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We probe the limits of nonlinear wave spreading in disordered chains which are known to localize linear waves. We particularly extend recent studies on the regimes of strong and weak chaos during subdiffusive spreading of wave packets [EPL…

Chaotic Dynamics · Physics 2011-07-18 J. D. Bodyfelt , T. V. Laptyeva , Ch. Skokos , D. O. Krimer , S. Flach

We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…

Probability · Mathematics 2026-03-20 Suhan Liu , Patrick Lopatto

The modified discrete nonlinear Schr\"odinger equation is used to study the formation of stationary localized states in a one-dimensional lattice with a single impurity and an asymmetric dimer impurity. A periodically modulated and a…

Disordered Systems and Neural Networks · Physics 2015-06-25 Bikash C. Gupta , Sang Bub Lee

A one-dimensional boundary of a two-dimensional topological superconductor can host a number of topologically protected chiral modes. Combining two topological superconductors with different topological indices, it is possible to achieve a…

Mesoscale and Nanoscale Physics · Physics 2022-08-17 Daniil S. Antonenko , Eslam Khalaf , Pavel M. Ostrovsky , Mikhail A. Skvortsov

We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly…

We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…

Mathematical Physics · Physics 2018-01-03 Frédéric Klopp , Michael Loss , Shu Nakamura , Günter Stolz

In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of…

Condensed Matter · Physics 2009-10-28 J. Magnen , G. Poirot , V. Rivasseau

We consider a class of ensembles of lattice Schr\"odinger operators with deterministic random potentials, including quasi-periodic potentials with Diophantine frequencies, depending upon an infinite number of parameters in an auxiliary…

Mathematical Physics · Physics 2011-04-07 Victor Chulaevsky

A non-perturbative local moment approach to single-particle dynamics of the general asymmetric Anderson impurity model is developed. The approach encompasses all energy scales and interaction strengths. It captures thereby strong coupling…

Strongly Correlated Electrons · Physics 2009-11-07 Matthew T. Glossop , David E. Logan

We present a systematic study of the role of Anderson orthogonality for the dynamics after a quantum quench in quantum impurity models, using the numerical renormalization group. As shown by Anderson in 1967, the scattering phase shifts of…

Strongly Correlated Electrons · Physics 2013-01-16 Wolfgang Münder , Andreas Weichselbaum , Moshe Goldstein , Yuval Gefen , Jan von Delft

We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…

Mathematical Physics · Physics 2014-12-30 David Damanik , Robert Sims , Günter Stolz

We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we…

Spectral Theory · Mathematics 2019-07-24 David Damanik , Jake Fillman , Mark Helman , Jacob Kesten , Selim Sukhtaiev

We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of…

Disordered Systems and Neural Networks · Physics 2009-10-30 Michael Hilke

We consider the notion of equilibration for an isolated quantum system exhibiting Anderson localization. The system is assumed to be in a pure state, i.e., described by a wave-function undergoing unitary dynamics. We focus on the simplest…

Quantum Physics · Physics 2018-03-09 Giorgio J. Moro , Giulia DalľOsto , Barbara Fresch

Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…

Disordered Systems and Neural Networks · Physics 2026-03-31 Ziyue Qi , Yi Zhang , Mingpu Qin , Hongming Weng , Kun Jiang

We prove that at large disorder, Anderson localization in $\Z^d$ is stable under localized time-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The formulation of this problem is…

Spectral Theory · Mathematics 2007-05-23 Avy Soffer , Wei-Min Wang

Mosaic lattice models have been recently introduced as a special class of disordered systems displaying resonance energies, multiple mobility edges and anomalous transport properties. In such systems on-site potential disorder, either…

Disordered Systems and Neural Networks · Physics 2025-03-25 Stefano Longhi

We study the spreading dynamics of an initially localized wave packet in 1D nonlinear Schr\"{o}dinger lattices with random potential. It is shown that adding small dielectric coupling to surrounding random medium results in asymptotic…

Disordered Systems and Neural Networks · Physics 2025-07-31 Alexander V. Milovanov , Alexander Iomin

We establish the phenomenon of Anderson localisation for a quantum two-particle system on a d-dimensional lattice with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.

Mathematical Physics · Physics 2009-11-13 Victor Chulaevsky , Yuri Suhov

By employing Random Matrix Theory (RMT) and first-principle calculations, we investigated the behavior of Anderson localization in 1D, 2D and 3D systems characterized by a varying disorder. In particular, we considered random binary layer…

Optics · Physics 2012-08-23 D. Molinari , A. Fratalocchi