A note on the RAGE Theorem and phase-averaged dispersion for the Fibonacci Hamiltonian

Gaétan Leclerc

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arXiv · 2512.06844

A note on the RAGE Theorem and phase-averaged dispersion for the Fibonacci Hamiltonian

Gaétan Leclerc

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Abstract

We find a weaker condition on spectral measures, "eventual absolute continuity", that ensure quantum delocalization as in the RAGE Theorem in the case of purely absolutely continuous spectrum. We then adapt these idea to strongly improve some phase-averaged delocalization bounds for the Fibonacci quasicrystal.

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Gaétan Leclerc. 2025-12-07. A note on the RAGE Theorem and phase-averaged dispersion for the Fibonacci Hamiltonian. https://arxiv.org/abs/2512.06844

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