Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy
  Space   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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The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
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The categories of this paper are: nlin
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
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The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
26
The categories of this paper are: bayes-an