---
_id: '2759'
abstract:
- lang: eng
text: We consider the evolution of N bosons interacting with a repulsive short range
pair potential in three dimensions. The potential is scaled according to the Gross-Pitaevskii
scaling, i.e. it is given by N 2 V(N(x i - x j )). We monitor the behaviour of
the solution to the N-particle Schrödinger equation in a spatial window where
two particles are close to each other. We prove that within this window a short-scale
interparticle structure emerges dynamically. The local correlation between the
particles is given by the two-body zero energy scattering mode. This is the characteristic
structure that was expected to form within a very short initial time layer and
to persist for all later times, on the basis of the validity of the Gross-Pitaevskii
equation for the evolution of the Bose-Einstein condensate. The zero energy scattering
mode emerges after an initial time layer where all higher energy modes disperse
out of the spatial window. We can prove the persistence of this structure up to
sufficiently small times before three-particle correlations could develop.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Alessandro
full_name: Michelangeli, Alessandro
last_name: Michelangeli
- first_name: Benjamin
full_name: Schlein, Benjamin
last_name: Schlein
citation:
ama: Erdös L, Michelangeli A, Schlein B. Dynamical formation of correlations in
a Bose-Einstein condensate. Communications in Mathematical Physics. 2009;289(3):1171-1210.
doi:10.1007/s00220-009-0828-y
apa: Erdös, L., Michelangeli, A., & Schlein, B. (2009). Dynamical formation
of correlations in a Bose-Einstein condensate. Communications in Mathematical
Physics. Springer. https://doi.org/10.1007/s00220-009-0828-y
chicago: Erdös, László, Alessandro Michelangeli, and Benjamin Schlein. “Dynamical
Formation of Correlations in a Bose-Einstein Condensate.” Communications in
Mathematical Physics. Springer, 2009. https://doi.org/10.1007/s00220-009-0828-y.
ieee: L. Erdös, A. Michelangeli, and B. Schlein, “Dynamical formation of correlations
in a Bose-Einstein condensate,” Communications in Mathematical Physics,
vol. 289, no. 3. Springer, pp. 1171–1210, 2009.
ista: Erdös L, Michelangeli A, Schlein B. 2009. Dynamical formation of correlations
in a Bose-Einstein condensate. Communications in Mathematical Physics. 289(3),
1171–1210.
mla: Erdös, László, et al. “Dynamical Formation of Correlations in a Bose-Einstein
Condensate.” Communications in Mathematical Physics, vol. 289, no. 3, Springer,
2009, pp. 1171–210, doi:10.1007/s00220-009-0828-y.
short: L. Erdös, A. Michelangeli, B. Schlein, Communications in Mathematical Physics
289 (2009) 1171–1210.
date_created: 2018-12-11T11:59:27Z
date_published: 2009-08-01T00:00:00Z
date_updated: 2021-01-12T06:59:30Z
day: '01'
doi: 10.1007/s00220-009-0828-y
extern: 1
intvolume: ' 289'
issue: '3'
month: '08'
page: 1171 - 1210
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4133'
quality_controlled: 0
status: public
title: Dynamical formation of correlations in a Bose-Einstein condensate
type: journal_article
volume: 289
year: '2009'
...