Related papers: Eigensystem multiscale analysis for Anderson local…
In this article we study the problem of localization of eigenvalues for the non-homogeneous hierarchical Anderson model. More specifically, given the hierarchical Anderson model with spectral dimension $0<d<1$ with a random potential acting…
We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional…
The application of numerical techniques to the study of energy landscapes of large systems relies on sufficient sampling of the stationary points. Since the number of stationary points is believed to grow exponentially with system size, we…
Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold…
In the theory of Anderson localization, a landscape function predicts where wave functions localize in a disordered medium, without requiring the solution of an eigenvalue problem. It is known how to construct the localization landscape for…
An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that…
In a recent experiment [X. Yu et al., arXiv:2602.07654], energy-resolved measurements of an atomic matter wave spreading in a speckle potential enabled the direct observation of the three-dimensional Anderson transition. In this work, we…
The strong long-range interaction leads to localization in the closed quantum system without disorders. Employing the exact diagonalization method, the author numerically investigates thermalization and many-body localization in…
In recent years it became clear that the metallic regime of systems that exhibit a many body localization (MBL) behavior show properties which are quite different than the vanilla metallic region of the single particle Anderson regime. Here…
The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and…
The location of the mobility edge is a long standing problem in Anderson localization. In this paper, we show that the effective confining potential introduced in the localization landscape (LL) theory predicts the onset of delocalization…
We give a widely self-contained introduction to the mathematical theory of the Anderson model. After defining the Anderson model and determining its almost sure spectrum, we prove localization properties of the model. Here we discuss…
A model in which a three-dimensional elastic medium is represented by a network of identical masses connected by springs of random strengths and allowed to vibrate only along a selected axis of the reference frame, exhibits an Anderson…
Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are…
We prove exponential and dynamical localization for the Schr\"odinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of…
We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical…
We reinvestigate the large degeneracy solution of the multichannel Kondo problem, and show how in the universal regime the complicated integral equations simplifying the problem can be mapped onto a first order differential equation. This…
Transitions from delocalized to localized eigenstates have been extensively studied in both quadratic and interacting models. The delocalized regime typically exhibits diffusion and quantum chaos, and its properties comply with the random…
The present paper is devoted to new, improved bounds for the eigenfunctions of random operators in the localized regime. We prove that, in the localized regime with good probability, each eigenfunction is exponentially decaying outside a…
Based on the statistical dynamical mean field theory, we investigate, in a generic model for a strongly coupled disordered electron-phonon system, the competition between polaron formation and Anderson localization. The statistical…