Abstract
The power law 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 is found at all the transition stages, and it is shown that the exponent is related to the chaotic component of the classical phase space of the quantum system.
- Received 29 April 2004
DOI:https://doi.org/10.1103/PhysRevLett.94.084101
©2005 American Physical Society