The Aharonov–Bohm effect in a closed flux line

Michael Berry, Andrei L. Shelankov

For flux , the Aharonov-Bohm wavefunction AB ( r , ) is represented exactly in terms of Fresnel integrals. Numerical evidence shows that in the complex AB plane the wave clings to the Cornu spiral for all positions r except very close to the flux line, that is, the argument w ( r , ) of the Fresnel integrals is almost real. This is confirmed by deriving an asymptotic expansion for w in powers of 1/ r .

Stella Huérfano, M. A. López, M. Socolovsky

Donald H. Kobe

Gu Zhi-Yu, Qian Shang-Wu

The problem of Aharonov-Bohm (AB) scattering on two parallel flux lines of arbitrary magnitude is solved exactly; the expression for the scattering cross-section in the region of geometric shadow is derived. It is shown that in the particular case of two antiparallel lines of the same magnetic flux, though the return flux does not exist, the AB scattering still exists.

Masashi Wakamatsu

Whether the time-dependent Aharonov-Bohm (AB) effect even exists or not has been the subject of long-standing debate. There are two factors complicating the problem. First, in the closed spacetime line integral of the vector potential that is thought to give the AB-phase shift, how to treat the time-varying vector potential is highly nontrivial. Second, the time-varying magnetic flux generates induced electric field even outside the solenoid. In the present paper, motivated by a recent work by Gao, we re-investigate the role of the induced electric field with the utmost care. This analysis reveals a highly nontrivial effect of the induced electric field, which turns out to be useful for verifying the very existence of the time-dependent AB-effect.

Vladimir D. Skarzhinsky