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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…

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

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an a-periodic Kronig-Penney model in one dimension. The exact expression for the…

chao-dyn · Physics 2007-05-23 Holger Schanz , Uzy Smilansky

In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by…

Analysis of PDEs · Mathematics 2026-04-22 Shihe Liu , Yunfeng Shi , Zhifei Zhang

We study the persistence of localization for a strongly disordered tight-binding Anderson model on the lattice $\mathbb{Z}^d$, periodically driven on each site. Under two different sets of conditions, we show that Anderson localization…

Mathematical Physics · Physics 2016-07-26 Raphael Ducatez , François Huveneers

We show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Piet W. Brouwer , Alexander Altland

We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…

Disordered Systems and Neural Networks · Physics 2009-10-31 L. Tessieri , F. M. Izrailev

We consider a class of unbounded quasiperiodic Schr\"odinger-type operators on $\ell^2(\mathbb Z^d)$ with monotone potentials (akin to the Maryland model) and show that the Rayleigh--Schr\"odinger perturbation series for these operators…

Spectral Theory · Mathematics 2022-06-01 Ilya Kachkovskiy , Leonid Parnovski , Roman Shterenberg

We study multi-frequency quasi-periodic Schr\"odinger operators on $\mathbb{Z}$ in the regime of positive Lyapunov exponent and for general analytic potentials. Combining Bourgain's semi-algebraic elimination of multiple resonances with the…

Spectral Theory · Mathematics 2016-10-04 Michael Goldstein , Wilhelm Schlag , Mircea Voda

In this paper we address the question of proving Anderson localization (AL) for the operator [H(x,\omega)\psi](n) := - \vp(n+1) - \vp(n-1) + V\bigl(T^n_\omega x\bigr)\psi(n), n\in\mathbb Z where T:\tor^2\to\tor^2 is either the shift or the…

Dynamical Systems · Mathematics 2007-05-23 Jackson Chan , Michael Goldstein , Wilhelm Schlag

This paper formulates the finite and full-scale localization for multi-frequency quasi-periodic CMV matrices. This can be viewed as the CMV counterpart to the localization results by Goldstein, Schlag, and Voda [arXiv:1610.00380 (math.SP],…

Spectral Theory · Mathematics 2026-04-14 Bei Zhang , Daxiong Piao

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

Anderson localization is related to exponential localization of a particle in the configuration space in the presence of a disorder potential. Anderson localization can be also observed in the momentum space and corresponds to quantum…

Atomic Physics · Physics 2017-06-07 Krzysztof Giergiel , Krzysztof Sacha

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 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 review the present status of the Anderson transition in the spectrum of the Dirac operator of QCD-like theories on the lattice. Localized modes at the low-end of the spectrum have been found in SU(2) Yang-Mills theory with overlap and…

High Energy Physics - Lattice · Physics 2015-06-22 Matteo Giordano , Tamas G. Kovacs , Ferenc Pittler

In this paper, we establish Anderson localization for a class of Jacobi matrices associated with skew shifts on $\mathbb{T}^{d}$, $d\geq3$.

Functional Analysis · Mathematics 2019-08-02 Jia Shi , Xiaoping Yuan

Anderson localization is studied for two-dimensional Dirac fermions in the presence of strong random scattering. Averaging with respect to the latter leads to a graphical representation of the correlation function with entangled random…

Disordered Systems and Neural Networks · Physics 2014-12-25 K. Ziegler

We study the interplay of interactions and quasiperiodic driving in the Lieb-Liniger model of one-dimensional bosons subjected to a sequence of delta kicks. Building on the known mapping between the kicked rotor and the Anderson model, we…

Quantum Gases · Physics 2026-04-20 H. Olsen , P. Vignolo , M. Albert

In this paper, we establish quantitative Green's function estimates for some higher dimensional lattice quasi-periodic (QP) Schr\"odinger operators. The resonances in the estimates can be described via a pair of symmetric zeros of certain…

Mathematical Physics · Physics 2023-03-16 Hongyi Cao , Yunfeng Shi , Zhifei Zhang