自旋-1/2 Aharonov-Bohm束缚态的普适临界g因子
Universal critical $g$ factor for spin-1/2 Aharonov-Bohm bound states
- Air Institute（空气研究所）
- Universidade Federal do Maranhão（马拉尼昂联邦大学）
- Universidade Estadual de Ponta Grossa（蓬塔格罗萨州立大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
该研究证明自旋-1/2 Aharonov-Bohm束缚态的临界g因子普适为2，与磁通扇区无关，并确认Hagen结论适用于物理选择的延拓成员，反常磁矩是束缚的必要充分条件。
中文摘要 AI 辅助
自旋-1/2 Aharonov-Bohm哈密顿量是否支持束缚态这一问题，自Hagen得出结论认为狄拉克粒子不存在此类态以来，一直存在争议。在此，我们表明Hagen的解对应于描述奇异塞曼相互作用的一参数自伴延拓族中的特定成员，并确定微观物理所选择的成员。将延拓参数与有限半径磁通管匹配，恰好得到$\ u=0$当$g=2$时，且在每个磁通扇区均如此。因此，临界$g$因子是普适的，$g_c=2$，既不依赖于磁通扇区，也不依赖于正则化半径。磁通扇区控制束缚态能量的深度，我们得到一个闭式表达式，表明束缚随磁通的整数部分显著加深。因此，Hagen的结论得到确认并加以精确化：它不是关于延拓族中任意一个成员的陈述，而是关于当磁矩取狄拉克值时物理所选择的成员，且反常磁矩是奇异通道中束缚的必要且充分条件。
英文摘要
Whether the spin-1/2 Aharonov-Bohm Hamiltonian supports bound states has remained controversial since Hagen concluded that no such states exist for a Dirac particle. Here, we show that Hagen's solution corresponds to a particular member of the one-parameter family of self-adjoint extensions that describe the singular Zeeman interaction, and we identify which member the microscopic physics selects. Matching the extension parameter to a finite-radius flux tube yields $ν=0$ precisely at $g=2$, and it does so in every flux sector. The critical $g$ factor is therefore universal, $g_c=2$, and depends on neither the flux sector nor the regularization radius. The flux sector controls the depth of the bound state energy, and we obtain a closed-form expression showing that binding deepens markedly with the integer part of the flux. Hagen's conclusion is thus confirmed and sharpened: it is not a statement about one arbitrary member of a family of extensions, but about the member that the physics selects when the magnetic moment takes its Dirac value, and an anomalous moment is a necessary and sufficient condition for binding in the singular channel.
