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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

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 prove the complete spectral and the strong dynamical Anderson localization in a two-particle random Schr\"odinger operators with the Poisson potential. The results apply with sufficiently weak interaction between the particle system.

Mathematical Physics · Physics 2020-07-16 Trésor Ekanga

For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…

Mathematical Physics · Physics 2016-12-04 Trésor Ekanga

We establish Anderson localization for long-range quasi-periodic operators with large trigonometric potentials and Diophantine frequencies, the proof is based on a novel dynamical rigidity argument.

Spectral Theory · Mathematics 2026-03-12 Zhenfu Wang , Jiangong You , Qi Zhou

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 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 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

Uncorrelated disorder potential in one-dimensional lattice definitely induces Anderson localization, while quasiperiodic potential can lead to both localized and extended phases, depending on the potential strength. We investigate the…

Disordered Systems and Neural Networks · Physics 2021-09-27 R. Wang , K. L. Zhang , Z. Song

We establish the phenomenon of Anderson localisation for a quantum two-particle system on a d-dimensional lattice with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.

Mathematical Physics · Physics 2009-11-13 Victor Chulaevsky , Yuri Suhov

We consider quasiperiodic operators on $\mathbb Z^d$ with unbounded monotone sampling functions ("Maryland-type"), which are not required to be strictly monotone and are allowed to have flat segments. Under several geometric conditions on…

Spectral Theory · Mathematics 2021-06-30 Ilya Kachkovskiy , Stanislav Krymski , Leonid Parnovski , Roman Shterenberg

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 consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of…

Disordered Systems and Neural Networks · Physics 2009-10-30 Michael Hilke

The center of mass of a bright soliton in a Bose-Einstein condensate may reveal Anderson localization in the presence of a weak disorder potential. We analyze the effects of interactions between two bright solitons on the Anderson…

Quantum Gases · Physics 2012-09-19 Marcin Płodzień , Krzysztof Sacha

Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…

Mesoscale and Nanoscale Physics · Physics 2009-01-23 A. Furusaki

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

We establish Anderson localization for general analytic $k$-frequency quasi-periodic operators on $\mathbb{Z}^d$ for \textit{arbitrary} $k,d$.

Spectral Theory · Mathematics 2021-11-03 Svetlana Jitomirskaya , Wencai Liu , Yunfeng Shi

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…

Mathematical Physics · Physics 2022-11-09 Chen Jia , Ziqi Liu , Zhimin Zhang

We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…

Mathematical Physics · Physics 2013-12-17 Constanze Liaw

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…