Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An integrable (classical and quantum) four-wave mixing Hamiltonian
  system   A four-wave mixing Hamiltonian system on the classical as well as on the
quantum level is investigated. In the classical case, if one assumes the
frequency resonance condition of the form $\omega_0 -\omega_1 +\omega_2
-\omega_3=0$, this Hamiltonian system is integrated in quadratures and the
explicit formulas of solutions are presented. Under the same condition the
spectral decomposition of quantum Hamiltonian is found and thus, the Heisenberg
equation for this system is solved. Some applications of the obtained results
in non-linear optics are disscused.

10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat