Related papers: Localization for One Dimensional, Continuum, Berno…
We consider a continuous one dimensional model of two charged interacting particles in a random potential. The electric repulsion is strictly one dimensional and it inhibits Anderson localization. In fact, the spectrum is continuous. The…
We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all ernergies in $(2,+\infty)$ except those in a discrete set, which leads to absence of…
The scaling theory of Anderson localization is based on a global conductance $g_L$ that remains a random variable of order O(1) at criticality. One realization of such a conductance is the Landauer transmission for many transverse channels.…
We use dynamic coherent backscattering to study one of the Anderson mobility gaps in the vibrational spectrum of strongly disordered three-dimensional mesoglasses. Comparison of experimental results with the self-consistent theory of…
Localization properties of non-interacting quantum particles in one-dimensional incommensurate lattices are investigated with an exponential short-range hopping that is beyond the minimal nearest-neighbor tight-binding model. Energy…
Distributions of inelastically scattered neutrons can be quantum dynamically described by a scattering kernel. We present an accurate and computationally efficient rejection method for sampling a given scattering kernel of any isotropic…
We present a new mechanism for generating exponential hierarchies in four-dimensional field theories inspired by Anderson localization in one dimension, exploiting an analogy between the localization of electron energy eigenstates along a…
We use trace class scattering theory to exclude the possibility of absolutely continuous spectrum in a large class of self-adjoint operators with an underlying hierarchical structure and provide applications to certain random hierarchical…
The linear system of differential equations for determination of transmission and reflection amplytudes of scattered electron in the field of one dimensional arbitrary potential is obtained. It is shown that in general the scattering…
We use the transfer tensor method to analyze localization and transport in simple disordered systems, specifically the Anderson and Aubry-Andr\'e-Harper models. Emphasis is placed on the memory effects that emerge when ensemble-averaging…
The Anderson model serves to study the absence of wave propagation in a medium in the presence of impurities, and is one of the most studied examples in the theory of quantum disordered systems. In these notes we give a review of the…
In this paper, we prove the Anderson localization near the spectral edge for some alloy-type Anderson-Bernoulli model on $\mathbb{Z}^d$ with exponential long-range hopping. This extends the work of Bourgain [Geometric Aspects of Functional…
The invariant imbedding evolution equations for the amplitude reflection and transmission coefficients of a disordered 1D chain are shown to follow from the continuum limit, for weak disorder, of recursion relations between reflection…
As a supplement of our previous work, we consider the localized region of the random Schroedinger operators on $l^2({\bf Z}^d)$ and study the point process composed of their eigenvalues and corresponding localization centers. For the…
Transport of coherent waves in multiple-scattering media may exhibit fundamental, non intuitive phenomena such as halt of diffusion by disorder called Anderson localization. For electromagnetic waves, this phenomenon was observed only in…
Localization of electronic states in disordered thin layered systems with b layers is studied within the Anderson model of localization using the transfer-matrix method and finite-size scaling of the inverse of the smallest Lyapunov…
We examine the use of distributions in numerical treatments of Anderson localisation and supply evidence that treating exponential localisation on Bethe lattices recovers the overall picture known from hypercubic lattices in 3d.
Localization properties of particles in one-dimensional incommensurate lattices without interaction are investigated with models beyond the tight-binding Aubry-Andr\'e (AA) model. Based on a tight-binding t_1 - t_2 model with finite…
The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…
The phenomenon of Anderson localization is studied for a class of one-particle Schr\"odinger operators with random Zeeman interactions. These operators arise as follows: Static spins are placed randomly on the sites of a simple cubic…