Magnetic Force Exerted by the Aharonov-Bohm Line (II)

TL;DR

This paper investigates the magnetic force exerted by the Aharonov-Bohm flux line, demonstrating that quantum interference causes a deflection akin to a Lorentz force, and confirms the Iordanskii force in superfluid helium-4.

Contribution

It introduces a new paraxial solution to the AB scattering problem and clarifies the origin of the magnetic force and asymmetry in scattering.

Findings

Finite-width beams are deflected by the AB line as if by a Lorentz force.

Quantum interference in the forward direction causes asymmetry and magnetic force.

Confirms the Iordanskii force acting on vortex lines in superfluid helium-4.

Abstract

The controversial question of the transverse force exerted by the Aharonov-Bohm (AB) magnetic flux line is reconsidered with the help of a new paraxial solution to the AB-scattering problem. It is shown that despite the left-right symmetry in the AB scattering cross-section, a beam of a finite width is deflected by the AB-line as if by the ``Lorentz'' force. The asymmetry and the magnetic force originate from the quantum interference in the forward direction within the angular size of the incident wave. In the context of the superfluid He-4 theory, the paper confirmes the Iordanskii force acting on the vortex line.