Diffraction and quasiclassical limit of the Aharonov--Bohm effect

TL;DR

This paper demonstrates that the Aharonov-Bohm effect persists in the quasiclassical limit through diffraction phenomena, with the effect influenced by space geometry and particle spin.

Contribution

It reveals the persistence of the Aharonov-Bohm effect in the quasiclassical limit via diffraction, considering Euclidean and conical spaces, and highlights spin dependence in conical space.

Findings

Aharonov-Bohm effect persists in quasiclassical limit due to diffraction.

Diffraction types depend on space geometry: Fraunhofer in Euclidean, Fresnel in conical.

Effect can be controlled by magnetic flux, influenced by particle spin in conical space.

Abstract

Since the Aharonov-Bohm effect is the purely quantum effect that has no analogues in classical physics, its persistence in the quasiclassical limit seems to be hardly possible. Nevertheless, we show that the scattering Aharonov-Bohm effect does persist in the quasiclassical limit owing to the diffraction, i.e. the Fraunhofer diffraction in the case when space outside the enclosed magnetic flux is Euclidean, and the Fresnel diffraction in the case when the outer space is conical. Hence, the enclosed magnetic flux can serve as a gate for the propagation of short-wavelength, almost classical, particles. In the case of conical space, this quasiclassical effect which is in principle detectable depends on the particle spin.