Spectral analysis of The magnetic Laplacian acting on discrete funnels

TL;DR

This paper investigates the spectral properties of the discrete magnetic Laplacian on funnel-like graphs, using perturbation techniques and positive commutator methods to establish propagation estimates and the Limiting Absorption Principle.

Contribution

It introduces a novel analysis of the magnetic Laplacian on discrete funnels with long-range metric perturbations, extending spectral theory tools to this setting.

Findings

Established propagation estimates for the magnetic Laplacian.

Proved a Limiting Absorption Principle away from embedded eigenvalues.

Applied positive commutator techniques to discrete funnel graphs.

Abstract

We study perturbations of the discrete magnetic Laplacian associated to discrete analogs of funnels. We perturb the metric in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away from possible embedded eigenvalues. The approach is based on a positive commutator technique.