New Asymptotic Law Governing Overall Temporal Correlations in Chaotic Systems: Ensemble Homogenization and Order-q Power Spectrum
- 1 February 1991
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 85 (2) , 187-204
- https://doi.org/10.1143/ptp.85.187
Abstract
A new statistical-physical asymptotic law relevant to explicit correlation in temporal fluctuations generated by chaotic dynamics is found. Homogenizing the ensemble members, we can introduce the order-q power spectrum Iq(ω) in the “thermodynamic” limit, whose poles are proved to be determined by the eigenvalues of the order-q evolution operator Hq previously introduced. It is a natural extension of the conventional power spectrum I(ω)(= Iq=0(ω)), and enables us to study various correlation characteristics by controlling the value of parameter q. This manifests that the intensive variable q governs overall temporal-correlation characteristics as well as the global aspect described by fluctuation-spectrum theory.Keywords
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