Related papers: Anderson localization for block jacobi operators w…
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…
We prove non-perturbative Anderson localization for quasi-periodic Jacobi block matrix operators assuming non-vanishing of all Lyapunov exponents. The base dynamics on tori $\mathbb{T}^b$ is assumed to be a Diophantine rotation. Results on…
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 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.
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…
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 prove that at large disorder, with large probability and for a set of Diophantine frequencies of large measure, Anderson localization in $\Bbb Z^d$ is {\it stable} under localized time-quasi-periodic perturbations by proving that the…
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 prove that at large disorder, Anderson localization in $\Z^d$ is stable under localized time-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The formulation of this problem is…
We consider a system of two discrete quasiperiodic 1D particles as an operator on $\ell^2(\mathbb Z^2)$ and establish Anderson localization at large disorder, assuming the potential has no cosine-type symmetries. In the presence of…
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…
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 continuous one-dimensional multifrequency Schr\"odinger operators, with analytic potential, and prove Anderson localization in the regime of positive Lyapunov exponent for almost all phases and almost all Diophantine…
We establish large sets of Anderson localized states for the quasi-periodic nonlinear wave equation on $\mathbb Z^d$, thus extending nonlinear Anderson localization from the random \cite{BW08} to a deterministic setting.
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…
In this paper, we use Cartan estimate for meromorphic functions to prove Anderson localization for a class of long-range operators with singular potenials.
We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schr\"odinger operators on $\mathbb{Z}^d$ with bounded or unbounded Lipschitz monotone potentials via multi-scale analysis based on…
We consider an integer lattice quasiperiodic Schrodinger operator. The underlying dynamics is either the skew-shift or the multi-frequency shift by a Diophantine frequency. We assume that the potential function belongs to a Gevrey class on…
The arithmetic version of Anderson localization (AL), i.e., AL with explicit arithmetic description on both the localization frequency and the localization phase, was first given by Jitomirskaya \cite{J} for the almost Mathieu operators…