Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Colored $1/f^{\alpha}$ noise and the Order to Chaos Transition in
  Quantum Mechanics   The spectral statistic $\delta_n$ measures the fluctuations of the number of
energy levels around its mean value. It has been shown that chaotic quantum
systems display $1/f$ noise (pink noise) in the power spectrum $S(f)$ of the
$\delta_n$ statistic, whereas integrable ones exibit $1/f^2$ noise (brown
noise). These results have been explained on the basis of the random matrix
theory and periodic orbit theory. Recently we have analyzed the order to chaos
transition in terms of the power spectrum $S(f)$ by using the Robnik billiard
(Phys. Rev. Lett. {\bf 94}, 084101 (2005)). We have numerically found a net
power law $1/f^{\alpha}$, with $1\leq \alpha \leq 2$, at all the transition
stages. Similar results have been obtained by Santhanam and Bandyopadhyay
(Phys. Rev. Lett. {\bf 95}, 114101 (2005)) analyzing two coupled quartic
oscillators and a quantum kicked top. All these numerical results suggest that
the exponent $\alpha$ is related to the chaotic component of the classical
phase space of the quantum billiard, but a satisfactory theoretical explanation
is still lacking.

13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci