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

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.

5 pages, 3 figures, RevTeX

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Cited by in corpus (5)

• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• The spin Sutherland model of D_N type and its associated spin chain
• Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
• Spectral fluctuation and $\frac{1}{f^{\alpha }}$ noise in the energy level statistics of interacting trapped bosons
• Rational quantum integrable systems of D_N type with polarized spin reversal operators