Related papers: Localization properties of the sparse Barrat-M\'ez…
We present an experimental signature of the Anderson localisation of microcavity polaritons, and provide a systematic study of the dependence on disorder strength. We reveal a controllable degree of localisation, as characterised by the…
The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…
In this paper, we use recent breakthroughs in the study of coupled subwavelength resonator systems to reveal new insight into the mechanisms responsible for the fundamental features of Anderson localization. The occurrence strong…
We present a thorough pedagogical analysis of the single particle localization phenomenon in a quasiperiodic lattice in one dimension. Description of disorder in the lattice is represented by the Aubry-Andr\'e model. Characterization of…
This work introduces a variant of resolvent analysis that identifies forcing and response modes that are sparse in both space and time. This is achieved through the use of a sparse principal component analysis (PCA) algorithm, which…
We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of…
Complex networks with directed, local interactions are ubiquitous in nature, and often occur with probabilistic connections due to both intrinsic stochasticity and disordered environments. Sparse non-Hermitian random matrices arise…
We study Anderson localization in a disordered potential combined with an inhomogeneous trap. We show that the spectrum displays both localized and extended states, which coexist at intermediate energies. In the region of coexistence, we…
We examine the localization properties of the 2D Anderson Hamiltonian with off-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we find states in…
We review recent works that relate entanglement of random vectors to their localization properties. In particular, the linear entropy is related by a simple expression to the inverse participation ratio, while next orders of the entropy of…
We theoretically investigate excitation dynamics in one-dimensional arrays of quantum emitters coupled to a waveguide, focusing on localization and long-time population trapping. By combining time-domain simulations with spectral analysis…
Information of localization properties of eigenvectors of the complex network has applicability in many different areas which include networks centrality measures, spectral partitioning, development of approximation algorithms, and disease…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
We derive exact expressions for the mean value of Meyer-Wallach entanglement Q for localized random vectors drawn from various ensembles corresponding to different physical situations. For vectors localized on a randomly chosen subset of…
We investigate two one-dimensional tight-binding models with disorder that have extended states at zero energy. We use exact and partial diagonalisation of the Hamiltonian to obtain the eigenmodes and the associated participation ratios,…
This work considers methods for imposing sparsity in Bayesian regression with applications in nonlinear system identification. We first review automatic relevance determination (ARD) and analytically demonstrate the need to additional…
We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral…
We consider the class of spatially decaying systems, where the underlying dynamics are spatially decaying and the sensing and controls are spatially distributed. This class of systems arise in various applications where there is a notion of…
A growing intuition in machine learning suggests a link between sparsity and interpretability. We introduce a novel self-ablation mechanism to investigate this connection ante-hoc in the context of language transformers. Our approach…
In sufficiently strong scattering media, light transport is suppressed and modes are exponentially localized. Anderson-like localized states have long been recognized as potential candidate for high-Q optical modes for low-threshold, cost…