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. (c) 2022 Elsevier Inc. All rights reserved.
Quantum magnetic billiards: Boundary conditions and gauge transformations
Giuliano Angelone;Paolo Facchi;Davide Lonigro
2022-01-01
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. (c) 2022 Elsevier Inc. All rights reserved.File in questo prodotto:
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