Quantum waveguides with magnetic fields

TL;DR

This paper develops a method to analyze the spectral properties of quantum waveguides under magnetic fields by constructing effective Hamiltonians, extending previous results to more general and explicit cases.

Contribution

It introduces a new approach for deriving effective Hamiltonians for magnetic quantum waveguides, including explicit examples not previously studied.

Findings

Effective Hamiltonians enable detailed spectral analysis.

New explicit examples of magnetic waveguides analyzed.

Method applies to moderate and strong magnetic fields.

Abstract

We study generalised quantum waveguides in the presence of moderate and strong external magnetic fields. Applying recent results on the adiabatic limit of the connection Laplacian we show how to construct and compute effective Hamiltonians that allow, in particular, for a detailed spectral analysis of magnetic waveguide Hamiltonians. We apply our general construction to a number of explicit examples, most of which are not covered by previous results.