# Dynamical formation of correlations in a Bose-Einstein condensate

Erdös L, Michelangeli A, Schlein B. 2009. Dynamical formation of correlations in a Bose-Einstein condensate. Communications in Mathematical Physics. 289(3), 1171–1210.

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Author

Erdös, László

^{IST Austria}^{}; Michelangeli, Alessandro; Schlein, BenjaminAbstract

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.

Publishing Year

Date Published

2009-08-01

Journal Title

Communications in Mathematical Physics

Volume

289

Issue

3

Page

1171 - 1210

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### Cite this

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-yErdös, 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-yErdös, 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.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.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.