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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.06016 |
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| _version_ | 1866914262400630784 |
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| author | Gao, Ju Shen, Fang |
| author_facet | Gao, Ju Shen, Fang |
| contents | We present an angular--momentum--resolved energetic formulation of the Aharonov--Bohm (AB) response for a confined Dirac electron based on two gauge--invariant interaction functionals: a magnetization--field functional and a current--potential functional. Using exact Dirac eigenmodes in a cylindrical cavity threaded by a solenoidal flux, we show that the magnetization--field functional yields a core--localized interaction energy restricted to the $l=0$ channel, with all higher angular--momentum contributions suppressed and vanishing entirely in the limit $a\!\to\!0$. The current--potential functional, by contrast, produces a finite, mode--dependent energy shift for $l\!\ge\!1$ in the same limit, arising from a local interaction between the solenoidal vector potential and the spatially distributed Dirac current, and explicitly encoding the geometric and topological structure of the coupling energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06016 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Angular--Momentum--Resolved Aharonov--Bohm Coupling Energy Gao, Ju Shen, Fang Quantum Physics We present an angular--momentum--resolved energetic formulation of the Aharonov--Bohm (AB) response for a confined Dirac electron based on two gauge--invariant interaction functionals: a magnetization--field functional and a current--potential functional. Using exact Dirac eigenmodes in a cylindrical cavity threaded by a solenoidal flux, we show that the magnetization--field functional yields a core--localized interaction energy restricted to the $l=0$ channel, with all higher angular--momentum contributions suppressed and vanishing entirely in the limit $a\!\to\!0$. The current--potential functional, by contrast, produces a finite, mode--dependent energy shift for $l\!\ge\!1$ in the same limit, arising from a local interaction between the solenoidal vector potential and the spatially distributed Dirac current, and explicitly encoding the geometric and topological structure of the coupling energy. |
| title | Angular--Momentum--Resolved Aharonov--Bohm Coupling Energy |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.06016 |