相关论文: A new approach to the analytic solution of the And…
We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from…
The Anderson localization problem in one and two dimensions is solved analytically via the calculation of the generalized Lyapunov exponents. This is achieved by making use of signal theory. The phase diagram can be analyzed in this way. In…
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the…
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the…
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…
Localization of wave functions in disordered systems can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is an analytic…
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.…
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…
We reply to comments by P.Marko$\breve{s}$, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…
We study Anderson transition for light in three dimensions by performing large-scale ab-initio simulations of electromagnetic wave transport in disordered ensembles of conducting spheres. A mobility edge that separates diffusive transport…
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…
Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…
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.…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. We find that off-diagonal one- and two-particle propagators behave as gaussian random variables w.r.t. momentum summations. With this…
The goal of this paper is two-fold. First, based on the interpretation of a quantum tight-binding model in terms of a classical Hamiltonian map, we consider the Anderson localization (AL) problem as the Fermi-Pasta-Ulam (FPU) effect in a…
Although it is recognized that Anderson localization takes place for all states at a dimension $d$ less or equal $2$, while delocalization is expected for hopping $V(r)$ decreasing with the distance slower or as $r^{-d}$, the localization…
We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized…
Taking into account that a proper description of disordered systems should focus on distribution functions, the authors develop a powerful numerical scheme for the determination of the probability distribution of the local density of states…