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We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between…

These lectures present some basic ideas and techniques in the spectral analysis of lattice Schrodinger operators with disordered potentials. In contrast to the classical Anderson tight binding model, the randomness is also allowed to…

Analysis of PDEs · Mathematics 2021-04-30 Wilhelm Schlag

We consider the Anderson model at large disorder on $\mathbb{Z}^2$ where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These…

Analysis of PDEs · Mathematics 2022-03-18 Linjun Li

We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the…

Statistical Mechanics · Physics 2009-11-10 S. Ciliberti , T. S. Grigera , V. Martin-Mayor , G. Parisi , P. Verrocchio

We explore the properties of discrete random Schroedinger operators in which the random part of the potential is supported on a sub-lattice. In particular, we provide new conditions on the sub-lattice under which Anderson localisation…

Mathematical Physics · Physics 2017-08-07 Alexander Elgart , Sasha Sodin

Localization due to disorder has been one of the most intriguing theoretical concepts evolved in condensed matter. Here, we expand the theory of localization by considering two types of disorder at the same time, namely the original…

Disordered Systems and Neural Networks · Physics 2023-03-03 Mouyang Cheng , Haoxiang Chen , Ji Chen

In the present note we show dynamical localization for an Anderson model with missing sites in a discrete setting at the bottom of the spectrum in arbitrary dimension $d$. In this model, the random potential is defined on a relatively dense…

Mathematical Physics · Physics 2013-04-30 Constanza Rojas-Molina

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…

Disordered Systems and Neural Networks · Physics 2015-03-19 Alexander Croy , Philipp Cain , Michael Schreiber

In this paper we review results of Anderson localization for different random families of operators which enter in the framework of random quasi-one-dimensional models. We first recall what is Anderson localization from both physical and…

Mathematical Physics · Physics 2023-07-04 Hakim Boumaza

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are…

Chaotic Dynamics · Physics 2015-06-04 J. Flores , L. Gutiérrez , R. A. Méndez-Sánchez , G. Monsivais , P. Mora , A. Morales

We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model (PAM) on a supercritical Galton-Watson random tree with bounded degrees. We identify the second-order contribution to this asymptotics in…

Probability · Mathematics 2020-07-29 Frank den Hollander , Wolfgang König , Renato S. dos Santos

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 consider discrete one-dimensional Schr\"odinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical…

Spectral Theory · Mathematics 2025-04-14 David Damanik , Anton Gorodetski , Victor Kleptsyn

We prove Anderson localization at the internal band-edges for periodic magnetic Schr{\"o}dinger operators perturbed by random vector potentials of Anderson-type. This is achieved by combining new results on the Lifshitz tails behavior of…

Mathematical Physics · Physics 2007-08-15 F. Ghribi , P. D. Hislop , F. Klopp

We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering…

Disordered Systems and Neural Networks · Physics 2013-03-28 Marie Piraud , Laurent Sanchez-Palencia

For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…

Mathematical Physics · Physics 2016-12-04 Trésor Ekanga

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…

High Energy Physics - Phenomenology · Physics 2018-06-06 Nathaniel Craig , Dave Sutherland

In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by…

Analysis of PDEs · Mathematics 2026-04-22 Shihe Liu , Yunfeng Shi , Zhifei Zhang

We study localization properties of the eigenstates and wave transport in one-dimensional system consisting of a set of barriers/wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced…

Disordered Systems and Neural Networks · Physics 2015-06-16 I. F. Herrera-Gonzalez , F. M. Izrailev , N. M. Makarov

I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and…

Spectral Theory · Mathematics 2010-06-29 Helge Krueger