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

TL;DR

This paper introduces a weaker spectral measure condition called 'eventual absolute continuity' that guarantees quantum delocalization, and applies these ideas to improve phase-averaged delocalization bounds for Fibonacci quasicrystals.

Contribution

It proposes a new spectral measure condition and enhances phase-averaged delocalization bounds specifically for Fibonacci quasicrystals.

Findings

Weaker condition on spectral measures ensures quantum delocalization.

Improved phase-averaged delocalization bounds for Fibonacci quasicrystals.

Extension of RAGE Theorem concepts to new spectral measure conditions.

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.