Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schr\"odinger Evolution of Self-Gravitating Disks   An understanding of the long-term evolution of self-gravitating disks ranks
among the classic outstanding problems of astrophysics. In this work, we show
that the secular inclination dynamics of a geometrically thin quasi-Keplerian
disk, with a surface density profile that scales as the inverse square-root of
the orbital radius, are described by the time-dependent Schr\"odinger equation.
Within the context of this formalism, nodal bending waves correspond to the
eigenmodes of a quasiparticle's wavefunction, confined in an infinite square
well with boundaries given by the radial extent of the disk. We further show
that external secular perturbations upon self-gravitating disks exhibit a
mathematical similarity to quantum scattering theory. Employing this framework,
we derive an analytic criterion for the gravitational rigidity of a
nearly-Keplerian disk under external perturbations. Applications of the theory
to circumstellar disks and Galactic nuclei are discussed.

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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th