noise and the Order to Chaos
Transition in Quantum Mechanics.
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 statistic, whereas
integrable ones exhibit 1/f2 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. 94, 084101 (2005)). We
have numerically found a net power law , with 
, at all the transition stages. Similar results have
been obtained by Santhanam and Bandyopadhyay (Phys. Rev. Lett.
95, 114101 (2005)) analyzing two coupled quartic oscillators
and a quantum kicked top. All these numerical results suggest that
the exponent 
is related to the chaotic component of the
classical phase space of the quantum billiard, but a satisfactory
theoretical explanation is still lacking.
Key words: Quantum chaos; Numerical simulations of chaotic systems
