All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations

Oliveira, César R. de; Monteiro, Wagner

doi:10.2422/2036-2145.201908_008

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2021

2024

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“…Quantum magnetic billiards are also extensively studied in the mathematical literature, which ranges e.g. from the rigorous analysis of magnetic Hamiltonians and of their spectral properties [20,21], to the description of gauge fields in non-trivial topologies and geometries [22,23].…”

Section: Introductionmentioning

confidence: 99%

Quantum magnetic billiards: boundary conditions and gauge transformations

Angelone,

Facchi,

Lonigro

2021

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%