Niels Benedikter, Gustavo de Oliveira, Benjamin Schlein
Starting from first principle many-body quantum dynamics, we show that the dynamics of Bose-Einstein condensates can be approximated by the time-dependent nonlinear Gross-Pitaevskii equation, giving a bound on the rate of convergence. Initial data are constructed on the bosonic Fock space applying an appropriate Bogoliubov transformation on a coherent state with expected number of particles $N$. The Bogoliubov transformation plays a crucial role; it produces the correct microscopic correlations among the particles. Our analysis shows that, up to a small error of the order $N^{-1/2}$, the form of the initial data is preserved by the many body evolution.
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http://arxiv.org/abs/1208.0373
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