Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric phases in the simple harmonic and perturbative Mathieu's
  oscillator systems   Geometric phases of simple harmonic oscillator system are studied. Complete
sets of "eigenfunctions" are constructed, which depend on the way of choosing
classical solutions. For an eigenfunction, two different motions of the
probability distribution function (pulsation of the width and oscillation of
the center) contribute to the geometric phase which can be given in terms of
the parameters of classical solutions. The geometric phase for a general wave
function is also given. If a wave function has a parity under the inversion of
space coordinate, then the geometric phase can be defined under the evolution
of half of the period of classical motions. For the driven case, geometric
phases are given in terms of Fourier coefficients of the external force. The
oscillator systems whose classical equation of motion is Mathieu's equation are
perturbatively studied, and the first term of nonvanishing geometric phase is
calculated.

5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci