Angular--Momentum--Resolved Aharonov--Bohm Coupling Energy

TL;DR

The paper addresses whether the Aharonov–Bohm effect in a confined Dirac system can be understood as a local energy coupling rather than solely a nonlocal phase. It computes exact Dirac eigenmodes in a cylindrical cavity and evaluates both the wave–particle (WP) and wave–entity (WE) couplings using the same current densities, deriving explicit energy shifts. The WP picture yields a core‑localized $l=0$ contribution, while the WE framework adds a regulator‑dependent and a regulator‑independent, $l$‑linear, mode‑resolved energy shift $\Delta \Omega_{\mathrm{WE}} = l\,\Omega(R)\,[C_l(a)+F_l(R)]$, unifying spin and orbital AB responses in a local interaction. The results predict observable energy splittings at microwave frequencies for nanoscale cavities, offering a concrete route to test locality in AB physics and to probe the role of current density in AB coupling.

Abstract

The Aharonov--Bohm (AB) effect is conventionally interpreted as a phase shift acquired by charged particles encircling a flux, with no fields acting locally along their paths. Here we show that a confined Dirac electron exhibits a distinct AB \emph{coupling energy} arising from a \emph{local current--potential interaction}, whose form depends on the chosen prescription. In the \emph{wave--particle} (WP) prescription the response is confined to the flux core: only the $l=0$ mode leaves a finite remnant as the core shrinks, while all higher modes vanish. In the \emph{wave--entity} (WE) prescription the $l=0$ result coincides with WP, but for $l\!\ge\!1$ the response becomes a quantized, $l$--linear energy shift. The AB effect thereby emerges as a quantized, mode--resolved energy law that establishes locality through standard field coupling and distinguishes between electron prescriptions.