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arXiv · 2104.06086

Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space

Xuwen Chen·Justin Holmer
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Abstract

We consider the derivation of the defocusing cubic nonlinear Schr\"{o}dinger equation (NLS) on $\mathbb{R}^{3}$ from quantum $N$-body dynamics. We reformat the hierarchy approach with Klainerman-Machedon theory and prove a bi-scattering theorem for the NLS to obtain convergence rate estimates under $H^{1}$ regularity. The $H^{1}$ convergence rate estimate we obtain is almost optimal for $H^{1}$ datum, and immediately improves if we have any extra regularity on the limiting initial one-particle state.

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Xuwen Chen, Justin Holmer. 2021-04-13. Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space. https://doi.org/10.1007/s40818-022-00126-5

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