Anderson localization on quantum graphs coded by elements of a subshift of finite type

TL;DR

This paper investigates Anderson localization phenomena in quantum graphs whose edge configurations are governed by subshifts of finite type, demonstrating localization under these conditions.

Contribution

It introduces a new class of quantum graphs based on subshifts of finite type and proves Anderson localization for these models.

Findings

Proved Anderson localization for quantum graphs with subshift of finite type.

Established spectral properties of Schrödinger operators on these graphs.

Connected graph dynamics with symbolic dynamical systems.

Abstract

We study Schr\"odinger operators on quantum graphs where the number of edges between points is determined by orbits of a "shift of finite type". We prove Anderson localization for these systems.