On the spectral unfolding of chaotic and mixed systems
arXiv:1803.00392 · doi:10.1016/j.physa.2017.08.158
Abstract
Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral unfolding procedure is used to separate the local level fluctuations from overall energy dependence of the level separation. The unfolding procedure is not unique. Several studies showed that statistics of long-term correlation in the spectrum are very sensitive to the choice of the unfolding function in polynomial unfolding. This can give misleading results regarding the chaoticity of quantum systems. In this letter, we consider the spectra of ordered eigenvalues of large random matrices. We show that the main cause behind the reported sensitivity to the unfolding polynomial degree is the inclusion of specific extreme eigenvalue(s) in the unfolding process.
arXiv comment10 Figures. arXiv admin note: text overlap with arXiv:1303.5980
References in corpus (13)
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Random Matrix Theories in Quantum Physics: Common Concepts
- Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
- Approximating the largest eigenvalue of network adjacency matrices
- Misleading signatures of quantum chaos
- Universality in Complex Networks: Random Matrix Analysis
- Spectral Analysis and the Dynamic Response of Complex Networks
- Random Matrix Spectra as a Time Series
- Unfolding of the Spectrum for Chaotic and Mixed Systems
- Spectral transitions in networks
- Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks
- Level statistics for nearly integrable systems
Cited by in corpus (6)
- Spacing ratio characterization of the spectra of directed random networks
- Signatures of quantum chaos in low-energy mixtures of few fermions
- Normal mode analysis of spectra of random networks
- Entropy and Temperature in finite isolated quantum systems
- Localization transitions in quadratic systems without quantum chaos
- Normal mode analysis of disordered random-matrix ensembles