6 papers
Absence of singular continuous spectrum for perturbed discrete Schrödinger operators
Wencai Liu
We show that the spectral measure of discrete Schrödinger operators does not have singular continuous component if the potential $V(n)=O(n^{-…
Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators
Wencai Liu
In this paper, we consider the perturbed Stark operator \begin{equation*} Hu=H_0u+qu=-u^{\prime\prime}-xu+qu, \end{equation*} where is the power-decaying perturbation. The crit…
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators
Wencai Liu, Darren C. Ong
We are interested in diagonal perturbations of a periodic Jacobi operator that introduce embedded eigenvalues in its essential spectrum. Embedding multiple points in the essential…
Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian
Svetlana Jitomirskaya, Wencai Liu
We prove sharp criteria on the behavior of radial curvature for the existence of asymptotically flat or hyperbolic Riemannian manifolds with prescribed sets of eigenvalues embedded…
Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase
Svetlana Jitomirskaya, Wencai Liu
We prove sharp spectral transition in the arithmetics of phase between localization and singular continuous spectrum for Diophantine almost Mathieu operators. We also determine exa…
Inhomogeneous Diophantine approximation in the coprime setting
Svetlana Jitomirskaya, Wencai Liu
Given and , let \begin{equation*} ||γ-nx||^\prime=\min\{|γ-nx+m|:m\in Z, \gcd (n,m)=1\}, \end{equation*} %where is the largest common divisor of and…