Localization on a quantum graph with a random potential on the edges

TL;DR

This paper demonstrates spectral and dynamical localization in a quantum graph with random potentials, employing multiscale analysis similar to that used for random Schrödinger operators.

Contribution

It extends localization results to quantum graphs with random potentials using multiscale analysis techniques.

Findings

Spectral localization established for the quantum graph model.

Dynamical localization demonstrated under the given conditions.

Methodology parallels that of random Schrödinger operators.

Abstract

We prove spectral and dynamical localization on a cubic-lattice quantum graph with a random potential. We use multiscale analysis and show how to obtain the necessary estimates in analogy to the well-studied case of random Schroedinger operators.