Related papers: Wavefunction extreme value statistics in Anderson …
Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an…
The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional…
The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not…
We study the spatial structure of wave functions with exceptionally high local amplitudes in the Anderson model of localisation. By means of exact diagonalisations of finite systems, we obtain and analyse images of these wave functions: we…
We investigate the wave-packet dynamics of the power-law bond disordered one-dimensional Anderson model with hopping amplitudes decreasing as $H_{nm}\propto |n-m|^{-\alpha}$. We consider the critical case ($\alpha=1$). Using an exact…
We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed…
We investigate dynamical scaling properties of the 1D tight-binding Anderson model with a weak diagonal disorder, by means of the spreading of a wave packet. In the absence of disorder, and more generally in the ballistic regime, the…
We investigate the scaling properties of the two-dimensional (2D) Anderson model of localization with purely off-diagonal disorder (random hopping). In particular, we show that for small energies the infinite-size localization lengths as…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when…
We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the…
The distribution function of local amplitudes of single-particle states in disordered conductors is calculated on the basis of the supersymmetric $\sigma$-model approach using a saddle-point solution of its reduced version. Although the…
We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a…
The scaling properties of the wave functions in finite samples of the one dimensional Anderson model are analyzed. The states have been characterized using a new form of the information or entropic length, and compared with analytical…
The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared.…
In linear disordered systems Anderson localization makes any wave packet stay localized for all times. Its fate in nonlinear disordered systems is under intense theoretical debate and experimental study. We resolve this dispute showing that…
We conduct a numerical investigation into wave propagation and localization in one-dimensional lattices subject to nonlinear disorder, focusing on cases with fixed input conditions. Utilizing a discrete nonlinear Schr\"odinger equation with…
We investigate the one-dimensional propagation of waves in the Anderson localization regime, for a single-mode, surface disordered waveguide. We make use of both an analytical formulation and rigorous numerical simulation calculations. The…
To characterize a destruction of Anderson localization by nonlinearity, we study the spreading behavior of initially localized states in disordered, strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized linear or…
Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for the random on-site potential. We demonstrate that already in leading…