The Aharonov-Bohm effect for a knotted magnetic solenoid

TL;DR

This paper demonstrates that a charged particle's wave function acquires a phase shift due to the linking with a knotted magnetic solenoid, extending the Aharonov-Bohm effect to complex topological configurations.

Contribution

It introduces the concept of the Aharonov-Bohm effect for particles linked with knotted magnetic solenoids, connecting quantum phase shifts with knot topology.

Findings

Phase shift proportional to flux intersecting the Seifert surface

Linking with knotted solenoid causes observable quantum interference

Extends Aharonov-Bohm effect to knotted magnetic fields

Abstract

We show that the linking of a semiclassical path of a charged particle with a knotted magnetic solenoid results in the Aharonov-Bohm effect. The phase shift in the wave function is proportional to the flux intersecting a certain connected and orientable surface bounded by the knot (a Seifert surface of the knot).