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Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation.
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Erdős, L., Schlein, B., Yau, H. T.: Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate. To appear in Annals Math
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