Related papers: Classical Representation of the 1D Anderson Model
A new super-symmetric representation for quantum disordered systems is derived. This representation is exact and is dual to that of the nonlinear sigma-model. The new formalism is tested by calculating the distribution of wave function…
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…
The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus…
Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold…
The statistics of eigenfunction amplitudes are studied in mesoscopic disordered electron systems of finite size. The exact eigenspectrum and eigenstates are obtained by solving numerically Anderson Hamiltonian on a three-dimensional lattice…
We consider the Anderson model at large disorder on $\mathbb{Z}^2$ where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These…
In a recent publication, J. Phys.: Condens. Matt. 14 13777 (2002), Kuzovkov et. al. announced an analytical solution of the two-dimensional Anderson localisation problem via the calculation of a generalised Lyapunov exponent using signal…
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 analyze the conductance distribution function in the one-dimensional Anderson model of localization, for arbitrary energy. For energy at the band center the distribution function deviates from the universal form assumed in…
The entanglement in one-dimensional Anderson model is studied. We show that the pairwise entanglement measured by the average concurrence has a direct relation to the localization length. The numerical study indicates that the disorder…
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…
Topological Anderson transitions, which are direct phase transitions between topologically distinct Anderson localised phases, allow for criticality in 1D disordered systems. We analyse the statistical properties of an emsemble of critical…
We consider a system of two discrete quasiperiodic 1D particles as an operator on $\ell^2(\mathbb Z^2)$ and establish Anderson localization at large disorder, assuming the potential has no cosine-type symmetries. In the presence of…
Several aspects of interplay between Anderson localization and coherent amplification/absorption, and aspect of mirrorless laser for a laser-active (amplifying) disordered dielectric medium have been addressed. We have calculated the…
Based on a selfconsistent theory of localization we study the electron transport properties of a disordered system in the framework of the Anderson model on a Bethe lattice. In the calculation of the dc conductivity we separately discuss…
A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to ohmic behavior when applied to the one-dimensional Anderson model. Here…
The one parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show this theory can be adapted to the context of quantum chaos provided that the classical phase space…
We consider time-dependent perturbations which are relatively bounded with respect to the square root of an unperturbed Hamiltonian operator, and whose commutator with the latter is controlled by the full perturbed Hamiltonian. The…
These lectures present some basic ideas and techniques in the spectral analysis of lattice Schrodinger operators with disordered potentials. In contrast to the classical Anderson tight binding model, the randomness is also allowed to…
We investigate light transport in three-dimensional disordered media composed of irregular dielectric particles using large scale full-wave simulations. For subwavelength particles with size parameter $kr \approx 1$ and high refractive…