Locality and causality in time-dependent Aharonov-Bohm interference

Abstract

Using the path-integral method we analyse the effect of a time-varying (stepped) enclosed magnetic flux on the Aharonov-Bohm (AB) phase shift in the two-slit interference pattern of electron wavepackets. We find the magnetic phase shift to vary continuously between zero and the full AB value depending on the timing of the flux increment. This behaviour is amenable to experimental verification. The special nature of the global features peculiar to the static AB effect emerges clearly from this study which supports a shift in emphasis away from the enclosed flux itself towards its vector potential, acting locally along the interfering Feynman (and, in a certain sense, the classical) trajectories.