Related papers: Anderson transition for Google matrix eigenstates
We study the hierarchical analogue of power-law random band matrices, a symmetric ensemble of random matrices with independent entries whose variances decay exponentially in the metric induced by the tree topology on $\mathbb{N}$. We map…
We present a comprehensive analysis of algebraic methods for controlling the stationary distribution of PageRank-like random walkers. Building upon existing literature, we compile and extend results regarding both structural control…
We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including…
Non-Hermitian random matrices provide a useful framework for understanding universal characteristics of dissipative quantum chaotic systems with loss or gain. We consider a model of two such system represented by two independent $N\times N$…
Anderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for {dynamical localization}. In the one-dimensional Hermitian Anderson model with uncorrelated diagonal…
The localization behavior of the Anderson model with anisotropic hopping integral t for weakly coupled planes and weakly coupled chains is investigated both numerically with the transfer matrix method and analytically within the…
By means of variable moment kernel polynomial method, we analyze the localization properties of $\beta$-graphyne sheet subjected to the Anderson disorder. To detect the localization transition we focus on the scaling behavior of the…
We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…
We study the typical behavior of a generalized version of Google's PageRank algorithm on a large family of inhomogeneous random digraphs. This family includes as special cases directed versions of classical models such as the…
We investigate a two leg ladder system subjected to an external magnetic field. In the absence of a magnetic field, the system is described by a clean tight binding model, with no disorder in either the onsite potential or the hopping…
We theoretically investigate the effects of atomic defect related short-range disorders and electron-electron interactions on Anderson type localization and the magnetic properties of hexagonal armchair graphene quantum dots using an…
Chiral Random Matrix Theory has proven to describe the spectral properties of low temperature QCD very well. However, at temperatures above the chiral symmetry restoring transition it can not provide a global description. The level-spacing…
Disorder in a 1D quantum lattice induces Anderson localization of the eigenstates and drastically alters transport properties of the lattice. In the original Anderson model, the addition of a periodic driving increases, in a certain range…
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
We compute the distribution function of single-level curvatures, $P(k)$, for a tight binding model with site disorder, on a cubic lattice. In metals $P(k)$ is very close to the predictions of the random-matrix theory (RMT). In insulators…
We address Anderson localization of light in disordered optical lattices where the disorder strength varies across the transverse direction. Such variation changes the preferred domains where formation of localized eigenmodes is most…
Systems which can spontaneously reveal periodic evolution are dubbed time crystals. This is in analogy with space crystals that display periodic behavior in configuration space. While space crystals are modelled with the help of space…
Anderson localisation is an important phenomenon arising in many areas of physics, and here we explore it in the context of quantum information devices. Finite dimensional spin chains have been demonstrated to be important devices for…