Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parametric down-conversion beyond the semi-classical approximation   Using a perturbative approach, we investigate the parametric down-conversion
process without the semi-classical approximation. A Wigner functional
formalism, which incorporates both the spatiotemproal degrees of freedom and
the particle-number degrees of freedom is used to perform the analysis. First,
we derive an evolution equation for the down-conversion process in the
nonlinear medium. Then we use the perturbative approach to solve the equation.
The leading order contribution is equivalent to the semi-classical solution.
The next-to-leading order contribution provides a solution that includes the
evolution of the pump field as a quantum field.

10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
2
The categories of this paper are: math
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys