Aharonov-Bohm effect revisited

Anton Zeilinger

Gregory Eskin

Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.

Hans Boersch, K. Geohmann, H. Hamisch +2 more

Jian Jing, Ling-Bao Kong, Qing xiang Wang +1 more

We revisit time-independent and time-dependent Aharonov-Bohm effects in the noncommutative space-time by investigating a relativistic spin-half particle in the background of a long-thin magnetic-flux-carried solenoid. Our results show that, up to the first order of the noncommutative parameter, there are no noncommutative corrections on the AB effects for both cases.

David Böhm, Basil J. Hiley

H. Fearn

Schrodinger's equation for an electron in a vector potential A has a one-to-one correspondence with the wave equation for an electric field in a moving medium. First the author points out a few errors in the literature concerning the Aharonov-Bohm (AB) effect then she explores the optical analogy further. The author finds that curl A plays a similar role to curl v where v is the velocity of the moving medium.