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We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…

Mathematical Physics · Physics 2026-03-19 Omar Hurtado

We consider a two dimensional magnetic Schroedinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove…

Mathematical Physics · Physics 2010-12-24 Laszlo Erdoes , David Hasler

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 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

We consider one-dimensional random Schr\"odinger operators with a background potential, arising in the inverse problem of scattering. We study the influence of the background potential on the essential spectrum of the random Schr\"odinger…

Mathematical Physics · Physics 2017-12-22 Hayk Asatryan , Werner Kirsch

We study the multi-particle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multi-particle lower edges of…

Mathematical Physics · Physics 2017-02-15 Trésor Ekanga

We prove that, for a density of disorder $\rho$ small enough, a certain class of discrete random Schr\"odinger operators on $\Z^d$ with diluted potentials exhibits a Lifschitz behaviour from the bottom of the spectrum up to energies at a…

Mathematical Physics · Physics 2012-02-23 Francisco W. Hoecker-Escuti

We prove that the eigenvalues of a continuum random Schr\"odinger operator $-\Delta+ V_{\omega}$ of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an $L^q$ norm of the potential for all…

Spectral Theory · Mathematics 2025-02-12 Jean-Claude Cuenin , Konstantin Merz

This paper considers the family of Schr\"odinger operators on $\ell^2(\mathbb{Z})$ given by independent but not necessarily identically distributed and possibly unbounded potentials. We assume a finite exponential moment and allow the…

Mathematical Physics · Physics 2026-04-03 Karl Zieber

We prove that the random Schrodinger operators on $\mathbb{R}^3$ with independent, identically distributed random variables and single-site potentials given by $\delta$-functions on $\mathbb{Z}^3$, exhibit both dynamical localization and…

Mathematical Physics · Physics 2025-09-03 Peter D. Hislop , Werner Kirsch , M. Krishna

We consider continuum one-dimensional Schr\"odinger operators with potentials that are given by a sum of a suitable background potential and an Anderson-type potential whose single-site distribution has a continuous and compactly supported…

Mathematical Physics · Physics 2015-01-05 David Damanik , Günter Stolz

This short note is a complement to our recent paper [2] where we established 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…

Mathematical Physics · Physics 2014-08-21 Victor Chulaevsky

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

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 effects of a bounded and compactly supported perturbation on multi-dimensional continuum random Schr\"odinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schr\"odinger…

Mathematical Physics · Physics 2021-03-03 Adrian Dietlein , Martin Gebert , Peter Müller

We analyse the spectral phase diagram of Schr\"odinger operators $ T +\lambda V$ on regular tree graphs, with $T$ the graph adjacency operator and $V$ a random potential given by iid random variables. The main result is a criterion for the…

Mathematical Physics · Physics 2013-07-09 Michael Aizenman , Simone Warzel

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

This work establishes the Anderson localization in both the spectral exponential and the strong dynamical localization for the multi-particle Anderson tight-binding model with correlated but strongly mixing random external potential. The…

Mathematical Physics · Physics 2017-02-24 Trésor Ekanga

We establish both Anderson localization and H\"older continuity of the integrated density of states for quasiperiodic Schr\"odinger operators on $\mathbb{Z}^d$ with any non-constant analytic potential and any Diophantine frequency in the…

Mathematical Physics · Physics 2026-04-14 Hongyi Cao , Yunfeng Shi , Zhifei Zhang

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr{\"o}dinger operator with magnetic field and a random potential which may be…

Mathematical Physics · Physics 2009-11-07 Thomas Hupfer , Hajo Leschke , Peter Müller , Simone Warzel