1 citations · 1 across the 6 of their papers we have counts for
7 papers
Dry Ten Martini Problem in the Subcritical Type I Regime
Xianzhe Li
We establish a resolvent factorization of the hyperbolic projection associated with the finite-range dual operators, by a kernel with exponential off-diagonal decay. As an applicat…
Transfer Operators, Canonical Center Dynamics, and Spectral Applications for Long-Range Operators
Xianzhe Li, Zhenfu Wang, Jiangong You +1
We introduce an operator-theoretic framework for long-range operators over general dynamical systems with analytic hopping and small potential. By establishing a partially hyperbol…
Monotonicity, global symplectification and the stability of Dry Ten Martini Problem
Xianzhe Li, Disheng Xu, Qi Zhou
We prove that, for every irrational frequency and every analytic Type I potential, each supercritical spectral energy satisfying the gap-labelling condition is an endpoint of an op…
Log-Hausdorff multifractality of the absolutely continuous spectral measure of the almost Mathieu operator
Jie Cao, Xianzhe Li, Baowei Wang +1
This paper focuses on the fractal characteristics of the absolutely continuous spectral measure of the subcritical almost Mathieu operator (AMO) and Diophantine frequency. In parti…
Exact local distribution of the absolutely continuous spectral measure
Xianzhe Li, Jiangong You, Qi Zhou
It is well-established that the spectral measure for one-frequency Schrödinger operators with Diophantine frequencies exhibits optimal -Hölder continuity within the absolutely…
Stability of Spectral Types of Quasi-Periodic Schrödinger Operators With Respect to Perturbations by Decaying Potentials
David Damanik, Xianzhe Li, Jiangong You +1
We consider perturbations of quasi-periodic Schrödinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under whi…
Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications
Xianzhe Li
We establish a quantitative version of strong almost reducibility result for quasi-periodic cocycle close to a constant in Gevrey class. We prove that,…