Absolutely Continuous Spectrum for Random Schroedinger Operators on Tree-Strips of finite cone type

TL;DR

This paper proves that for small disorder, the spectrum of random Schrödinger operators on tree-strips of finite cone type is almost surely purely absolutely continuous within a specific set, advancing understanding of spectral properties in complex structures.

Contribution

It establishes the absolute continuity of the spectrum for a new class of random Schrödinger operators on tree-strips of finite cone type under small disorder conditions.

Findings

Spectrum is almost surely purely absolutely continuous for small disorder.

Results apply to operators on tree-strips of finite cone type.

Advances understanding of spectral behavior in complex graph structures.

Abstract

A tree-strip of finite cone type is the product of a tree of finite cone type with a finite set. We consider random Schr\"odinger operators on these tree strips, similar to the Anderson model. We prove that for small disorder the spectrum is almost surely, purely, absolutely continuous in a certain set.