$1/f^{\alpha }$ Noise in Spectral Fluctuations of Quantum Systems

Abstract

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.

4 pages, 5 figures, accepted for publication in Phys. Rev. Lett

References in corpus (4)

• Theoretical derivation of 1/f noise in quantum chaos
• Berry-Robnik level statistics in a smooth billiard system
• Comment on Energy Level Statistics in the Mixed Regime
• Experimental study of generic billiards with microwave resonators

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