Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear
  optics   We develop the theory of weak wave turbulence in systems described by the
Schr\"odinger-Helmholtz equations in two and three dimensions. This model
contains as limits both the familiar cubic nonlinear Schr\"odinger equation,
and the Schr\"odinger-Newton equations. The latter, in three dimensions, are a
nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational
self-potential, and in two dimensions they describe nonlocal nonlinear optics
in the paraxial approximation. We show that in the weakly nonlinear limit the
Schr\"odinger-Helmholtz equations have a simultaneous inverse cascade of
particles and a forward cascade of energy. We interpret the inverse cascade as
a nonequilibrium condensation process, which is a precursor to structure
formation at large scales (for example the formation of galactic dark matter
haloes or optical solitons). We show that for the Schr\"odinger-Newton
equations in two and three dimensions, and in the two-dimensional nonlinear
Schr\"odinger equation, the particle and energy fluxes are carried by small
deviations from thermodynamic distributions, rather than the
Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a
differential approximation model to characterise such "warm cascade" states.

18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph