Related papers: Characterisation of Anderson localisation using di…
The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems.
We establish the phenomenon of Anderson localisation for a quantum two-particle system on a d-dimensional lattice with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.
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…
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…
Hyperbolic lattices, formed by tessellating the hyperbolic plane with regular polygons, exhibit a diverse range of exotic physical phenomena beyond conventional Euclidean lattices. Here, we investigate the impact of disorder on hyperbolic…
We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain \emph{typical local density of states} as an order parameter, thereby reproducing the essential features of a phase-diagram of…
We study the Anderson localization of atomic gases exposed to three-dimensional optical speckles by analyzing the statistics of the energy-level spacings. This method allows us to consider realistic models of the speckle patterns, taking…
We present a theory of Anderson localization on a one-dimensional lattice with translation-invariant hopping. We find by analytical calculation, the localization length for arbitrary finite-range hopping in the single propagating channel…
Localization of coherent propagating waves has been extensively studied over the years, primarily in homogeneous random media. However, significantly less attention has been given to wave localization in inhomogeneous systems, where the…
Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the…
A one-dimensional boundary of a two-dimensional topological superconductor can host a number of topologically protected chiral modes. Combining two topological superconductors with different topological indices, it is possible to achieve a…
As discovered by Philip Anderson in 1958, strong disorder can block propagation of waves and lead to the localization of wave-like excitations in space. Anderson localization of light is particularly exciting in view of its possible…
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…
Motivated by the analogy between many-body localization (MBL) and single-particle Anderson localization on hierarchical graphs, we study localization on the Husimi tree, a generalization of the Bethe lattice with a finite density of local…
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…
This paper considers the family of Schr\"odinger operators on $\ell^2(\mathbb{Z})$ given by independent but not necessarily identically distributed and possibly unbounded potentials. We assume a finite exponential moment and allow the…
We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity an unlimited spreading over the lattice…
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…
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…
Dyson insulators with random hoppings in a lattice approach localization faster compared to the usual Anderson insulators with site disorder. For even-$N$ lattice sites the Dyson insulators mimic topological insulators with a pseudo-gap at…