Related papers: Arithmetic version of Anderson localization via re…

This paper establishes several sharp spectral results for analytic quasiperiodic Schrodinger operators. Key contributions include: (1) exact exponential decay rates for spectral gaps of the almost Mathieu operator, addressing a question…

We consider a one-frequency, quasi-periodic, block Jacobi operator, whose blocks are generic matrix-valued analytic functions. We establish Anderson localization for this type of operator under the assumption that the coupling constant is…

For the almost Mathieu operator $(H_{\lambda,\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+2\lambda \cos2\pi(\theta+n\alpha)u_n$, Avila and Jitomirskaya guess that for a.e. $\theta$, $H_{\lambda,\alpha,\theta}$ satisfies Anderson localization if $…

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

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.

In this paper we review results of Anderson localization for different random families of operators which enter in the framework of random quasi-one-dimensional models. We first recall what is Anderson localization from both physical and…

We prove non-perturbative Anderson localization and almost localization for a family of quasi-periodic operators on the strip. As an application we establish Avila's almost reducibility conjecture for Schr\"odinger operators with…

We establish a topological criterion for connection between reducibility to constant rotations and dual localization, for the general family of analytic quasiperiodic Jacobi operators. As a corollary, we obtain the sharp arithmetic phase…

In this paper, we study block Jacobi operators on $\mathbb{Z}$ with quasi-periodic meromorphic potential. We prove the non-perturbative Anderson localization for such operators in the large coupling regime.

An ensemble of quasi-periodic discrete Schr\"{o}dinger operators with an arbitrary number of basic frequencies is considered, in a lattice of arbitrary dimension, in which the hull function is a realisation of a stationary Gaussian process…

We develop a quantitative version of Aubry duality and use it to obtain several sharp estimates for the dynamics of Schr\"odinger cocycles associated to a non-perturbatively small analytic potential and Diophantine frequency. In particular,…

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…

We establish Anderson localization for quasiperiodic operator families of the form $$ (H(x)\psi)(m)=\psi(m+1)+\psi(m-1)+\lambda v(x+m\alpha)\psi(m) $$ for all $\lambda>0$ and all Diophantine $\alpha$, provided that $v$ is a $1$-periodic…

In this paper, we study the quasi-periodic operators $H_{\epsilon,\omega}(x)$: $$(H_{\epsilon,\omega}(x)\vec{\psi})_n=\epsilon\sum_{k\in\mathbb{Z}}W_k\vec{\psi}_{n-k}+V(x+n\omega)\vec{\psi}_n,$$ where…

We study the unitary almost Mathieu operator (UAMO), a one-dimensional quasi-periodic unitary operator arising from a two-dimensional discrete-time quantum walk on $\mathbb Z^2$ in a homogeneous magnetic field. In the positive Lyapunov…

Let $\alpha\in \mathbb{R}\backslash \mathbb{Q}$ and $\beta(\alpha) = \limsup _{n \to \infty}(\ln q_{n+1})/ q_n <\infty$, where $p_n/q_n$ is the continued fraction approximations to $\alpha$. Let $(H_{\lambda,\alpha,\theta}u)…

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…

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…

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…

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…