Scale invariance in chaotic time series: Classical and quantum examples

Important aspects of chaotic behavior appear in systems of low dimension, as illustrated by the Map Module 1. It is indeed a remarkable fact that all systems tha make a transition from order to disorder display common properties, irrespective of their exacta functional form. We discuss evidence for 1/f power spectra in the chaotic time series associated in classical and quantum examples, the one-dimensional map module 1 and the spectrum of ⁴⁸Ca.

A Detrended Fluctuation Analysis (DFA) method is applied to investigate the scaling properties of the energy fluctuations in the spectrum of ⁴⁸Ca obtained with a large realistic shell model calculation (ANTOINE code) and with a random shell model (TBRE) calculation also in the time series obtained with the map mod 1. We compare the scale invariant properties of the ⁴⁸Ca nuclear spectrum sith similar analyses applied to the RMT ensambles GOE and GDE. A comparison with the corresponding power spectra is made in both cases. The possible consequences of the results are discussed.