$1/f^\alpha$ noise and integrable systems

TL;DR

This paper investigates spectral fluctuation behaviors in quantum systems, revealing that certain integrable spin chains exhibit a 1/f^4 noise decay, challenging previous assumptions about spectral noise signatures distinguishing chaos from integrability.

Contribution

It demonstrates that some integrable systems show a 1/f^4 spectral decay, providing a new perspective on spectral noise signatures and proposing an alternative characterization of quantum chaos.

Findings

Integrable spin chains of Haldane-Shastry type exhibit 1/f^4 spectral decay.

Spectral fluctuation analysis can distinguish between chaos and integrability.

A theoretical explanation for the 1/f^4 decay in certain integrable systems is provided.

Abstract

An innovative test for detecting quantum chaos based on the analysis of the spectral fluctuations regarded as a time series has been recently proposed. According to this test, the fluctuations of a fully chaotic system should exhibit 1/f noise, whereas for an integrable system this noise should obey the 1/f^2 power law. In this letter, we show that there is a family of well-known integrable systems, namely spin chains of Haldane-Shastry type, whose spectral fluctuations decay instead as 1/f^4. We present a simple theoretical justification of this fact, and propose an alternative characterization of quantum chaos versus integrability formulated directly in terms of the power spectrum of the spacings of the unfolded spectrum.