Exact distribution of spacing ratios for random and localized states in quantum chaotic systems

Tekur, S. Harshini; Kumar, Santosh; Santhanam, M. S.

doi:10.1103/physreve.97.062212

Cited by 26 publications

(9 citation statements)

References 66 publications

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“…[85,86], analytic expressions for the ratio distributions were obtained, including Wigner-like surmises for 3 × 3 matrices. The transition between Poisson and GOE statistics at the level of ratios [87], higher-order spacing ratios [86,[88][89][90][91] and nearest neighbor by nextto-nearest neighbor ratios (NN by NNN ratios) [63] have also been considered recently.…”

Section: Introductionmentioning

confidence: 99%

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

2020

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We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest-and next-to-nearest neighbor spacings. We show that this quantity can successfully detect the chaotic or regular nature of complex-valued spectra. This is done in two steps. First, we show that, if eigenvalues are uncorrelated, the distribution of complex spacing ratios is flat within the unit circle, whereas random matrices show a strong angular dependence in addition to the usual level repulsion. The universal fluctuations of Gaussian Unitary and Ginibre Unitary universality classes in the large-matrix-size limit are shown to be well described by Wigner-like surmises for small-size matrices with eigenvalues on the circle and on the two-torus, respectively. To study the latter case, we introduce the Toric Unitary Ensemble, characterized by a flat joint eigenvalue distribution on the two-torus. Second, we study different physical situations where nonhermitian matrices arise: dissipative quantum systems described by a Lindbladian, non-unitary quantum dynamics described by nonhermitian Hamiltonians, and classical stochastic processes. We show that known integrable models have a flat distribution of complex spacing ratios whereas generic cases, expected to be chaotic, conform to Random Matrix Theory predictions. Specifically, we were able to clearly distinguish chaotic from integrable dynamics in boundary-driven dissipative spin-chain Liouvillians and in the classical asymmetric simple exclusion process and to differentiate localized from delocalized phases in a nonhermitian disordered many-body system.

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Section: Introductionmentioning

confidence: 99%

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

2020

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“…In recent years, a number of generalizations have been added to the literature on higher-order level spacings [19][20][21][22][23][24][25][26] and non-hermitian Hamiltonians [27]. This short paper adds to the current literature by computing exact r-distribution functions for mixed Wigner surmises, such as two superimposed GUE spectra.…”

Section: Introductionmentioning

confidence: 99%

Exact gap-ratio results for mixed Wigner surmises of up to 4 eigenvalues

Fremling¹

2022

Preprint

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We compute some exact results for the gap-ratio of mixed Wigner surmises for up to four eigenvalues and 0 ≤ β ≤ 4. The main results concern equal mixtures of the GOE, GUE, and GSE random matrix classes. These give rise to 2×GOE, 2×GUE, and 2×GSE distributions. We find that 2×GOE, 2×GUE are well approximated by the surmises of only 2+2 eigenvalues that are GOE and GUE distributed, respectively. The same is not valid for 2×GSE, which is well estimated, by coincidence, by 2+2 eigenvalues of statistics intermediate between GUE and GSE.

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“…Variations of the spacing ratios have been studied in the recent past [23,[36][37][38]. In this work, we consider the non-overlapping k-th order spacing ratio, where no eigenvalue is shared between the spacings of numerator and denominator, defined as follows:…”

Section: Preliminariesmentioning

confidence: 99%

Superposition and higher-order spacing ratios in random matrix theory with application to complex systems

Bhosale

2019

Preprint

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Exact distribution of spacing ratios for random and localized states in quantum chaotic systems

Cited by 26 publications

References 66 publications

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

Exact gap-ratio results for mixed Wigner surmises of up to 4 eigenvalues

Superposition and higher-order spacing ratios in random matrix theory with application to complex systems

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