36 citations · 389 across the 48 of their papers we have counts for
12 papers · 1 filter
Exact dynamical decay rate for the almost Mathieu operator
Svetlana Jitomirskaya, Helge Krüger, Wencai Liu
We prove that the exponential decay rate in expectation is well defined and is equal to the Lyapunov exponent, for supercritical almost Mathieu operators with Diophantine frequenci…
Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators
Wencai Liu
For perturbed Stark operators , the author has proved that must be larger than $\frac{1}{\sqrt{2}}N^{\fra…
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^{-…
The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators
Wencai Liu
Let be a periodic operator on (or periodic Jacobi operator on ). It is known that the absolutely continuous spectrum of is consisted of spectral bands $\cup[α…
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…
Criteria for embedded eigenvalues for discrete Schrödinger operators
Wencai Liu
In this paper, we consider discrete Schrödinger operators of the form, \begin{equation*} (Hu)(n)= u({n+1})+u({n-1})+V(n)u(n). \end{equation*} We view as a perturbation of the f…
Almost Mathieu operators with completely resonant phases
Wencai Liu
Let and , where is the continued fraction approximations to . Let $(H_…
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…
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
Wencai Liu, Darren C. Ong
In this paper, we consider the Schrödinger equation, \begin{equation*} Hu=-u^{\prime\prime}+(V(x)+V_0(x))u=Eu, \end{equation*} where is 1-periodic and is a decayin…
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…