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We consider the evolution of $N$ bosons interacting with a repulsive shortrange pair potential in three dimensions. The potential is scaled according tothe Gross-Pitaevskii scaling, i.e. it is given by $N^2V(N(x_i-x_j))$. Wemonitor the behavior of the solution to the $N$-particle Schr\"odinger equationin a spatial window where two particles are close to each other. We prove thatwithin this window a short scale interparticle structure emerges dynamically.The local correlation between the particles is given by the two-body zeroenergy scattering mode. This is the characteristic structure that was expectedto form within a very short initial time layer and to persist for all latertimes, on the basis of the validity of the Gross-Pitaevskii equation for theevolution of the Bose-Einstein condensate. The zero energy scattering modeemerges after an initial time layer where all higher energy modes disperse outof the spatial window. We can prove the persistence of this structure up tosufficiently small times before three-particle correlations could develop.

Dynamical formation of correlations in a Bose-Einstein condensate