Related papers: Scattering approach to Anderson localisation
Anderson localization was discovered 50 years ago to describe the propagation of electrons in the presence of disorder. The main prediction back then, was the existence of disorder induced localized states, which do not conduct electricity.…
Anderson localization marks a halt of diffusive wave propagation in disordered systems. Despite extensive studies over the past 40 years, Anderson localization of light in three dimensions has remained elusive, leading to the question of…
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated…
We study the nonlinear Schr\"odinger equation posed on product spaces $\mathbf R^n\times \mathcal M^k$, for $n\geq 1$ and $k\geq1$, with $\mathcal M^k$ any $k$-dimensional compact Riemaniann manifold. The main results concern global…
We discuss a model of random segmented wire, with linear segments of 2D wires joined by circular bends. The joining vertices act as scatterers on the propagating electron waves. The model leads to resonant Anderson localization when all…
The parabolic Anderson model is the Cauchy problem for the heat equation on the integer lattice with a random potential $\xi$. We consider the case when $\{\xi(z):z\in\mathbb{Z}^d\}$ is a collection of independent identically distributed…
We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…
We propose a novel method to accelerate Lloyd's algorithm for K-Means clustering. Unlike previous acceleration approaches that reduce computational cost per iterations or improve initialization, our approach is focused on reducing the…
Continuous One-dimensional models supporting extended states are studied. These delocalized statesoccur at well defined values of the energy and are consequences of simple statistical correlation rules. We explicitly study alloys of…
The three-dimensional Anderson model with a rectangular distribution of site disorder displays two distinct localization-delocalization transitions, against varying disorder intensity, for a relatively narrow range of Fermi energies. Such…
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…
Anderson localization of light is a fundamental emergent phenomenon in disordered systems. In arrays of coupled waveguides, it suppresses transport and causes photons to remain localized near the excitation site as coupling disorder…
The Douglas--Rachford and Peaceman--Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable…
The localization length has been derived for one-dimensional bi-layered structures with random perturbations in the refractive indices for each type of layers. Main attention is paid to the comparison between conventional materials and…
We theoretically demonstrate features of Anderson localization in the Tonks-Girardeau gas confined in one-dimensional (1D) potentials with controlled disorder. That is, we investigate the evolution of the single particle density and…
We study the dependence on the spatial dimensionality of different quantities relevant in the description of the Anderson transition by combining numerical calculations in a $3 \leq d \leq 6$ disordered tight binding model with theoretical…
We consider wave propagation in a complex structure coupled to a finite number $N$ of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the…
Anderson localization is a regime in which diffusion is inhibited and waves (also electromagnetic waves) get localized. Here we exploit adaptive optics to achieve focusing in disordered optical fibers in the Anderson regime. By wavefront…
A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few $M$ frequencies a normal diffusion is realized, but the transition to…
We investigate a celebrated problem of one dimensional tight binding model in the presence of disorder leading to Anderson localization from a novel perspective. A binary disorder is assumed to be created by immobile heavy particles for the…