Geodesic
Derivation of the Gross-Pitaevskii dynamics through renormalized excitation number operators
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e107

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We revisit the time evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. We show that the system continues to exhibit BEC once the trap has been released and that the dynamics of the condensate is described by the time-dependent Gross-Pitaevskii equation. Like the recent work [15], we obtain optimal bounds on the number of excitations orthogonal to the condensate state. In contrast to [15], however, whose main strategy consists of controlling the number of excitations with regard to a suitable fluctuation dynamics $t\mapsto e^{-B_t} e^{-iH_Nt}$ with renormalized generator, our proof is based on controlling renormalized excitation number operators directly with regards to the Schrödinger dynamics $t\mapsto e^{-iH_Nt}$. 
Brennecke, Christian; Kroschinsky, Wilhelm. Derivation of the Gross-Pitaevskii dynamics through renormalized excitation number operators. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e107. doi: 10.1017/fms.2025.10073
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     title = {Derivation of the {Gross-Pitaevskii} dynamics through renormalized excitation number operators},
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