Magnetic quantum currents in the presence of a Neumann wall

TL;DR

This paper investigates low energy magnetic quantum currents near a boundary with Neumann conditions, establishing a Limiting Absorption Principle for the perturbed magnetic Neumann Laplacian.

Contribution

It introduces a new analysis of boundary currents and proves a Limiting Absorption Principle for the magnetic Neumann Laplacian under electric potential perturbations.

Findings

Established a Limiting Absorption Principle for the magnetic Neumann Laplacian.

Analyzed low energy boundary currents in a half-plane with magnetic field.

Provided mathematical framework for boundary current behavior under perturbations.

Abstract

We consider the Schr\"odinger operator with constant transverse magnetic field on a half-plane, endowed with Neumann boundary conditions. We study the low energy currents flowing along the boundary and we establish a Limiting Absorption Principle for the magnetic Neumann Laplacian under perturbation of an electric potential.