10 papers
Positivity and Continuity of Lyapunov Exponents for Multi-Frequency Skew-Shift Schrödinger Operators
Chao Wang, Yuanyuan Peng, Daxiong Piao
We study discrete Schrödinger operators on \(\ell^2(\mathbb Z)\) generated by the vector-frequency two-step skew shift \(T_ω(x,y)=(x+ω,x+y)\), with an arbitrary nonconstant real-an…
Necessary Conditions for Single-Critical-Point Higher-Order Szegő Sum Rules in OPUC
Daxiong Piao
We prove the necessity part of the higher-order Szegő theorem on the unit circle for the single-critical-point weights , . If are…
Single-Point Higher-Order Szegő Sum Rules in OPUC: Necessity for
Daxiong Piao
We give a direct algebraic proof of the necessity direction in the single-point higher-order Szegő sum rules on the unit circle for . More precisely, for $H_m(e^{iθ})=(1-\…
Anderson Localization for Schrödinger Operators with Monotone Potentials Generated by the Doubling Map
Yuanyuan Peng, Chao Wang, Daxiong Piao
In this paper, we consider the Schrödinger operators on , defined for all by \begin{equation} (H(x)u)_n = u_{n+1} + u_{n-1} + λf(2^{n} x) u_n, \q…
On the Genericity of the Spectrum Intervalization for Multi-Frequency Quasiperiodic Schrödinger Operators
Daxiong Piao
This paper proves a genericity conjecture by Goldstein, Schlag, and Voda[Invent. Math.\textbf{217}(2019)] for multi-frequency quasiperiodic Schrödinger operators. Specifically, we…
A Complete Proof of the Simon--Lukic Conjecture for Higher-Order Szegő Theorems
Daxiong Piao
This paper provides a complete proof of Simon-Lukic conjecture for orthogonal polynomials on the unit circle. For a probability measure with Verblun…
Construction and Characterization of Oscillatory Chain Sequences
Zejun Dai, Daxiong Piao, Jinglai Qiao
This paper initiates a theoretical investigation of -oscillatory chain sequences , generalizing Szwarc's classical framework for non-oscillatory chains \cite{…
Finite and full scale localization for the multi-frequency quasi-periodic CMV matrices
Bei Zhang, Daxiong Piao
This paper formulates the finite and full-scale localization for multi-frequency quasi-periodic CMV matrices. This can be viewed as the CMV counterpart to the localization results…
The spectrum of the multi-frequency quasi-periodic CMV matrices contains intervals
Bei Zhang, Daxiong Piao
We investigate the spectral structure of multi-frequency quasi-periodic CMV matrices with Verblunsky coefficients defined by shifts on the -dimensional torus. Under the positive…
Anderson localization for the multi-frequency quasi-periodic CMV matrices and quantum walks
Bei Zhang, Daxiong Piao
In this paper we prove Anderson localization for multi-frequency quasi-periodic extended CMV matrices with analytic Verblunsky coefficients in the regime of positive Lyapunov expon…