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Sharp arithmetic delocalization for quasiperiodic operators with potentials of semi-bounded variation
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We obtain the sharp arithmetic Gordon's theorem: that is, absence of eigenvalues on the set of energies with Lyapunov exponent bounded by the exponential rate of approximation of frequency by the rationals, for a large class of one-dimensional quasiperiodic Schr\"odinger operators, with no (modulus of) continuity required. The class includes all unbounded monotone potentials with finite Lyapunov exponents and all potentials of bounded variation. The main tool is a new uniform upper bound on iterates of cocycles of bounded variation.
Forward citations
Cited by 3 Pith papers
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Lower bounds on concentration through Borel transforms and quantitative singularity of spectral measures near the arithmetic transition
Packing and multifractal dimensions of almost Mathieu spectral measures have upper bounds that vanish at the arithmetic transition where ln lambda equals beta.
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Universality of Packing Dimension Estimates for Spectral Measures of Quasiperiodic Operators: Monotone Potentials
For γ-monotone quasiperiodic potentials, the upper packing dimension of spectral measures is at most 2(1-L/β) when L<β, and is zero when L≥β.
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A New Proof of the Sharp Gordon's Lemma: No Eigenvalues for Schr\"odinger Operators with Almost Repetition Potentials
A new Wronskian-based proof shows that if a one-dimensional Schrödinger potential has almost repetitions with rate γ > L(E), the operator has no eigenvalues.
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