Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbative Semiclassical Trace Formulae for Harmonic Oscillators   In this article we extend previous semiclassical studies by including more
general perturbative potentials of the harmonic oscillator in arbitrary spatial
dimensions. Our starting point is a radial harmonic potential with an arbitrary
even monomial perturbation, which we use to study the resulting $\mathrm{U}(D)$
to $\mathrm{O}(D)$ symmetry breaking. We derive the gross structure of the
semiclassical spectrum from periodic orbit theory, in the form of a
perturbative ($\hbar \rightarrow 0$) trace formula. We then show how to apply
the results to even order polynomial potentials, possibly including mean-field
terms. We have drawn the conclusion that the gross structure of the quantum
spectrum is determined from only classical circular- and diameter-orbits for
this class of systems.

35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin