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Related papers: Dynamical Localization for Unitary Anderson Models

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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

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

We study Anderson localization in a discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength $\theta$ and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field…

Disordered Systems and Neural Networks · Physics 2023-06-28 Ihor Vakulchyk , Sergej Flach

A technically convenient signature of localization, exhibited by discrete operators with random potentials, is exponential decay of the fractional moments of the Green function within the appropriate energy ranges. Known implications…

Mathematical Physics · Physics 2009-09-25 Michael Aizenman , Jeffrey H. Schenker , Roland M. Friedrich , Dirk Hundertmark

In an isolated single-particle quantum system a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that dissipation can drive…

Disordered Systems and Neural Networks · Physics 2017-02-22 I. Yusipov , T. Laptyeva , S. Denisov , M. Ivanchenko

We exhibit d-dimensional limit-periodic Schrodinger operators that are uniformly localized in the strongest sense possible. That is, for each of these operators, there is a uniform exponential decay rate such that every element of the hull…

Spectral Theory · Mathematics 2012-07-26 David Damanik , Zheng Gan

We investigate Anderson localization in a three dimensional (3d) kicked rotor. By a finite size scaling analysis we have identified a mobility edge for a certain value of the kicking strength $k = k_c$. For $k > k_c$ dynamical localization…

Disordered Systems and Neural Networks · Physics 2010-02-17 Jiao Wang , Antonio M. Garcia-Garcia

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

Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an…

Disordered Systems and Neural Networks · Physics 2022-06-14 Clément Hainaut , Jean-François Clément , Pascal Szriftgiser , Jean Claude Garreau , Adam Rançon , Radu Chicireanu

One of the fundamental results in the theory of localization for discrete Schr\"odinger operators with random potentials is the exponential decay of Green's function and the absence of continuous spectrum. In this paper we provide a new…

Mathematical Physics · Physics 2015-02-27 Alexander Elgart , Martin Tautenhahn , Ivan Veselić

We consider a one-dimensional continuum Anderson model where the potential decays in average like $|x|^{-\alpha}$, $\alpha>0$. We show dynamical localization for $0<\alpha<\frac12$ and provide control on the decay of the eigenfunctions.

Mathematical Physics · Physics 2020-10-28 Olivier Bourget , Gregorio R. Moreno Flores , Amal Taarabt

Dimension 2 is expected to be the lower critical dimension for Anderson localization in a time reversal-invariant disordered quantum system. Using an atomic quasiperiodic kicked rotor -- equivalent to a two-dimensional Anderson-like model…

Dynamical localization phenomena of monochromatically perturbed standard map (SM) and Anderson map (AM), which are both identified with a two-dimensional disordered system under suitable conditions, are investigated by the numerical…

Disordered Systems and Neural Networks · Physics 2018-01-24 Hiroaki S. Yamada , Fumihiro Matsui , Kensuke S. Ikeda

We consider a one-dimensional Anderson model where the potential decays in average like $n^{-\alpha}$, $\alpha>0$. This simple model is known to display a rich phase diagram with different kinds of spectrum arising as the decay rate…

Mathematical Physics · Physics 2020-01-23 Olivier Bourget , Gregorio R. Moreno Flores , Amal Taarabt

We present the first rigorous result on Anderson localization for interacting systems of quantum particles subject to a deterministic (e.g., almost periodic) disordered external potential. For a particular class of deterministic, fermionic,…

Mathematical Physics · Physics 2014-02-28 Victor Chulaevsky

Proofs of localization for random Schr\"odinger operators with sufficiently regular distribution of the potential can take advantage of the fractional moment method introduced by Aizenman-Molchanov, or use the classical Wegner estimate as…

Mathematical Physics · Physics 2024-05-30 Omar Hurtado

We consider discrete Schr\"odinger operators on $\ell^2(\mathbb{Z})$ with bounded random but not necessarily identically distributed values of the potential. We prove spectral localization (with exponentially decaying eigenfunctions) as…

Spectral Theory · Mathematics 2024-03-26 Anton Gorodetski , Victor Kleptsyn

We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-line Jacobi matrices whose…

Spectral Theory · Mathematics 2018-03-19 David Damanik , Selim Sukhtaiev

Anderson localization is a phase transition between a metallic phase, where wavefunctions are extended and delocalized in space, and an insulating phase, where wavefunctions are completely localized. These transitions are driven by…

Disordered Systems and Neural Networks · Physics 2026-01-30 Pasquale Marra

It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits localization phenomena, such as spectral, eigenstate, and weak dynamical localization, in an arbitrary (but fixed) energy interval in a non-trivial region of…

Mathematical Physics · Physics 2025-12-01 Alexander Elgart , Abel Klein