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

TL;DR

This paper investigates the spectral fluctuations of quantum systems, revealing a persistent 1/f^α power law across different chaos levels and linking the exponent to classical chaos features.

Contribution

It demonstrates that 1/f^α noise characterizes quantum spectral fluctuations during chaos transitions and relates the exponent to classical phase space properties.

Findings

1/f^α noise appears at all transition stages

The exponent α correlates with the chaotic component

Power law behavior persists across different regimes

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.