Related papers: Analytic and numerical toolkit for the Anderson mo…
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…
We derive a field-theoretical representation for the moments of the eigenstates in the generalized Anderson model. The representation is exact and can be used for the Anderson model with generic non-random hopping elements in any…
In this paper we discuss the continuity properties of the integrated density of states for random models based on that of the single site distribution. Our results are valid for models with independent randomness with arbitrary free parts.…
A self-consistent theory of the frequency dependent diffusion coefficient for the Anderson localization problem is presented within the tight-binding model of non-interacting electrons on a lattice with randomly distributed on-site energy…
Anderson localization is known to be inevitable in one dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess "additional" integrals of motion as well, so…
We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…
We describe how to use quantum linear algebra to simulate a physically realistic model of disordered non-interacting electrons. The physics of disordered electrons outside of one dimension challenges classical computation due to the…
A simple Kronig-Penney model for one-dimensional (1D) mesoscopic systems with $\delta $ peak potentials is used to study numerically the influence of a spatial disorder on the conductance fluctuations and distribution at different regimes.…
Bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating density of states (DoS), multifractal properties of eigenstates and the localization length. DoS divergence at…
We study the disorder-induced localisation transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal…
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…
It is believed that the two-dimensional (2D) Anderson model exhibits localization for any nonzero disorder in the thermodynamic limit and it is also well known that the finite-size effects are considerable in the weak disorder limit. Here…
A conducting 1D chain or 2D film inside (or on the surface of) an insulator is considered. Impurities displace the charges inside the insulator. This results in a long-range fluctuating electric field acting on the conducting line (plane).…
Anderson localization is related to exponential localization of a particle in the configuration space in the presence of a disorder potential. Anderson localization can be also observed in the momentum space and corresponds to quantum…
A new approach is applied to the 1D Anderson model by making use of a two-dimensional Hamiltonian map. For a weak disorder this approach allows for a simple derivation of correct expressions for the localization length both at the center…
We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands…
We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are…
We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns…
We study the quantum localization phenomena of noninteracting particles in one-dimensional lattices based on tight-binding models with various forms of hopping terms beyond the nearest neighbor, which are generalizations of the famous…
We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…