Uniform dynamical bounds for the Fibonacci Hamiltonian

TL;DR

This paper establishes uniform quantum dynamical bounds for Fibonacci Hamiltonian operators across phases, using combinatorial analysis to extend previous phase-specific results to a broader class.

Contribution

It provides the first uniform bounds in phase for Fibonacci Hamiltonians, advancing understanding of their quantum dynamical behavior at large coupling.

Findings

Bounds hold uniformly across phases

Results apply for sufficiently large coupling

Extends previous phase-specific bounds

Abstract

We prove quantum dynamical upper bounds for operators from the Fibonacci hull. These bounds hold for sufficiently large coupling and they are uniform in the phase. This extends recent work by Killip, Kiselev and Last who obtained these bounds for one particular phase. The main ingredient in our proof is a detailed combinatorial analysis of the sequences in the Fibonacci hull.