Quantum spectrum as a time series : Fluctuation measures

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 ${\Delta }_3$ statistics of RMT, unifying two different approaches.We exploit this connection to obtain theoretical estimates for the Hausdorff measure.

4+ pages. 2 figures

References in corpus (7)

• An integrated approach to the assessment of long range correlation in time series data
• Theoretical derivation of 1/f noise in quantum chaos
• On the Renormalization of the Kardar-Parisi-Zhang equation
• Spectral fluctuations and 1/f noise in the order-chaos transition regime
• Strength functions, entropies and duality in weakly to strongly interacting fermionic systems
• Chaos and localization in the wavefunctions of complex atoms NdI, PmI and SmI
• Quantum correlations from Brownian diffusion of chaotic level-spacings

Cited by in corpus (10)

• Comparison of detrending methods for fluctuation analysis
• Spectral fluctuations of billiards with mixed dynamics: from time series to superstatistics
• Random Matrix Spectra as a Time Series
• Exact distribution of spacing ratios for random and localized states in quantum chaotic systems
• Effects of scarring on quantum chaos in disordered quantum wells
• Nonextensive and superstatistical generalizations of random-matrix theory
• Long-range level correlations in quantum systems with finite Hilbert space dimension
• Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble
• Spectral fluctuation characterization of random matrix ensembles through wavelets
• Inferring long memory using extreme events