Quantum magnetic billiards: boundary conditions and gauge transformations

TL;DR

This paper investigates boundary conditions for a charged quantum particle in a magnetic field, emphasizing gauge covariance and introducing gauge covariant boundary conditions in quantum magnetic billiards.

Contribution

It introduces gauge covariant boundary conditions and provides a sufficient condition for gauge covariance in quantum magnetic billiards.

Findings

Gauge covariant boundary conditions are introduced.

A sufficient condition for gauge covariance is established.

All studied boundary conditions satisfy the gauge covariance condition.

Abstract

We study admissible boundary conditions for a charged quantum particle in a two-dimensional region subjected to an external magnetic field, i.e. a quantum magnetic billiard. After reviewing some physically interesting classes of admissible boundary conditions (magnetic Robin and chiral boundary conditions), we turn our attention to the role of gauge transformations in a magnetic billiard: in particular, we introduce gauge covariant boundary conditions, and find a sufficient condition for gauge covariance which is satisfied by all the aforementioned examples.