1/f(alpha) noise in spectral fluctuations of quantum systems

The power law 1/f(alpha) 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/f(alpha) is found at all the transition stages, and it is shown that the exponent alpha is related to the chaotic component of the classical phase space of the quantum system.