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Anderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for {dynamical localization}. In the one-dimensional Hermitian Anderson model with uncorrelated diagonal…

Disordered Systems and Neural Networks · Physics 2023-04-18 Stefano Longhi

A Dyson hierarchical model for Anderson localization, containing non-random hierarchical hoppings and random on-site energies, has been studied in the mathematical literature since its introduction by Bovier [J. Stat. Phys. 59, 745 (1990)],…

Disordered Systems and Neural Networks · Physics 2011-05-05 Cecile Monthus , Thomas Garel

We study the persistence of localization for a strongly disordered tight-binding Anderson model on the lattice $\mathbb{Z}^d$, periodically driven on each site. Under two different sets of conditions, we show that Anderson localization…

Mathematical Physics · Physics 2016-07-26 Raphael Ducatez , François Huveneers

Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for the random on-site potential. We demonstrate that already in leading…

Disordered Systems and Neural Networks · Physics 2007-05-23 M. Titov , H. Schomerus

We numerically analyze the energy level statistics of the Anderson model with Gaussian site disorder and constant hopping. The model is realized on different two-dimensional lattices, namely, the honeycomb, the kagom\'e, the square, and the…

Mesoscale and Nanoscale Physics · Physics 2015-11-20 Dayasindhu Dey , Manoranjan Kumar , Pragya Shukla

We study the properties of the spinor wavefunction in a strongly disordered environment on a two-dimensional lattice. By employing a transfer-matrix calculation we find that there is a transition from delocalized to localized states at a…

Disordered Systems and Neural Networks · Physics 2013-10-09 A. Hill , K. Ziegler

We prove exponential localization for the Schr\"odinger operator with a Poisson random potential at the bottom of the spectrum in any dimension. We also prove exponential localization in a prescribed interval for all large Poisson…

Mathematical Physics · Physics 2007-05-23 Francois Germinet , Peter Hislop , Abel Klein

In this paper, we use Cartan estimate for meromorphic functions to prove Anderson localization for a class of long-range operators with singular potenials.

Dynamical Systems · Mathematics 2021-03-17 Wenwen Jian , Jia Shi , Xiaoping Yuan

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…

Mathematical Physics · Physics 2016-06-29 Christian Sadel

We consider the $d$-dimensional Anderson model, and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large. We employ the random walk expansion of…

Mathematical Physics · Physics 2015-06-04 M. Kaminaga , M. Krishna , S. Nakamura

We investigate the scaling properties of eigenstates of a one-dimensional (1D) Anderson model in the presence of a constant electric field. The states show a transition from exponential to factorial localization. For infinite systems this…

Disordered Systems and Neural Networks · Physics 2009-10-31 Matthias Weiss , Tsampikos Kottos , Theo Geisel

We consider a discrete-time stochastic growth model on the $d$-dimensional lattice with non-negative real numbers as possible values per site. The growth model describes various interesting examples such as oriented site/bond percolation,…

Probability · Mathematics 2009-12-07 Nobuo Yoshida

We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schroedinger operators with non-monotone random potentials, on the d-dimensional lattice. Our results include dynamical…

Mathematical Physics · Physics 2016-11-18 Alexander Elgart , Mira Shamis , Sasha Sodin

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…

Mathematical Physics · Physics 2007-05-23 François Germinet , Peter D. Hislop , Abel Klein

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…

Mathematical Physics · Physics 2013-12-17 Constanze Liaw

We prove the complete spectral and the strong dynamical Anderson localization in a two-particle random Schr\"odinger operators with the Poisson potential. The results apply with sufficiently weak interaction between the particle system.

Mathematical Physics · Physics 2020-07-16 Trésor Ekanga

We have calculated wave functions and matrix elements of the dipole operator in the two- and three-dimensional Anderson model of localization and have studied their statistical properties in the limit of weak disorder. In particular, we…

Disordered Systems and Neural Networks · Physics 2025-10-01 Ville Uski , Bernhard Mehlig , Rudolf A. Roemer

We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the…

Disordered Systems and Neural Networks · Physics 2020-01-08 Ba Phi Nguyen , Duy Khuong Phung , Kihong Kim

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…

Strongly Correlated Electrons · Physics 2007-05-23 Franz X. Bronold , Andreas Alvermann , Holger Fehske

We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent provided by F\"urstenberg's theorem. That is, a…

Mathematical Physics · Physics 2017-08-04 Valmir Bucaj , David Damanik , Jake Fillman , Vitaly Gerbuz , Tom VandenBoom , Fengpeng Wang , Zhenghe Zhang