In one minute

A. L. Shelankov revisits the debated transverse force exerted by an Aharonov-Bohm magnetic flux line, using a new paraxial solution to Aharonov-Bohm scattering. Although the scattering cross-section is left-right symmetric, a beam of finite width is deflected by the flux line as if by a Lorentz force. The asymmetry and the force come from quantum interference in the forward direction, within the angular size of the incoming wave. The force is tied to the incident current at the line, and the S-matrix, not the scattering amplitude, is the right language for forward scattering. For superfluid helium-4, the result confirms the Iordanskii force on vortex lines.

Magnetic force exerted by the Aharonov-Bohm line