83, doi:10.1007/s00205-005-0388-z.
short: A. Elgart, L. Erdös, B. Schlein, H. Yau, Archive for Rational Mechanics and
Analysis 179 (2006) 265–283.
date_created: 2018-12-11T11:59:22Z
date_published: 2006-02-01T00:00:00Z
date_updated: 2019-04-26T07:22:19Z
day: '01'
doi: 10.1007/s00205-005-0388-z
extern: 1
intvolume: ' 179'
issue: '2'
month: '02'
page: 265 - 283
publication: Archive for Rational Mechanics and Analysis
publication_status: published
publisher: Springer
publist_id: '4147'
quality_controlled: 0
status: public
title: Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons
type: journal_article
volume: 179
year: '2006'
...