Related papers: Disorder in Gauge/Gravity Duality, Pole Spectrum S…
Motivated by questions of present interest in nuclear and condensed matter physics we consider the superposition of a diagonal matrix with independent random entries and a GUE. The relative strength of the two contributions is determined by…
Level statistics is a crucial tool in the exploration of localization physics. The level spacing distribution of the disordered localized phase follows Poisson statistics, and many studies naturally apply it to the quasiperiodic localized…
We investigate numerically the statistical properties of spectra of two-dimensional disordered systems by using the exact diagonalization and decimation method applied to the Anderson model. Statistics of spacings calculated for system…
Contrary to the theoretical predictions that all waves in two-dimensional disordered materials are localized, Anderson localization is observed only for sufficiently high frequencies in an isotropically jammed two-dimensional disordered…
Spectral statistics of quantum systems have been studied in detail using the nearest neighbour level spacings, which for generic chaotic systems follows random matrix theory predictions. In this work, the probability density of the closest…
The statistical distribution of levels of an integrable system is claimed to be a Poisson distribution. In this paper, we numerically generate an ensemble of N dimensional random diagonal matrices as a model for regular systems. We evaluate…
We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
The level statistics in the two dimensional disordered electron systems in magnetic fields (unitary ensemble) or in the presence of strong spin-orbit scattering (symplectic ensemble) are investigated at the Anderson transition points. The…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
We study the statistics of level spacing of geometric resonances in the disordered binary networks. For a definite concentration $p$ within the interval $[0.2,0.7]$, numerical calculations indicate that the unfolded level spacing…
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…
We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the…
The energy level statistics of 2D electrons with spin-orbit scattering are considered near the disorder induced metal-insulator transition. Using the Ando model, the nearest-level-spacing distribution is calculated numerically at the…
We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders behaves in a way similar to that of the single parametric Brownian ensembles. The latter appear during aPoisson…
We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles…
Using the level--spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically…
Consider a measure $\mu_\lambda = \sum_x \xi_x \delta_x$ where the sum is over points $x$ of a Poisson point process of intensity $\lambda$ on a bounded region in $d$-space, and $\xi_x$ is a functional determined by the Poisson points near…
The effects of dilution disorder and random-displacement disorder are analyzed for dipolar-coupled magnetic moments confined in a plane, which were originally placed on the square lattice. In order to distinguish the different phases, new…
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness…