Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles

Sarkar, Ayana; Kothiyal, Manuja; Kumar, Santosh

doi:10.1103/physreve.101.012216

Cited by 23 publications

(15 citation statements)

References 91 publications

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“…Prior studies on real and complex spacing ratios arising from Hermitian and non-Hermitian systems, respectively, have shown that such measures are able to distinguish between integrable and chaotic spectra, see e.g. [22,[43][44][45]. Here we showed that the same quantities can also differentiate the disconnected phase ( k < 1), in which the directed network is divided into several small components, and the phase ( k > 1), giant component connecting the majority of the emerges.…”

Section: Discussionmentioning

confidence: 99%

Spacing ratio characterization of the spectra of directed random networks

Peron,

de Resende,

Rodrigues

et al. 2020

Preprint

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Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however, depends crucially on eigenvalue unfolding procedures, which in many situations represent a major hindrance due to constraints in the calculation, specially in the case of complex spectra. Here we study the spectra of directed networks using the recently introduced ratios between nearest-and next-to-nearest eigenvalue spacing, thus circumventing the shortcomings imposed by spectral unfolding. Specifically, we characterize the eigenvalue statistics of directed Erdős-Rényi (ER) random networks by means of two adjacency matrix representations; namely (i) weighted non-Hermitian random matrices and (ii) a transformation on non-Hermitian adjacency matrices which produces weighted Hermitian matrices. For both representations, we find that the distribution of spacing ratios becomes universal for a fixed average degree, in accordance with undirected random networks. Furthermore, by calculating the average spacing ratio as a function of the average degree, we show that the spectral statistics of directed ER random networks undergoes a transition from Poisson to Ginibre statistics for model (i) and from Poisson to Gaussian Unitary Ensemble statistics for model (ii). Eigenvector delocalization effects of directed networks are also discussed.

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Section: Discussionmentioning

confidence: 99%

Spacing ratio characterization of the spectra of directed random networks

Peron,

de Resende,

Rodrigues

et al. 2020

Preprint

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“…One way to avoid the problem of unfolding is by using the idea of the ratio of two consecutive level spacings which is independent of the local density of states, and it does not require unfolding [44,[65][66][67][68][69]].…”

Section: Proposed Studymentioning

confidence: 99%

A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories

Abdel-Mageed

Salim

Osamy

et al. 2021

Advances in Mathematical Physics

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The prime numbers have attracted mathematicians and other researchers to study their interesting qualitative properties as it opens the door to some interesting questions to be answered. In this paper, the Random Matrix Theory (RMT) within superstatistics and the method of the Nearest Neighbor Spacing Distribution (NNSD) are used to investigate the statistical proprieties of the spacings between adjacent prime numbers. We used the inverse χ 2 distribution and the Brody distribution for investigating the regular-chaos mixed systems. The distributions are made up of sequences of prime numbers from one hundred to three hundred and fifty million prime numbers. The prime numbers are treated as eigenvalues of a quantum physical system. We found that the system of prime numbers may be considered regular-chaos mixed system and it becomes more regular as the value of the prime numbers largely increases with periodic behavior at logarithmic scale.

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“…The distribution intermediate of Poisson and GOE is described by Brody distribution [27]. Recently, intermediate semi-poissonian statistics [28] and crossover random matrix ensembles [29] are also reported. Going beyond this, recently, the distribution of the closest neighbor (CN) spacing, s CN and farther neighbor (FN) spacing, s F N from a given level are introduced [30].…”

Section: Introductionmentioning

confidence: 99%

Ordered Level Spacing Distribution in Embedded Random Matrix Ensembles

Rao,

Deota,

Chavda

2021

Preprint

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Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles

Cited by 23 publications

References 91 publications

Spacing ratio characterization of the spectra of directed random networks

Spacing ratio characterization of the spectra of directed random networks

A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories

Ordered Level Spacing Distribution in Embedded Random Matrix Ensembles

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