Article
Physics, Multidisciplinary
Cleverson A. Goulart, Mauricio P. Pato
Summary: The Dyson index, beta, plays a crucial role in random matrix theory by labeling ensembles' symmetries under unitary transformations. It measures the number of independent non-diagonal variables, with its values denoting orthogonal, unitary, and symplectic classes. In the case of beta ensembles, it can assume any positive value, losing its original function. However, non-Hermitian matrices can behave asymptotically as if they were generated with a value 2 beta when the Hermitian condition is removed, making the beta index operative again. This effect is observed in the beta-Hermite, beta-Laguerre, and beta-Jacobi ensembles.
Article
Optics
Hamed Ghaemi-Dizicheh, Henning Schomerus
Summary: This study is based on a general transport theory for nonreciprocal non-Hermitian systems and a topological model, providing conditions for various effects and determining their compatibility and tunability. It establishes distinct transport signatures of non-Hermitian, nonreciprocal, and topological behavior, such as reflectionless transport in a direction that depends on the topological phase and coherent perfect absorption in a system that is transparent when probed from one side.
Article
Mathematics, Applied
Dan Hu, Hajo Broersma, Jiangyou Hou, Shenggui Zhang
Summary: This paper investigates the asymptotic behavior of eigenvalues of the Hermitian adjacency matrix of random mixed graphs, presents and proves a separation result between the eigenvalues, and estimates the Hermitian spectral moments.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2022)
Article
Statistics & Probability
Kyle Luh, Sean O'Rourke
Summary: The study focused on the eigenvectors and eigenvalues of random matrices with iid entries, providing small ball probability bounds for linear combinations of unit eigenvectors. Generalizing previous works on random symmetric matrices, optimal estimates for the probability of simple spectrum in iid matrices were improved. The techniques also applied to establishing similar results for the adjacency matrix of a random directed graph, leading to controllability properties in network control systems on directed graphs.
ELECTRONIC JOURNAL OF PROBABILITY
(2021)
Article
Physics, Multidisciplinary
Cem Yuce
Summary: The combination of non-Hermitian skin effect and nonlinear effects can lead to novel phenomena, which may be utilized in nonlinear structure designs. In some cases, nonlinear non-Hermitian skin effect can give rise to fractal and continuum bands at the edges. The nonlinear exceptional point may disappear in an infinitely long lattice.
Article
Automation & Control Systems
Alexander Davydov, Saber Jafarpour, Francesco Bullo
Summary: This article investigates the necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. It introduces weak pairings as a framework for studying contractivity, establishes five equivalent characterizations for contraction, and extends the contraction framework to include continuous vector fields. The article also provides applications related to input-to-state stability and Lipschitz interconnection of contracting systems.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Physics, Fluids & Plasmas
Ioachim G. Dusa, Tilo Wettig
Summary: This study introduces complex spacing ratios for analyzing eigenvalue correlations in non-Hermitian systems and provides an approximate formula for the Ginibre universality class of random matrix theory, yielding results for the probability distribution of these ratios in the limit of large system size.
Article
Physics, Fluids & Plasmas
Adway Kumar Das, Anandamohan Ghosh
Summary: Centrosymmetry plays an important role in various complex systems, and we introduce the deformed centrosymmetric ensemble and propose two quantities to quantify centrosymmetry. By precisely controlling the extent of centrosymmetry, we study its manifestation on the transport properties of complex networks.
Article
Physics, Mathematical
Tamara Grava, Massimo Gisonni, Giorgio Gubbiotti, Guido Mazzuca
Summary: In this study, we investigate the properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. We provide an exact description of the limit density of states for the exponential Toda lattice and the Volterra lattice in the high temperature regime, and numerically derive the density of states for other systems.
JOURNAL OF STATISTICAL PHYSICS
(2023)
Article
Chemistry, Physical
Sangchul Oh, Sabre Kais
Summary: This study analyzes the statistical properties of bit strings sampled from Sycamore random circuits and finds that they show stripe patterns at specific qubits and have more bit 1 than 0 compared to classical random bit strings. The calculation of random matrices and Wasserstein distances also reveals that the Sycamore bit strings are farther from bit strings sampled from Haar-measure random quantum circuits than classical random bit strings.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2022)
Article
Materials Science, Multidisciplinary
Christian P. Chen, Henning Schomerus
Summary: By adopting a geometric perspective on Fock space, this study provides insights into the eigenstates in many-body localized fermionic systems. It reveals that individual many-body localized eigenstates can be well approximated by a Slater determinant of single-particle orbitals, while the orbitals of different eigenstates in a given system exhibit varying degrees of compatibility. This incompatibility between states of fixed and differing particle number, as well as inside and outside the many-body localized regime, offers detailed insights into the emergence and nature of quasiparticlelike excitations in such systems.
Article
Physics, Condensed Matter
Yi-Bin Guo, Yi-Cong Yu, Rui-Zhen Huang, Li-Ping Yang, Run-Ze Chi, Hai-Jun Liao, Tao Xiang
Summary: The study investigates the entanglement properties of non-Hermitian free fermionic models with translation symmetry using the correlation matrix technique, revealing a logarithmic correction to the area law in both one-dimensional and two-dimensional systems. In particular, for one-dimensional one-band systems, each Fermi point contributes exactly 1/2 to the coefficient c of the logarithmic correction. Numerical calculations and finite-size scaling analysis confirm this relation between c and Fermi point in more general one-dimensional and two-dimensional cases. Additionally, the study also explores single-particle and density-density correlation functions.
JOURNAL OF PHYSICS-CONDENSED MATTER
(2021)
Article
Materials Science, Multidisciplinary
Dechi Peng, Shujie Cheng, Gao Xianlong
Summary: In this paper, the authors study a non-Hermitian Aubry-Andre-Harper model with power law hoppings and quasiperiodic parameter. They find that the number of a-dependent regimes depends on the strength of the non-Hermiticity. They also investigate the presence of two types of edges in the single-particle spectrum, which are related to the power law index a. Through analysis and specific examples, they reveal the intermediate phase and locate the ergodic-to-localized edge.
Article
Mathematics, Applied
Dan Hu, Hajo Broersma, Jiangyou Hou, Shenggui Zhang
Summary: This paper focuses on studying the spectra of the Hermitian adjacency matrix and the normalized Hermitian Laplacian matrix of general random mixed graphs, deriving new probability inequalities and upper bounds on eigenvalues. The research also shows that the eigenvalues of the normalized Hermitian Laplacian matrix can be approximated by a closely related weighted expectation matrix, with error bounds depending on the minimum expected degree of the underlying undirected graph.
ELECTRONIC JOURNAL OF COMBINATORICS
(2021)
Article
Mathematics, Applied
Peter Benner, Xin Liang, Suzana Miodragovic, Ninoslav Truhar
Summary: This paper presents new relative perturbation bounds for eigenvectors and eigenvalues of regular quadratic eigenvalue problems, applying to various applications and demonstrating the quality of the bounds through numerical experiments.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Physics, Condensed Matter
Sergey E. Skipetrov
EUROPEAN PHYSICAL JOURNAL B
(2020)
Article
Nanoscience & Nanotechnology
Benoit Tallon, Philippe Roux, Guillaume Matte, Jean Guillard, Sergey E. Skipetrov
Article
Materials Science, Multidisciplinary
Martin Lott, Philippe Roux, Leonard Seydoux, Benoit Tallon, Adrien Pelat, Sergey Skipetrov, Andrea Colombi
PHYSICAL REVIEW MATERIALS
(2020)
Article
Acoustics
Benoit Tallon, Philippe Roux, Guillaume Matte, Jean Guillard, Sergey E. Skipetrov
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2020)
Article
Physics, Multidisciplinary
Antton Goicoechea, John H. Page, Sergey E. Skipetrov
Summary: The study found that in an ensemble of resonant point scatterers embedded in an anisotropic background medium, localized modes have anisotropic spatial shapes, but their anisotropy is weaker than expected from purely geometric considerations. The modes with the longest lifetimes are the most anisotropic, and their anisotropy increases with the size of the disordered medium.
Article
Multidisciplinary Sciences
Benoit Tallon, Philippe Roux, Guillaume Matte, Jean Guillard, John H. Page, Sergey E. Skipetrov
Summary: The study observed a significant slowdown in acoustic wave transport in dense fish shoals in open-sea fish cages, with the energy transport velocity found to be about 10 times smaller than the speed of sound in water, indicating a slow transport of ultrasonic waves. While the swim bladder of the fish plays an important role in wave scattering, other organs must also be considered to explain the ultra-low energy transport velocities observed.
SCIENTIFIC REPORTS
(2021)
Article
Physics, Multidisciplinary
Nicholas Bender, Alexey Yamilov, Arthur Goetschy, Hasan Yilmaz, Chia Wei Hsu, Hui Cao
Summary: Diffusion makes it hard to predict and control wave transport in a medium. This study introduces the 'deposition matrix' to predict the ultimate limit on energy enhancement at any depth and finds that the maximum energy enhancement occurs at three-fourths the thickness of the diffusive system. Experimental verification confirms these predictions and reveals the mechanisms behind energy enhancement or suppression.
Article
Optics
Geoffroy J. Aubry, Nathan Fuchs, Sergey Skipetrov, Frank Scheffold
Summary: Frequency-dependent intensity correlation function measurements can be used to determine the optical turbidity of solid disordered dielectrics. We demonstrate how to apply this measurement method through a speckle frequency correlation experiment, and provide a practical example.
Correction
Optics
Geoffroy J. Aubry, Nathan Fuchs, Sergey Skipetrov, Frank Scheffold
Summary: This publisher's note provides a correction to Opt. Lett. 47, 1439 (2022).
Article
Optics
Shu Zhang, Jorn Peuser, Chi Zhang, Frederic Cardinaux, Pavel Zakharov, Sergey E. Skipetrov, Roberto Cerbino, Frank Scheffold
Summary: We propose a laser-speckle imaging technique called Echo speckle imaging (ESI) that can quantify the local dynamics in biological tissue and soft materials. With a noise level around or below 10% of the measured signal, the spatial resolution is not affected. This is achieved through unconventional speckle beam illumination, creating changing and statistically independent illumination conditions, significantly improving measurement accuracy. Control experiments on dynamically homogeneous and heterogeneous soft materials and tissue phantoms demonstrate the effectiveness of the method.
Article
Physics, Multidisciplinary
Alexey Yamilov, Sergey E. Skipetrov, Tyler W. Hughes, Momchil Minkov, Zongfu Yu, Hui Cao
Summary: Recent numerical calculations show that Anderson localization of light can be achieved in three dimensions with a random arrangement of metallic spheres, but not with dielectric ones. This finding challenges the existence of three-dimensional localization of light, which has remained elusive despite extensive studies over the past 40 years. The researchers conducted brute-force numerical simulations using advanced techniques and demonstrated the three-dimensional localization of vector electromagnetic waves in randomly assembled metallic spheres, highlighting the absence of localization in dielectric spheres.
Article
Physics, Multidisciplinary
R. Monsarrat, R. Pierrat, A. Tourin, A. Goetschy
Summary: In this article, an in-depth analysis of the order-to-disorder transition in 2D resonant systems is presented. The localization of 2D vector waves in the presence of correlated disorder is observed, while no localization is found for white noise disorder. The formation of pseudogaps in the density of states is associated with the localization phenomenon. Two complementary models are developed to explain these observations, providing explicit theoretical evaluations in agreement with numerical simulations. The generality of the framework allows for applications in various scattering systems.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Optics
S. E. Skipetrov, P. Wulles
Summary: We study the influence of disorder on topological phenomena in honeycomb lattices of atoms coupled by the electromagnetic field. Disorder can induce transitions between different topological phases and drive the system into a topological Anderson insulator state. The nontrivial topology of the photonic band structure can suppress Anderson localization of disorder-induced modes in the band gap of the ideal lattice. Moreover, disorder can open a topological pseudogap and introduce spatially localized modes in an otherwise topologically trivial system.
Article
Physics, Multidisciplinary
Pauline Boucher, Arthur Goetschy, Giacomo Sorelli, Mattia Walschaers, Nicolas Treps
Summary: This study investigates the transmission properties and efficiency evaluation methods of multi-plane light converters, finding that in the case of a large number of shaped modes, they behave like a random scattering medium with a limited number of controlled channels.
PHYSICAL REVIEW RESEARCH
(2021)
Article
Materials Science, Multidisciplinary
B. A. van Tiggelen, S. E. Skipetrov
Summary: In this paper, the elastic scattering of longitudinal electromagnetic waves in a medium filled with pointlike, electric dipoles is studied. Two new channels are created by the interference between longitudinal and transverse waves, with one allowing energy transport. Different transport mechanisms couple in the strongly scattering regime, imposing a minimum conductivity of electromagnetic waves and preventing Anderson localization of light in the medium. This study extends the self-consistent theory of localization and compares the predictions to numerical simulations.
