Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the derivation of the Hartree equation in the mean field limit:
  Uniformity in the Planck constant   In this paper the Hartree equation is derived from the $N$-body
Schr\''odinger equation in the mean-field limit, with convergence rate
estimates that are uniform in the Planck constant $\hbar$. Specifically, we
consider the two following cases:(a) T\''oplitz initial data and Lipschitz
interaction forces, and (b) analytic initial data and interaction potential,
over short time intervals independent of $\hbar$. The convergence rates in
these two cases are $1/\sqrt{\log\log N}$ and $1/N$ respectively. The treatment
of the second case is entirely self-contained and all the constants appearing
in the final estimate are explicit. It provides a derivation of the Vlasov
equation from the $N$-body classical dynamics using BBGKY hierarchies instead
of empirical measures.

0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph