Related papers: Anomalously Localized States in the Anderson Model
Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal…
We study statistical properties of the ensemble of large $N\times N$ random matrices whose entries $ H_{ij}$ decrease in a power-law fashion $H_{ij}\sim|i-j|^{-\alpha}$. Mapping the problem onto a nonlinear $\sigma-$model with non-local…
The one-dimensional (1d) Anderson model (AM) has statistical anomalies at any rational point $f=2a/\lambda_{E}$, where $a$ is the lattice constant and $\lambda_{E}$ is the de Broglie wavelength. We develop a regular approach to anomalous…
Mosaic lattice models have been recently introduced as a special class of disordered systems displaying resonance energies, multiple mobility edges and anomalous transport properties. In such systems on-site potential disorder, either…
Ammann-Beenker lattice is a two-dimensional quasicrystal with eight-fold symmetry, which can be described as a projection of a cut from a four-dimensional simple cubic lattice. We consider the vertex tight-binding model on this lattice and…
Anderson localization is a fundamental phenomenon in disordered quantum systems, where transport is suppressed by wave interference from extensive randomness. Moving beyond traditional multi-impurity scenarios, we investigate…
We investigate, both experimentally and theoretically, possible routes towards Anderson-like localization of Bose-Einstein condensates in disordered potentials. The dependence of this quantum interference effect on the nonlinear…
The spectra of particles in disordered lattices can either be completely extended or localized or can be intermediate which hosts both the localized and extended states separated from each other. In this work, however, we show that in the…
Mobility edge transitions from localized to extended states have been observed in two and three dimensional systems, for which sound theoretical explanations have also been derived. One-dimensional lattice models have failed to predict…
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 spreading of initially localized states in a nonlinear disordered lattice described by the nonlinear Schr\"odinger equation with random on-site potentials - a nonlinear generalization of the Anderson model of localization. We…
Wave localization is a fundamental phenomenon that appears universally in both natural materials and artificial structures and plays a crucial role in understanding the various physical properties of a system. Usually, a localized state has…
According to the Onsager's semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this…
Anderson localization does not lead to an exponential decay of intensity of an incident wave with the depth inside a strongly disordered three-dimensional medium. Instead, the average intensity is roughly constant in the first half of a…
By the certain macroscopic perturbations in condensed matter anomalous electron wells can be formed due to a local reduction of electromagnetic zero point energy. These wells are narrow, of the width $\sim 10^{-11}cm$, and with the depth…
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…
Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus ("arithmetic random waves"). We study…
Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the…
We frame the transverse Anderson localization of light in a one-dimensional disordered optical lattice in the language of localized propagating eigenmodes. The modal analysis allows us to explore localization behavior of a disordered…
Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system can usually not be chosen or controlled. We show that the unique control available for ultracold atomic gases…