A new Canonical Center Bundle framework for long-range operators coincides with finite-range approximations and yields absolute continuity of the IDS plus Anderson localization for analytic quasi-periodic Schrödinger operators with Diophantine frequency.
Avila, KAM, Lyapunov exponents, and the spectral dichotomy for typical one-frequency Schrödinger operators, arXiv:2307.1107 (2023)
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Transfer Operators, Canonical Center Dynamics, and Spectral Applications for Long-Range Operators
A new Canonical Center Bundle framework for long-range operators coincides with finite-range approximations and yields absolute continuity of the IDS plus Anderson localization for analytic quasi-periodic Schrödinger operators with Diophantine frequency.