Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wave packet revivals and the energy eigenvalue spectrum of the quantum
  pendulum   The rigid pendulum, both as a classical and as a quantum problem, is an
interesting system as it has the exactly soluble harmonic oscillator and the
rigid rotor systems as limiting cases in the low- and high-energy limits
respectively. The energy variation of the classical periodicity ($\tau$) is
also dramatic, having the special limiting case of $\tau \to \infty$ at the
'top' of the classical motion (i.e. the separatrix.) We study the
time-dependence of the quantum pendulum problem, focusing on the behavior of
both the (approximate) classical periodicity and especially the quantum revival
and superrevival times, as encoded in the energy eigenvalue spectrum of the
system. We provide approximate expressions for the energy eigenvalues in both
the small and large quantum number limits, up to 4th order in perturbation
theory, comparing these to existing handbook expansions for the characteristic
values of the related Mathieu equation, obtained by other methods. We then use
these approximations to probe the classical periodicity, as well as to extract
information on the quantum revival and superrevival times. We find that while
both the classical and quantum periodicities increase monotonically as one
approaches the 'top' in energy, from either above or below, the revival times
decrease from their low- and high-energy values until very near the separatrix
where they increase to a large, but finite value.

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio