Almost Ballistic Transport for the Weakly Coupled Fibonacci Hamiltonian

TL;DR

This paper analyzes the transport properties of the weakly coupled Fibonacci Hamiltonian, showing that transport exponents approach one as coupling decreases and exceed the spectrum's fractal dimension at small couplings.

Contribution

It provides new estimates for transport exponents and demonstrates their behavior in the weak coupling regime of the Fibonacci Hamiltonian.

Findings

Transport exponents approach one as coupling tends to zero.

Transport exponents exceed the fractal dimension of the spectrum at small coupling.

Provides bounds and estimates for transport exponents in the Fibonacci model.

Abstract

We prove estimates for the transport exponents associated with the weakly coupled Fibonacci Hamiltonian. It follows in particular that the upper transport exponent $\tilde \alpha^\pm_u$ approaches the value one as the coupling goes to zero. Moreover, for sufficiently small coupling, $\tilde \alpha^\pm_u$ strictly exceeds the fractal dimension of the spectrum.