Type I energies with positive Lyapunov exponent and gap-labelling condition bound open spectral gaps for irrational frequencies and trig-polynomial potentials, making the all-gaps-open property robust for perturbed almost-Mathieu operators.
Y., and You, J., Kotani theory, Puig’s argument, and stability of The Ten Martini Problem, preprint (2023)
3 Pith papers cite this work. Polarity classification is still indexing.
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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.
The spectrum of the mosaic Almost Mathieu operator is proven to be a Cantor set for all noncritical parameters via an extended duality-reducibility correspondence.
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Monotonicity, global symplectification and the stability of Dry Ten Martini Problem
Type I energies with positive Lyapunov exponent and gap-labelling condition bound open spectral gaps for irrational frequencies and trig-polynomial potentials, making the all-gaps-open property robust for perturbed almost-Mathieu operators.
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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.
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Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator
The spectrum of the mosaic Almost Mathieu operator is proven to be a Cantor set for all noncritical parameters via an extended duality-reducibility correspondence.