5 papers
The Ultimate Ishii-Pastur Theorem for Whole-Line Ergodic Block Jacobi Operators
Zhenfu Wang, Bei Zhang, Qi Zhou
We establish an ultimate Ishii-Pastur theorem for whole-line ergodic block Jacobi operators. We prove that, for almost every realization, the restriction of a maximal spectral meas…
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…
Anderson localization of long-range quasi-periodic operators via Dynamical Rigidity
Zhenfu Wang, Jiangong You, Qi Zhou
We establish Anderson localization for long-range quasi-periodic operators with large trigonometric potentials and Diophantine frequencies, the proof is based on a novel dynamical…
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…
Sharp Spectral Gaps, Arithmetic Localization, and Reducibility via Resonance Analys
Lingrui Ge, Jiangong You, Qi Zhou
This paper establishes several sharp spectral results for analytic quasiperiodic Schrodinger operators. Key contributions include: (1) exact exponential decay rates for spectral ga…