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Quantitative Derivation of the Gross‐Pitaevskii Equation

Quantitative Derivation of the Gross‐Pitaevskii Equation

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 the convergence. Initial data are constructed on the bosonic Fock space applying an appropriate Bogoliubov transformation on a coherent state …