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We study Anderson localization in a generalized discrete time quantum walk - a unitary map related to a Floquet driven quantum lattice. It is controlled by a quantum coin matrix which depends on four angles with the meaning of potential and…

Disordered Systems and Neural Networks · Physics 2017-10-25 I. Vakulchyk , M. V. Fistul , P. Qin , S. Flach

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr\"odinger operators, acting on $L^2(\R)\otimes \C^N$, for arbitrary $N\geq 1$. We prove that, under suitable assumptions on the…

Mathematical Physics · Physics 2009-12-15 Hakim Boumaza

We establish localization type dynamical bounds as a corollary of positive Lyapunov exponents for general operators with quasiperiodic potentials defined by piecewise Holder functions.

Mathematical Physics · Physics 2017-09-21 Svetlana Jitomirskaya , Rajinder Mavi

We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns…

Disordered Systems and Neural Networks · Physics 2012-06-01 L. Tessieri , I. F. Herrera-González , F. M. Izrailev

We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ with power-law long-range hopping and analytic cosine type potentials. As applications, we prove the arithmetic version of…

Mathematical Physics · Physics 2025-11-07 Yunfeng Shi , Li Wen

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

The paper explores the prospects of observing the phenomenon of dynamical Anderson localisation via non-resonant Raman-type rotational excitation of molecules by periodic trains of short laser pulses. We define conditions for such an…

Quantum Physics · Physics 2013-08-14 Johannes Floß , Shmuel Fishman , Ilya Sh. Averbukh

We study a multi-particle quantum graph with random potential. Taking the approach of multiscale analysis we prove exponential and strong dynamical localization of any order in the Hilbert-Schmidt norm near the spectral edge. Apart from the…

Mathematical Physics · Physics 2013-11-11 Mostafa Sabri

We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between…

We study a particular class of families of multi-dimensional lattice Schr\"o\-dinger operators with deterministic (including quasi-periodic) potentials generated by the "hull" given by an orthogonal series over the Haar wavelet basis on the…

Mathematical Physics · Physics 2014-02-18 Victor Chulaevsky

We consider discrete one-dimensional Schr\"odinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical…

Spectral Theory · Mathematics 2025-04-14 David Damanik , Anton Gorodetski , Victor Kleptsyn

We study multi-frequency quasiperiodic Schr\"{o}dinger operators on $\mathbb{Z} $. We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of…

Spectral Theory · Mathematics 2017-09-01 Michael Goldstein , Wilhelm Schlag , Mircea Voda

We realize experimentally an atom-optics quantum chaotic system, the quasiperiodic kicked rotor, which is equivalent to a 3D disordered system, that allow us to demonstrate the Anderson metal-insulator transition. Sensitive measurements of…

We consider the Anderson model at large disorder on $\mathbb{Z}^2$ where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These…

Analysis of PDEs · Mathematics 2022-03-18 Linjun Li

We extend the bootstrap multiscale analysis developed by Germinet and Klein to the multi-particle continuous Anderson Hamiltonian, obtaining Anderson localization with finite multiplicity of eigenvalues, decay of eigenfunction correlations,…

Mathematical Physics · Physics 2014-04-16 Abel Klein , Son Nguyen

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

Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…

Disordered Systems and Neural Networks · Physics 2026-03-31 Ziyue Qi , Yi Zhang , Mingpu Qin , Hongming Weng , Kun Jiang

Anderson localization describes disorder-induced phase transitions, distinguishing between localized and extended states. In quasiperiodic systems, a third multifractal state emerges, characterized by unique energy and wave functions.…

Disordered Systems and Neural Networks · Physics 2025-10-15 Shan-Zhong Li , Yi-Cai Zhang , Yucheng Wang , Shanchao Zhang , Shi-Liang Zhu , Zhi Li

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

A statistical analysis of the ionization yield of one-dimensional, periodically driven hydrogen Rydberg states is provided. We find excellent agreement with predictions for the conductance across an Anderson-localized, quasi…

Chaotic Dynamics · Physics 2007-05-23 Sandro Wimberger , Andreas Buchleitner