Absolutely Continuous Spectrum for random Schroedinger operators on the Fibonacci and similar tree-strips

TL;DR

This paper proves that small disorder random Schrödinger operators on certain tree-strip structures, like Fibonacci trees, exhibit purely absolutely continuous spectrum within specific energy ranges, advancing understanding of spectral properties in complex graph models.

Contribution

It establishes the presence of purely absolutely continuous spectrum for small disorder in Schrödinger operators on Fibonacci-like tree-strip graphs, a novel spectral result for these structures.

Findings

Purely absolutely continuous spectrum in certain energy sets

Spectral properties depend on small disorder levels

Extension of spectral theory to Fibonacci and similar tree-strips

Abstract

We will consider cross products of finite graphs with a class of trees that have arbitrarily but finitely long line segments, such as the Fibonacci tree. Such cross products are called tree-strips. We prove that for small disorder random Schr\"odinger operators on such tree-strips have purely absolutely continuous spectrum in a certain set.