Related papers: Localization in one-dimensional chains with L\'evy…
The existence of Anderson localization, characterized by vanishing diffusion due to strong disorder, has been demonstrated in numerous ways. A systematic approach based on the Anderson quantum model of the Fermi gas in random lattices that…
We study numerically a spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schr\"odinger lattice with disorder. We demonstrate that above a certain critical strength of nonlinearity the Anderson…
We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic…
We study theoretically Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potential. We focus explicitly on the effect of disorder correlations, considering a short-range…
We study localization in two- and three channel quasi-1D systems using multichain tight-binding Anderson models with nearest-neighbour interchain hopping. In the three chain case we discuss both the case of free- and that of periodic…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
The recent realization of a "Levy glass" (a three-dimensional optical material with a Levy distribution of scattering lengths) has motivated us to analyze its one-dimensional analogue: A linear chain of barriers with independent spacings s…
We study elastic electron scattering and localization by ubiquitous isotopic disorder in one-dimensional systems appearing due to interaction with phonon modes localized at isotope impurities. By using a tight-binding model with intersite…
We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical…
We study numerically the transport and localization properties of waves in ordered and disordered ladder-shaped lattices with local $\mathcal{PT}$ symmetry. Using a transfer matrix method, we calculate the transmittance and the reflectance…
Anderson localization of wave-functions at zero energy in quasi-1D systems of $N$ disordered chains with inter-chain coupling $t$ is examined. Localization becomes weaker than for the 1D disordered chain ($t=0$) when $t$ is smaller than the…
The phenomenon of electronic wave localization through disorder was introduced by Anderson in 1958 in the context of electron transport in solids. It remains an important area of fundamental and applied research. Localization of all wave…
We study the localization of classical waves in weakly scattering 2D systems with anisotropic disorder. The analysis is based on a perturbative path-integral technique combined with a spectral filtering that accounts for the first-order…
Quantum particles in a disordered potential, photons or classical waves in a random medium, or the universe expansion in a fluctuating cosmic field, all share Anderson localization as a communality. In general, localization is enhanced for…
We show that electron states in disordered graphene, with an onsite potential that induces inter-valley scattering, are localised for all energies at disorder as small as 1/6 of the band width of clean graphene. We clarify that, in order…
L\'evy flights constitute a broad class of random walks that occur in many fields of research, from animal foraging in biology, to economy to geophysics. The recent advent of L\'evy glasses allows to study L\'evy flights in controlled way…
It is considered an equation for the Lyapunov exponent $% \gamma $ in a random metric for a scalar propagating wave field. At first order in frequency this equation is solved explicitly. The localization length $L_{c}$ (reciprocal of…
We have developed an approach allowing us to resolve the problem of non-conventional Anderson localization emerging in bilayered periodic-on-average structures with alternating layers of right-handed and left-handed materials. Recently, it…
We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can…
Diffusive transport is among the most common phenomena in nature [1]. However, as predicted by Anderson [2], diffusion may break down due to interference. This transition from diffusive transport to localization of waves should occur for…