Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivation of the nonlinear Schr\"odinger equation from a many body
  Coulomb system   We consider the time evolution of N bosonic particles interacting via a mean
field Coulomb potential. Suppose the initial state is a product wavefunction.
We show that at any finite time the correlation functions factorize in the
limit $N \to \infty$. Furthermore, the limiting one particle density matrix
satisfies the nonlinear Hartree equation. The key ingredients are the
uniqueness of the BBGKY hierarchy for the correlation functions and a new
apriori estimate for the many-body Schr\"odinger equations.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con