标题： 经典束缚态和量子准束缚态电子在磁单极子附近的平面上 显示英文标题

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

摘要： 在三维空间中，一个在磁单极子场中运动的电子没有束缚态。 在本文中，我们探讨当电子被限制在一个与磁单极子相邻的二维平面上时的物理情况。 我们发现经典问题中存在束缚态，而量子问题中存在准束缚态，此外还存在连续的散射态。 我们使用几种互补的近似方法计算了准束缚态的寿命，在寿命相对较短的情况下，这些方法的结果有很好的一致性。 实现单个准束缚态所需的临界磁单极子磁荷约为$18Q_D$，其中$Q_D$是狄拉克单极子的磁荷。 我们检查了在目前可用的单极子类比物中实现这种磁荷的可行性：自旋冰、人工自旋冰和磁针。 显示英文摘要

摘要： 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.