Related papers: Anderson Localization for Long-Range operators wit…
We discuss the techniques and results of the multi-particle Anderson localization theory for disordered quantum systems with nontrivial interaction. After a detailed presentation of the approach developed earlier by Aizenman and Warzel, we…
We extend the bootstrap multiscale analysis developed by Germinet and Klein to the multi-particle continuous Anderson Hamiltonian, obtaining Anderson localization with finite multiplicity of eigenvalues, decay of eigenfunction correlations,…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
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…
We consider a one-dimensional continuum Anderson model where the potential decays in average like $|x|^{-\alpha}$, $\alpha>0$. We show dynamical localization for $0<\alpha<\frac12$ and provide control on the decay of the eigenfunctions.
It is classical, following Furstenberg's theorem on positive Lyapunov exponent for products of random SL$(2, \mathbb R)$ matrices, that the one dimensional random Schr\"odinger operator has Anderson localization at arbitrary disorder. This…
The arithmetic version of Anderson localization (AL), i.e., AL with explicit arithmetic description on both the localization frequency and the localization phase, was first given by Jitomirskaya \cite{J} for the almost Mathieu operators…
We establish exponential localization for a multi-particle Anderson model in a Euclidean space of an arbitrary dimension, in presence of a non-trivial short-range interaction and an alloy-type random external potential. Specifically, we…
We consider a magnetic Schr\"odinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well…
This work relates quantitatively homogenization to Anderson localization for acoustic operators in disordered media. By blending dispersive estimates for homogenized operators and quantitative homogenization of the wave equation, we derive…
We consider Anderson localization and the associated metal-insulator transition for non-interacting fermions in D = 1, 2 space dimensions in the presence of spatially correlated on-site random potentials. To assess the nature of the…
We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…
We show persistence of both Anderson and dynamical localization in Schr\"odinger operators with non-positive (attractive) random decaying potential. We consider an Anderson-type Schr\"odinger operator with a non-positive ergodic random…
A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A…
We consider an integer lattice quasiperiodic Schrodinger operator. The underlying dynamics is either the skew-shift or the multi-frequency shift by a Diophantine frequency. We assume that the potential function belongs to a Gevrey class on…
The paper explores the prospects of observing the phenomenon of dynamical Anderson localisation via non-resonant Raman-type rotational excitation of molecules by periodic trains of short laser pulses. We define conditions for such an…
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…
The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems.
In this paper we consider the discrete one-dimensional Schroedinger operator with quasi-periodic potential v_n = \lambda v (x + n \omega). We assume that the frequency \omega satisfies a strong Diophantine condition and that the function v…
Anderson transition of the phonon modes is studied numerically. The critical exponent for the divergence of the localization length is estimated using the transfer matrix method, and the statistics of the modes is analyzed. The latter is…