36 citations · 389 across the 48 of their papers we have counts for
6 papers · 2 filters
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…
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…