Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms

TL;DR

This paper introduces the magnetic Hodge Laplacian, a new operator extending magnetic Laplacian concepts to differential forms, and explores its spectral properties and differences from existing operators.

Contribution

It presents the magnetic Hodge Laplacian, generalizing the magnetic Laplacian to differential forms, and analyzes its spectral characteristics.

Findings

Spectral results for the magnetic Hodge Laplacian are established.

Comparisons made between magnetic Hodge Laplacian and classical operators.

Differences and similarities with existing Laplacians are discussed.

Abstract

In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral results, which are known for the magnetic Laplacian on functions or for the Hodge Laplacian on differential forms, and discuss similarities and differences of this new ``magnetic-type'' operator.