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Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…

Mathematical Physics · Physics 2022-11-09 Chen Jia , Ziqi Liu , Zhimin Zhang

We study spectral properties of partial differential operators modelling composite materials with highly contrasting constituents, comprised of soft spherical inclusions with random radii dispersed in a stiff matrix. Such operators have…

Spectral Theory · Mathematics 2025-12-03 Matteo Capoferri , Matthias Täufer

We observe a singularity in the electronic properties of the Anderson Model of Localization with bounded diagonal disorder, which is clearly distinct from the well-established mobility edge (localization-delocalization transition) that…

Disordered Systems and Neural Networks · Physics 2015-05-28 S. Johri , R. N. Bhatt

The interplay between Anderson localization and total internal reflection of electromagnetic waves incident near the critical angle on randomly-stratified dielectric media is investigated theoretically. Using an exact analytical formula for…

Optics · Physics 2017-11-22 Kihong Kim

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…

Mathematical Physics · Physics 2010-04-09 Anne Boutet de Monvel , Victor Chulaevsky , Peter Stollmann , Yuri Suhov

The localization properties of electrons moving in a plane perpendicular to a spatially-correlated static magnetic field of random amplitude and vanishing mean are investigated. We apply the method of level statistics to the eigenvalues and…

Disordered Systems and Neural Networks · Physics 2007-05-23 H. Potempa , L. Schweitzer

We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a…

Disordered Systems and Neural Networks · Physics 2017-10-11 Jakob Lindinger , Alberto Rodríguez

A class of stationary rigidly rotating perfect fluid coupled with non-linear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Humberto Salazar , Ruben Cordero

We present an eigensystem multiscale analysis for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model in an energy interval. In particular, it yields…

Mathematical Physics · Physics 2016-11-09 Alexander Elgart , Abel Klein

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

The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional…

Classical Physics · Physics 2023-07-19 R. A. Mendez-Sanchez , L. Gutierrez , A. Morales , J. Flores , A. Diaz-de-Anda , G. Monsivais

When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…

Computational Physics · Physics 2022-10-05 Zitao Mai , Ya Yan Lu

We consider the Anderson model with Bernoulli potential on the 3D lattice, and prove localization of eigenfunctions corresponding to eigenvalues near zero, the lower boundary of the spectrum. We follow the framework by Bourgain-Kenig and…

Analysis of PDEs · Mathematics 2021-03-16 Linjun Li , Lingfu Zhang

Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional…

Quantum Physics · Physics 2023-12-15 Michael I. Tribelsky

We develop a novel approach to the Anderson localisation problem in a $d$-dimensional disordered sample of dimension $L\times M^{d-1}$. Attaching a perfect lead with the cross-section $M^{d-1}$ to one side of the sample, we derive evolution…

Mesoscale and Nanoscale Physics · Physics 2018-08-17 A. Ossipov

The scaling properties of the wave functions in finite samples of the one dimensional Anderson model are analyzed. The states have been characterized using a new form of the information or entropic length, and compared with analytical…

Condensed Matter · Physics 2016-08-31 Imre Varga , János Pipek

Following a number of recent studies of resolvent and spectral convergence of non-uniformly elliptic families of differential operators describing the behaviour of periodic composite media with high contrast, we study the corresponding…

Spectral Theory · Mathematics 2017-02-16 Mikhail Cherdantsev , Kirill Cherednichenko , Shane Cooper

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

As recently discovered [PRL ${\bf 109}$ 190601(2012)], Anderson localization in a bulk disordered system triggers the emergence of a coherent forward scattering (CFS) peak in momentum space, which twins the well-known coherent…

Quantum Gases · Physics 2014-10-13 Kean Loon Lee , Benoît Grémaud , Christian Miniatura

We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…

Mathematical Physics · Physics 2014-07-18 Victor Chulaevsky