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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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.
Moments of Leb restricted to the intersection spectrum Σ_{α,λ} of the AMO are polynomials in λ with trigonometric-polynomial coefficients in α, implying continuous weak-* dependence of μ⁻_{α,λ} on parameters and analyticity in λ away from λ=1.
Geometric Binder cumulants derived from a generalized Bargmann invariant detect gap closure in quantum systems for identifying phase transitions.
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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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Generalized Aubry-Andr\'e formula and continuity of the intersection spectrum of the Almost Mathieu operator
Moments of Leb restricted to the intersection spectrum Σ_{α,λ} of the AMO are polynomials in λ with trigonometric-polynomial coefficients in α, implying continuous weak-* dependence of μ⁻_{α,λ} on parameters and analyticity in λ away from λ=1.