The Aharonov-Bohm effect: the role of tunneling and associated forces

TL;DR

This paper investigates the Aharonov-Bohm effect, demonstrating that a flux-dependent force persists due to tunneling effects even with infinite shielding, providing a natural explanation for the phenomenon.

Contribution

It reveals that a flux-dependent force remains in the Aharonov-Bohm effect due to tunneling, even with infinite shielding, offering a new physical insight.

Findings

A flux-dependent force persists despite infinite shielding.

Tunneling effects influence the Aharonov-Bohm effect.

Radial wavefunction derivatives explain the residual force.

Abstract

Through tunneling, or barrier penetration, small wavefunction tails can enter a finitely shielded cylinder with a magnetic field inside. When the shielding increases to infinity the Lorentz force goes to zero together with these tails. However, it is shown, by considering the radial derivative of the wavefunction on the cylinder surface, that a flux dependent force remains. This force explains in a natural way the Aharonov-Bohm effect in the idealized case of infinite shielding.