4 papers · 1 filter
Upper bounds on transport exponents for long range operators
Svetlana Jitomirskaya, Wencai Liu
We present a simple method, not based on the transfer matrices, to prove vanishing of dynamical transport exponents. The method is applied to long range quasiperiodic operators.
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…
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…