Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum and Classical Fidelity for Singular Perturbations of the
  Inverted and Harmonic Oscillator   Let us consider the quantum/versus classical dynamics for Hamiltonians of the
form \beq \label{0.1} H\_{g}^{\epsilon} := \frac{P^2}{2}+ \epsilon
\frac{Q^2}{2}+ \frac{g^2}{Q^2} \edq where $\epsilon = \pm 1$, $g$ is a real
constant. We shall in particular study the Quantum Fidelity between
$H\_{g}^{\epsilon}$ and $H\_{0}^{\epsilon}$ defined as \beq \label{0.2}
F\_{Q}^{\epsilon}(t,g):= < \exp(-it H\_{0}^{\epsilon})\psi, exp(-itH\_{g}^
{\epsilon})\psi > \edq for some reference state $\psi$ in the domain of the
relevant operators. We shall also propose a definition of the Classical
Fidelity, already present in the literature (\cite{becave1}, \cite{becave2},
\cite{ec}, \cite{prozni}, \cite{vepro}) and compare it with the behaviour of
the Quantum Fidelity, as time evolves, and as the coupling constant $g$ is
varied.

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The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin