Proposed Aharonov-Casher effect: Another example of an Aharonov-Bohm effect arising from a classical lag

Aharonov-Casher and scalar Aharonov-Bohm topological effects

We reexamine the topological and nonlocal natures of the Aharonov-Casher and scalar Aharonov-Bohm phase effects. The underlying U(1) gauge structure is exhibited explicitly. And the conditions for developing topological Aharonov-Casher and scalar Aharonov-Bohm phases are clarified. We analyze the arguments of M. Peshkin and H. J. Lipkin [Phys. Rev. Lett. 74, 2847 (1995)] in detail and show that they are based on the wrong Hamiltonian which yields their conclusion incorrect.

Topological phases for composite particles with dynamic properties

We show that, if a given electromagnetic property of a particle is allowed to vary during an evolution where the particle will accrue a topological phase, then it is both the time average and the statistical variance of this property which will affect the observable phenomena. The time average is shown to affect the topological aspect of the phase. This is in addition to a second smaller dynamical phase term, which depends upon only the variance of the changing property. The theory is illustrated in reference to the time dependence of the dipole moment in both the Aharonov-Casher and He-McKellar-Wilkens effects.