Related papers: Experimental observation of the mobility edge in a…
It is shown that a non-periodic Kronig-Penney model exhibits mobility edges if the positions of the scatterers are correlated at long distances. An analytical expression for the energy-dependent localization length is derived for weak…
We analyse the single-mode transmission of microwaves in a guide with internal random structure. The waveguide contains scatterers characterised by random heights and positions, corresponding to compositional and structural disorder. We…
We present analytical results on transport properties of many-mode waveguides with randomly stratified disorder having long-range correlations. To describe such systems, the theory of 1D transport recently developed for a correlated…
This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the…
We study the effects of random positional disorder in the transmission of waves in a 1D Kronig-Penny model. For weak disorder we derive an analytical expression for the localization length and relate it to the transmission coefficient for…
Wave propagation in complex media is a universal problem spanning optics, acoustics, mechanics, and condensed matter physics. While disorder usually causes strong scattering, recent theory predicts that a special class of correlated…
Transport properties of one-dimensional Kronig-Penney models with binary correlated disorder are analyzed using an approach based on classical Hamiltonian maps. In this method, extended states correspond to bound trajectories in the phase…
Tight-binding 1D random system with long-range correlations is studied numerically using the localisation criterium, which represents the number of sites, covered by the wave function. At low degrees of disorder the signs of a mobility…
We study the one-dimensional tight-binding model with quasi-periodic disorders, where the quasi-period is tuned to be very large. It is found that this type of model with large quasi-periodic disorders can also support the mobility edges,…
We present first analytical results on transport properties of many-mode waveguides with rough surfaces having long-range correlations. We show that propagation of waves through such waveguides reveals a quite unexpected phenomena of a…
Periodic and disordered media are known to possess different transport properties, either classically or quantum-mechanically. This has been exhibited by effects such as Anderson localization in systems with disorder and the existence of…
We study the mobility edges in a variety of one-dimensional tight binding models with slowly varying quasi-periodic disorders. It is found that the quasi-periodic disordered models can be approximated by an ensemble of periodic models. The…
We introduce a theoretical formalism to describe disorder-induced extrinsic scattering in slow-light photonic crystal waveguides. This work details and extends the optical scattering theory used in a recent \emph{Physical Review Letter} [M.…
We study the one-dimensional tight-binding models which include a slowly varying, incommensurate off-diagonal modulation on the hopping amplitude. Interestingly, we find that the mobility edges can appear only when this off-diagonal…
The main purpose of the present paper is to introduce a scattering approach to the study of the Kronig-Penney model in a quadratic channel with $\delta$ interactions, which was discussed in full generality in the first paper of the present…
Nonlinear Kronig-Penney model has been frequently employed to study transmission problem of electron wave in a nonlinear electrified chain or in a doped semiconductor superlattice. Here from an integral equation we derive a novel exact…
Here we present a simple extension to the age-old Kronig-Penney model, which is made to be bipartite by varying either the scatterer separations or the potential heights. In doing so, chiral (sublattice) symmetry can be introduced. When…
The correlated motion of electrons in a one dimensional system with an externally applied longitudinal electric field is discussed. Within the tight binding model we show that in addition to the well known Bloch oscillations the…
We provide a derivation of the tight-binding model that emerges from a full consideration of a particle bound in a periodic one-dimensional array of square well potentials, separated by barriers of height $V_0$ and width $b$. We derive the…
We analyse the anomalous properties of specific electronic states in the Kronig-Penney model with weak compositional and structural disorder. Using the Hamiltonian map approach, we show that the localisation length of the electronic states…