---
res:
bibo_abstract:
- '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.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Alexander
foaf_name: Elgart, Alexander
foaf_surname: Elgart
- foaf_Person:
foaf_givenName: László
foaf_name: László Erdös
foaf_surname: Erdös
foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-5366-9603
- foaf_Person:
foaf_givenName: Benjamin
foaf_name: Schlein, Benjamin
foaf_surname: Schlein
- foaf_Person:
foaf_givenName: Horng
foaf_name: Yau, Horng-Tzer
foaf_surname: Yau
bibo_doi: 10.1007/s00205-005-0388-z
bibo_issue: '2'
bibo_volume: 179
dct_date: 2006^xs_gYear
dct_publisher: Springer@
dct_title: Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons@
...