36 citations · 389 across the 48 of their papers we have counts for
50 papers
Irreducibility of the Bloch variety for periodic Schrödinger operators in arbitrary dimension
Wencai Liu
Let and . We prove that the Bloch variety of is irreducible modulo periodicity. The proof combines holomorphic continuation of spect…
Optimal bounds for embedded eigenvalues of one-dimensional discrete Schrödinger operators with decaying potentials
Jifeng Chu, Wencai Liu, Kang Lyu
In this paper, we consider one-dimensional discrete Schrödinger operators \begin{align} Hu(n)=(Δ+V)u(n)\nonumber \end{align} on with a self-adjoint boundary co…
A doubled Gordon threshold for palindromic quasiperiodic Schrödinger operators
Wencai Liu
We consider one-frequency quasiperiodic Schrödinger operators \[ (H_{v,α,θ}u)(n) = u(n+1)+u(n-1) + v(θ+nα)u(n) \] acting on , where and $v\in…
Proof of geometric Borg's Theorem in arbitrary dimensions
Wencai Liu
Let be the discrete Schrödinger operator, where is the discrete Laplacian on and potential is -periodic with $Γ=q_1\mathb…
Algebraic Properties of the Fermi Variety for Periodic Graph Operators
Jake Fillman, Wencai Liu, Rodrigo Matos
We present a method to estimate the number of irreducible components of the Fermi varieties of periodic Schrödinger operators on graphs in terms of suitable asymptotics. Our main t…
Floquet isospectrality for periodic graph operators
Wencai Liu
Let with arbitrary positive integers , . Let be the discrete Schröd…
Power law logarithmic bounds of moments for long range operators in arbitrary dimension
Wencai Liu
We show that the sublinear bound of the bad Green's functions implies explicit logarithmic bounds of moments for long range operators in arbitrary dimension.
Bloch varieties and quantum ergodicity for periodic graph operators
Wencai Liu
For periodic graph operators, we establish criteria to determine the overlaps of spectral band functions based on Bloch varieties. One criterion states that for a large family of p…
Fermi isospectrality of discrete periodic Schrödinger operators with separable potentials on
Wencai Liu
Let with and . Let be the discrete periodic Schrödinger operator on , where $Δ…
Distributions of resonances of supercritical quasi-periodic operators
Wencai Liu
We discover that the distribution of (frequency and phase) resonances plays a role in determining the spectral type of supercritical quasi-periodic Schrödinger operators. In partic…
One dimensional discrete Schrödinger operators with resonant embedded eigenvalues
Wencai Liu, Kang Lyu
In this paper, we introduce a new family of functions to construct Schrödinger operators with embedded eigenvalues. This particularly allows us to construct discrete Schrödinger op…
Small denominators and large numerators of quasiperiodic Schrödinger operators
Wencai Liu
We initiate an approach to simultaneously treat numerators and denominators of Green's functions arising from quasi-periodic Schrödinger operators, which in particular allows us to…
Topics on Fermi varieties of discrete periodic Schrödinger operators
Wencai Liu
This is a survey of recent progress on the irreducibility of Fermi varieties, rigidity results and embedded eigenvalue problems of discrete periodic Schrödinger operators.
Irreducibility of the Bloch Variety for Finite-Range Schrödinger Operators
Jake Fillman, Wencai Liu, Rodrigo Matos
We study the Bloch variety of discrete Schrödinger operators associated with a complex periodic potential and a general finite-range interaction, showing that the Bloch variety is…
Fermi isospectrality for discrete periodic Schrodinger operators
Wencai Liu
Let , where , . Let be the discrete Schrödinger operator, where …
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.
Revisiting the Christ-Kiselev's multi-linear operator technique and its applications to Schrödinger operators
Wencai Liu
We established a generalized version of the Christ-Kiselev's multi-linear operator technique to deal with the spectral theory of Schrödinger operators. As applications, several spe…
Quantitative inductive estimates for Green's functions of non-self-adjoint matrices
Wencai Liu
We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's esti…
Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues
Wencai Liu
Let be a discrete periodic Schrödinger operator on : where is the discrete Laplacian and is periodic.…
Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case
Svetlana Jitomirskaya, Wencai Liu
We construct Riemannian manifolds with singular continuous spectrum embedded in the absolutely continuous spectrum of the Laplacian. Our manifolds are asymptotically hyperbolic wit…
Anderson localization for multi-frequency quasi-periodic operators on
Svetlana Jitomirskaya, Wencai Liu, Yunfeng Shi
We establish Anderson localization for general analytic -frequency quasi-periodic operators on for \textit{arbitrary} .
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^{-…