### Gross-Pitaevskii equation and dynamical formation of correlations in the Bose-Einstein condensate

Erdos, L *(Ludwig-Maximilians-Universität München)*

Thursday 14 August 2008, 14:00-15:00

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

The time dependent Gross-Pitaevskii equation, a cubic nonlinear Schrodinger equation with a specific coupling constant, describes the dynamics of an initially trapped Bose-Einstein condensate. The rigorous proof of this fact, starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit, indicates the emergence and the persistence of an explicit short scale correlation structure in the condensate. We prove that the interparticle structure emerges dynamically in a small spatial window where two particles are close to each other