Colored Noise in Quantum Chaos

TL;DR

This paper introduces spectral statistics for quantum systems that exhibit colored noise patterns, with the noise type depending on whether the system is chaotic or regular, revealing a connection between spectral properties and underlying dynamics.

Contribution

It derives a new set of spectral statistics that characterize quantum chaos and regularity through specific colored noise behaviors, highlighting a dependence on the type of quantum system.

Findings

Chaotic quantum systems show 1/f^{3} noise in spectral statistics.

Regular quantum systems exhibit 1/f^{4} noise.

Spectral noise characteristics depend critically on the system's dynamical nature.

Abstract

We derive a set of spectral statistics whose power spectrum is characterized, in the case of chaotic quantum systems, by colored noise $1/f^{\gamma}$, where the integer parameter $\gamma$ critically depends on the specific energy-level statistic considered. In the case of regular quantum systems these spectral statistics show $1/f^{\gamma+1}$ noise.