1/ fα Noise in spectral fluctuations of quantum systems

The power law 1 / fα in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of time, the level fluctuations can be characterized by the power spectrum. Using a family of quantum billiards, we analyze the order-to-chaos transition in terms of this power spectrum. A power law 1 / fα is found at all the transition stages, and it is shown that the exponent α is related to the chaotic component of the classical phase space of the quantum system. © 2005 The American Physical Society.