Related papers: Sharp arithmetic delocalization for quasiperiodic …
In this paper we consider the discrete one-dimensional Schroedinger operator with quasi-periodic potential v_n = \lambda v (x + n \omega). We assume that the frequency \omega satisfies a strong Diophantine condition and that the function v…
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 study discrete quasiperiodic Schr\"odinger operators on $\ell^2(\zee)$ with potentials defined by $\gamma$-H\"older functions. We prove a general statement that for $\gamma >1/2$ and under the condition of positive Lyapunov exponents,…
We consider a similar type of scenario for the disappearance of uniform of hyperbolicity as in Bjerkl\"ov and Saprykina (2008, Nonlinearity 21), where it was proved that the minimum distance between invariant stable and unstable bundles has…
We study discrete Schroedinger operators with analytic potentials. In particular, we are interested in the connection between the absolutely continuous spectrum in the almost periodic case and the spectra in the periodic case. We prove a…
For a one-dimensional discrete Schr\"odinger operator with a weakly coupled potential given by a strongly mixing dynamical system with power law decay of correlations, we derive for all energies including the band edges and the band center…
We study lower bounds on the Lyapunov exponent associated with one-frequency quasiperiodic Schr\"odinger operators with an added finite valued background potential. We prove that, for sufficiently large coupling constant, the Lyapunov…
We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by H\"older continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded…
We consider discrete Schr"odinger operators on the line with potentials generated by a minimal homeomorphism on a compact metric space and a continuous sampling function. We introduce the concepts of topological and metric repetition…
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…
In this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalue and the Bloch function of the periodic Schrodinger operator of arbitrary dimension, when corresponding quasimomentum lies near a diffraction hyperplane.…
We consider the Schr\"odinger operator with a periodic potential $p$ on the real line. We assume that $p$ belongs to the Sobolev space $\mH_m$ on the circle for some $m\ge -1$, and we determine the asymptotics of the quasimomentum and the…
We study Schrodinger operators with a one-frequency analytic potential, focusing on the transition between the two distinct local regimes characteristic respectively of large and small potentials. From the dynamical point of view, the…
We consider perturbations of quasi-periodic Schr\"odinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under which various spectral properties are preserved. In the…
We prove quantitative unique continuation results for the semiclassical Schrodinger operator on smooth, compact domains. These take the form of exponentially decreasing (in h) local L^{2} lower bounds for exponentially precise quasimodes.…
We establish localization type dynamical bounds as a corollary of positive Lyapunov exponents for general operators with quasiperiodic potentials defined by piecewise Holder functions.
This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called…
We show that a one-frequency analytic SL(2,R) cocycle with Diophantine rotation vector is analytically linearizable if and only if the Lyapunov exponent is zero through a complex neighborhood of the circle. More generally, we show (without…
We prove that the eigenvalues of a continuum random Schr\"odinger operator $-\Delta+ V_{\omega}$ of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an $L^q$ norm of the potential for all…
We consider semiclassical Schr\"odinger operators acting in $L^2(\mathbb{R}^d)$ with $d\geq3$. For these operators we establish a sharp spectral asymptotics without full regularity. For the counting function we assume the potential is…