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Square-Root Profiles and Sharp Fourier Decay of Quasiperiodic Spectral Measures
Zhenfu Wang, Qi Zhou
We study spectral measures of one-dimensional quasiperiodic Schrödinger operators. For subcritical Schrödinger operator with Diophantine frequency, we prove sharp measurable-set bo…
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…
Spectrum of Hatano-Nelson model with strictly ergodic potentials
Xueyin Wang, Zhenfu Wang, Jiangong You +1
We provide a precise formula for the spectrum of the Hatano-Nelson model with strictly ergodic potentials in terms of its Lyapunov exponent. As applications, one clearly observes t…