Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A quantum model for collective recoil lasing   Free Electron Laser (FEL) and Collective Atomic Recoil Laser (CARL) are
described by the same model of classical equations for properly defined scaled
variables. These equations are extended to the quantum domain describing the
particle's motion by a Schr\"{o}dinger equation coupled to a self-consistent
radiation field. The model depends on a single collective parameter $\bar \rho$
which represents the maximum number of photons emitted per particle. We
demonstrate that the classical model is recovered in the limit $\bar \rho\gg
1$, in which the Wigner function associated to the Schr\"{o}dinger equation
obeys to the classical Vlasov equation. On the contrary, for $\bar \rho\le 1$,
a new quantum regime is obtained in which both FELs and CARLs behave as a
two-state system coupled to the self-consistent radiation field and described
by Maxwell-Bloch equations.

15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex