Quantum spectrum as a time series: Fluctuation measures

2005/08/31 by M. S. Santhanam, Jayendra N. Bandyopadhyay, D. Angom +1 · 3 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Quantum Mechanics and Applications #Theoretical and Computational Physics #cond-mat.other #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physreve.73.015201

published as Phys. Rev. E 73, 015201(R) (2006) · 4+ pages. 2 figures

openalex publication_date 2006/01/06 · arxiv created 2006/03/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The fluctuations in the quantum spectrum could be treated like a time series. In this framework, we explore the statistical self-similarity in the quantum spectrum using the detrended fluctuation analysis (DFA) and random matrix theory (RMT). We calculate the Hausdorff measure for the spectra of atoms and Gaussian ensembles and study their self-affine properties. We show that DFA is equivalent to the Delta3 statistics of RMT, unifying two different approaches. We exploit this connection to obtain theoretical estimates for the Hausdorff measure.

Citations

• Mosaic organization of DNA nucleotides
• Spectral Fluctuations and1/fNoise in the Order-Chaos Transition Regime
• Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series

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• Spectral fluctuations of billiards with mixed dynamics: From time series to superstatistics