Wencai Liu

activity

20132026

most citedArithmetic Spectral Transitions for the Maryland Model

36 citations · 389 across the 48 of their papers we have counts for

collaborators

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27 papers · 1 filter

math-ph2026

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 $ℓ^{2} (N)$ with a self-adjoint boundary co…

math-ph2026

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 $ℓ^{2} (Z)$ , where $α \in / Q$ and $v\in…

math-ph2022★ 6 cited

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.

math-ph2022★ 1 cited

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…

math-ph2022★ 6 cited

Fermi isospectrality of discrete periodic Schrödinger operators with separable potentials on $Z^{2}$

Wencai Liu

Let $Γ = q_{1} Z \oplus q_{2} Z$ with $q_{1} \in Z_{+}$ and $q_{2} \in Z_{+}$ . Let $Δ + X$ be the discrete periodic Schrödinger operator on $Z^{2}$ , where $Δ…

math-ph2022

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…

math-ph2022

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…

math-ph2022

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…

math-ph2021★ 15 cited

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.

math-ph2021★ 19 cited

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…

math-ph2021★ 4 cited

Fermi isospectrality for discrete periodic Schrodinger operators

Wencai Liu

Let $Γ = q_{1} Z \oplus q_{2} Z \oplus \dots \oplus q_{d} Z$ , where $q_{l} \in Z_{+}$ , $l = 1, 2, \dots, d$ . Let $Δ + V$ be the discrete Schrödinger operator, where $Δ$ …

math-ph2021★ 10 cited

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.

math-ph2020★ 4 cited

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…

math-ph2020★ 33 cited

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…

math-ph2020★ 23 cited

Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues

Wencai Liu

Let $H_{0}$ be a discrete periodic Schrödinger operator on $ℓ^{2} (Z^{d})$ : $H_{0} = - Δ + V,$ where $Δ$ is the discrete Laplacian and $V : Z^{d} \to C$ is periodic.…

math-ph2018★ 11 cited

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…

math-ph2018★ 1 cited

Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators

Wencai Liu

For perturbed Stark operators $H u = - u^{''} - xu + q u$ , the author has proved that $lim sup_{x \to \infty} x^{\frac{1}{2}} ∣ q (x) ∣$ must be larger than $\frac{1}{\sqrt{2}}N^{\fra…

math-ph2018★ 13 cited

Absence of singular continuous spectrum for perturbed discrete Schrödinger operators

Wencai Liu

We show that the spectral measure of discrete Schrödinger operators $(H u) (n) = u (n + 1) + u (n - 1) + V (n) u (n)$ does not have singular continuous component if the potential $V(n)=O(n^{-…

math-ph2018★ 5 cited

The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators

Wencai Liu

Let $H_{0}$ be a periodic operator on $R^{+}$ (or periodic Jacobi operator on $N$ ). It is known that the absolutely continuous spectrum of $H_{0}$ is consisted of spectral bands $\cup[α…

math-ph2018★ 13 cited

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 $q$ is the power-decaying perturbation. The crit…

math-ph2018★ 23 cited

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…

math-ph2017★ 2 cited

Continuous quasiperiodic Schrödinger operators with Gordon type potentials

Wencai Liu

Let us concern the quasi-periodic Schrödinger operator in the continuous case, \begin{equation*} (Hy)(x)=-y^{\prime\prime}(x)+V(x,ωx)y(x), \end{equation*} where $V : (R / Z)^{2} \to R$ …

math-ph2017★ 1 cited

Sharp bound on the largest positive eigenvalue for one-dimensional Schrödinger operators

Wencai Liu

Let $H = - D^{2} + V$ be a Schrödinger operator on $L^{2} (R)$ , or on $L^{2} (0, \infty)$ . Suppose the potential satisfies $lim sup_{x \to \infty} ∣ x V (x) ∣ = a < \infty$ . We prove that $H$ a…

math-ph2016★ 1 cited

The spectra of surface Maryland model for all phases

Wencai Liu

We study the discrete Schrödinger operators $H_{λ, α, θ}$ on $ℓ^{2} (Z^{d + 1})$ with surface potential of the form $V (n, x) = λ δ (x) tan π (α \cdot n + θ)$ , and $H_{λ, α, θ}^{+}$ on $\e…

Optimal bounds for embedded eigenvalues of one-dimensional discrete Schrödinger operators with decaying potentials

A doubled Gordon threshold for palindromic quasiperiodic Schrödinger operators

Power law logarithmic bounds of moments for long range operators in arbitrary dimension

Bloch varieties and quantum ergodicity for periodic graph operators

Fermi isospectrality of discrete periodic Schrödinger operators with separable potentials on Z2

Distributions of resonances of supercritical quasi-periodic operators

One dimensional discrete Schrödinger operators with resonant embedded eigenvalues

Small denominators and large numerators of quasiperiodic Schrödinger operators

Topics on Fermi varieties of discrete periodic Schrödinger operators

Irreducibility of the Bloch Variety for Finite-Range Schrödinger Operators

Fermi isospectrality for discrete periodic Schrodinger operators

Upper bounds on transport exponents for long range operators

Revisiting the Christ-Kiselev's multi-linear operator technique and its applications to Schrödinger operators

Quantitative inductive estimates for Green's functions of non-self-adjoint matrices

Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues

Exact dynamical decay rate for the almost Mathieu operator

Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators

Absence of singular continuous spectrum for perturbed discrete Schrödinger operators

The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators

Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators

Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase

Continuous quasiperiodic Schrödinger operators with Gordon type potentials

Sharp bound on the largest positive eigenvalue for one-dimensional Schrödinger operators

The spectra of surface Maryland model for all phases

Fermi isospectrality of discrete periodic Schrödinger operators with separable potentials on $Z^{2}$