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We prove exponential and dynamical localization at low energies for the Schr\"odinger operator with an attractive Poisson random potential in any dimension. We also conclude that the eigenvalues in that spectral region of localization have…

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

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

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

This paper concerns the numerical approximation of low-energy eigenstates of the linear random Schr\"odinger operator. Under oscillatory high-amplitude potentials with a sufficient degree of disorder it is known that these eigenstates…

Numerical Analysis · Mathematics 2019-11-11 Robert Altmann , Daniel Peterseim

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 a two dimensional magnetic Schroedinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate…

Mathematical Physics · Physics 2011-01-12 Laszlo Erdos , David Hasler

We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…

Mathematical Physics · Physics 2012-05-08 Victor Chulaevsky

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

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

The two main results of the article are concerned with Anderson Localization for one-dimensional lattice Schroedinger operators with quasi-periodic potentials with d frequencies. First, in the case d = 1 or 2, it is proved that the spectrum…

Mathematical Physics · Physics 2016-09-07 Jean Bourgain , Michael Goldstein

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 study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of…

Mathematical Physics · Physics 2013-01-01 François Germinet , Abel Klein

We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e.…

Mathematical Physics · Physics 2015-05-30 Zhenwei Cao , Alexander Elgart

We establish non-perturbative Anderson localization for a wide class of 1D quasiperiodic operators with unbounded monotone potentials, extending the classical results on Maryland model and perturbative results for analytic potentials by…

Spectral Theory · Mathematics 2018-11-20 Ilya Kachkovskiy

We consider a random Schr\"odinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, $Q_r$, and a random transversally periodic potential, $\kappa Q_t$, with coupling constant…

Mathematical Physics · Physics 2018-01-03 Richard Froese , Darrick Lee , Christian Sadel , Wolfgang Spitzer , Günter Stolz

We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by H\"older continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded…

Spectral Theory · Mathematics 2024-02-02 Artur Avila , David Damanik , Zhenghe Zhang

We propose a new method to prove Anderson localization for quasiperiodic Schr\"odinger operators and apply it to the quasiperiodic model considered by Sinai and Fr\"ohlich-Spencer-Wittwer. More concretely, we prove Anderson localization for…

Spectral Theory · Mathematics 2021-07-20 Lingrui Ge , Jiangong You , Xin Zhao

In this note we review some results on localization and related properties for random Schr\"odinger operators arising in aperiodic media. These include the Anderson model associated to disordered quasycrystals and also the so-called Delone…

Mathematical Physics · Physics 2021-02-24 Constanza Rojas-Molina

We consider continuous one-dimensional multifrequency Schr\"odinger operators, with analytic potential, and prove Anderson localization in the regime of positive Lyapunov exponent for almost all phases and almost all Diophantine…

Spectral Theory · Mathematics 2016-08-24 Ilia Binder , Damir Kinzebulatov , Mircea Voda

We consider the random Schr\"odinger operator on $\mathbb{R}$ obtained by perturbing the Laplacian with a white noise. We prove that Anderson localization holds for this operator: almost surely the spectral measure is pure point and the…

Probability · Mathematics 2022-12-12 Laure Dumaz , Cyril Labbé