Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum derivation of Manley Rowe type relations   The Ermakov Lewis quantum invariant for the time dependent harmonic
oscillator is expressed in terms of number and phase operators. The
identification of these variables is made in accordance with the correspondence
principle and the amplitude and phase representation of the classical
orthogonal functions invariant. The relationship between the number and phase
operators is established through this invariant as the system evolves from one
frequency to another. In the specific case where the excitations represent the
photon number, these relations are equivalent to the power density transport
equations derived in nonlinear optical processes.

36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an