Pseudo-Hermitian ensemble of random Gaussian matrices

Marinello, G.; Pato, M. P.

doi:10.1103/physreve.94.012147

Cited by 10 publications

(21 citation statements)

References 26 publications

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“…As expected, the ellipse is widened for increasing disorder. This elliptical pattern, instead of a circular one, is a consequence of the existence of the real nearest-neighbor couplings 82,83 . We can also observe that, in general, the modes around the center of the elliptical pattern are the most extended (c) W=5 Figure 1.…”

Section: Non-hermitian Disorder In Coupled Systemsmentioning

confidence: 93%

Non-Hermitian disorder in two-dimensional optical lattices

2020

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In this paper, we study the properties of two-dimensional lattices in the presence of non-Hermitian disorder. In the context of coupled mode theory, we consider random gain-loss distributions on every waveguide channel (on site disorder). Our work provides a systematic study of the interplay between disorder and non-Hermiticity. In particular, we study the eigenspectrum in the complex frequency plane and we examine the localization properties of the eigenstates, either by the participation ratio or the level spacing, defined in the complex plane. A modified level distribution function vs disorder seems to fit our computational results. arXiv:1909.13816v1 [cond-mat.dis-nn]

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Section: Non-hermitian Disorder In Coupled Systemsmentioning

confidence: 93%

Non-Hermitian disorder in two-dimensional optical lattices

2020

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“…which can distort a symmetric matrix into pseudosymmetric matrix P (k) = (R + R t )K, note that KP K −1 = P t , namely, P (k) are pseudo-symmetric under K. This metric has also been utilized earlier [18]. Another class of pseudo-symmetric matrices is Q(k) which is distortion a symmetric matrix by a factor k as…”

Section: Various Real Pseudo-symmetric Matricesmentioning

confidence: 99%

“…The fact that real symmetric and Hermitian random matrices make two separate classes of ensembles GOE and GUE having distinct statistical properties, motivates us to separate pesudo-symmetric real matrices from the more general pseudo-Hermitian matrices [16][17][18][19]. In the present work, we invoke a lesser class of matrices which are real pseudo-symmetric under a metric η such that ηHη −1 = H t , these are essentially non-symmetric ones.…”

Section: Introductionmentioning

confidence: 99%

Pseudosymmetric random matrices: Semi-Poisson and sub-Wigner statistics

Kumar

Ahmed

2017

Phys. Rev. E

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Real non-symmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudo-symmetric as ηM η −1 = M t , where the metric η could be secular (a constant matrix) or depending upon the matrix elements of M . Here, we construct ensembles of a large number N of pseudo-symmetric n × n (n large) matrices using N (n(n + 1)/2 ≤ N ≤ n 2 ) independent and identically distributed (iid) random numbers as their elements. Based on our numerical calculations, we conjecture that for these ensembles the Nearest Level Spacing Distributions (NLSDs: p(s)) are sub-Wigner as p abc (s) = ase −bs c (0 < c < 2) and the distributions of their eigenvalues fit well to D( ) = A[tanh{( + B)/C} − tanh{( − B)/C}] (exceptions also discussed). These sub-Wigner NLSD are encountered in Anderson metal-insulator transition and topological transitions in a Josephson junction. Interestingly, p(s) for c = 1 is called semi-Poisson and we show that it lies close to the form p(s) = 0.59sK0(0.45s 2 ) derived for the case of 2 × 2 pseudo-symmetric matrix where the eigenvalues are most aptly conditionally real: E1,2 = a ± √ b 2 − c 2 which represent characteristic coalescing of eigenvalues in PT(Parity-Time)-symmetric systems.

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“…12, it is shown that for the pHGOE class, the result can be fitted with both Eqs. (11) and (10), yielding a value compatible with µ = 2 which implies in a cubic repulsion. In Fig.…”

Section: B Complex Eigenvalues Statisticsmentioning

confidence: 96%

“…From the matrices of these ensembles, an ensemble of pseudo-Hermtian Gaussian matrices can be constructed as [10,11] A = P HP + QHQ + r(P HQ − QHP ),…”

Section: Overview Of the Pseudo-hermitian Gaussian Ensemble Stud-iedmentioning

confidence: 99%

Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices

Marinello

Pato

2019

Phys. Scr.

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We investigate the statistical properties of eigenvalues of pseudo-Hermitian random matrices whose eigenvalues are real or complex conjugate. It is shown that when the spectrum splits into separated sets of real and complex conjugate eigenvalues, the real ones show characteristics of an intermediate incomplete spectrum, that is, of a so-called thinned ensemble. On the other hand, the complex ones show repulsion compatible with cubic-order repulsion of non normal matrices for the real matrices, but higher order repulsion for the complex and quaternion matrices.

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Pseudo-Hermitian ensemble of random Gaussian matrices

Cited by 10 publications

References 26 publications

Non-Hermitian disorder in two-dimensional optical lattices

Non-Hermitian disorder in two-dimensional optical lattices

Pseudosymmetric random matrices: Semi-Poisson and sub-Wigner statistics

Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices

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