Classically Bound and Quantum Quasi-Bound States of an Electron on a Plane Adjacent to a Magnetic Monopole

• URL: http://arxiv.org/abs/2501.04406v1
• Date: Wed, 08 Jan 2025 10:36:13 GMT
• Title: Classically Bound and Quantum Quasi-Bound States of an Electron on a Plane Adjacent to a Magnetic Monopole
• Authors: J. Martin, A. Baskerville, V. L. Campo, J. Minns, J. Pooley, S. T. Carr, C. A. Hooley, G. Möller, J. Quintanilla,
• Abstract summary: We find bound states in the classical version of the problem and quasi-bound states in the quantum one. The threshold monopole magnetic charge required to realise a single quasi-bound state is approximately $18Q_D$. We examine the feasibility of achieving this magnetic charge in currently available monopole analogues: spin ice, artificial spin ice, and magnetic needles.
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• Abstract: In three-dimensional space an electron moving in the field of a magnetic monopole has no bound states. In this paper we explore the physics when the electron is restricted to a two-dimensional plane adjacent to a magnetic monopole. We find bound states in the classical version of the problem and quasi-bound states in the quantum one, in addition to a continuum of scattering states. We calculate the lifetimes of the quasi-bound states using several complementary approximate methods, which agree well in the cases where the lifetimes are relatively short. The threshold monopole magnetic charge required to realise a single quasi-bound state is approximately $18Q_D$, where $Q_D$ is the magnetic charge of a Dirac monopole. We examine the feasibility of achieving this magnetic charge in currently available monopole analogues: spin ice, artificial spin ice, and magnetic needles.

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