Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Wigner-Poisson-Fokker-Planck system: global-in-time solution and
  dispersive estimates   This paper is concerned with the Wigner-Poisson-Fokker-Planck system, a
kinetic evolution equation for an open quantum system with a non-linear Hartree
potential. Existence, uniqueness and regularity of global solutions to the
Cauchy problem in 3 dimensions are established. The analysis is carried out in
a weighted L^2-space, such that the linear quantum Fokker-Planck operator
generates a dissipative semigroup.The non-linear potential can be controled by
using the parabolic regularization of the system. The main technical difficulty
for establishing global-in-time solutions is to derive a-priori estimates on
the electric field:Inspired by a strategy for the classical
Vlasov-Fokker-Planck equation, we exploit dispersive effects of the free
transport operator. As a ``by-product'' we also derive a new a-priori estimate
on the field in the Wigner-Poisson equation.

17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat