Level fluctuations, quantum chaos and 1/f noise
Chaos in quantum systems is generally understood to imply presence of universal spectral fluctuations as predicted by the random matrix theory. In this work, we attempt to look for quantum signatures of chaos based on inherent properties of the spectrum. We show that the spectra of quantum chaos displays $1/f$ noise as distinct from regular systems that display $1/f^2$ noise. This property can be used as alternative characterisation of quantum chaos. Further this idea can be carried forward to map the regime of fractional Brownian motion to standard random matrix ensembles. We discuss its applications for experimentally observed time series.