ar X iv : c on d - m at / 9 80 31 05 v 1 1 0 M ar 1 99 8 Aharonov - Bohm and Aharonov - Casher Effects : Connections to Dynamics of Topological Singularities

We analyze the physical processes involved in the Aharonov-Bohm (A-B) and the Aharonov-Casher (A-C) effects, showing that an incomplete A-B effect knowledge can lead a totally wrong conclusion on the A-C effect. Based on this we demonstrate that the Magnus force, the net force, is the only transverse force on a moving vortex, in analogous to the net charge in A-C effect. This conclusion has been arrived both theoretically and experimentally. Let us begin with a well accepted situation, the connection between the A-B effect [1] and the A-C effect [2]. The A-C phenomenon is the effect of charges on a moving magnetic flux line, the dual effect of A-B phenomenon of the magnetic flux line effect on moving charges. Within the non-relativistic formulation, those two effects can be formally related to each other by a Galilean transformation. However, the crucial difference between A-B and A-C effects in real calculations is that, for the A-B effect a moving charge 'sees' the net magnetic flux, but for the A-C effect a moving magnetic flux line 'sees' the net charge. It is rather easy to conceive the situation of a flux line in a condensed matter: suppose one knows perfectly well a large A-B effect for conduction electrons, can he draw a definite conclusion on the A-C effect for the moving flux line? The answer is NO, because the net charge for the A-C effect comes from various contributions, and the contribution from conduction electrons is only one of them. For example, the A-C effect can be zero in the case of charge neutrality, and, be either positive or negative depending on the net charge feel by the flux line. Until effect for conduction electrons alone can not yield any information on the A-C effect for a moving flux line. This illustrates the pitfall in using the incomplete A-B effect information to 1