Quantum tunneling and the Aharonov-Bohm effect

CHANG-SOO PARK, D. K. PARK

The role of Aharonov–Bohm effect in quantum tunneling is examined when a potential is defined on the S1 and has N-fold symmetry. We show that the low-lying energy levels split from the N-fold degenerate ground state oscillate with the Aharonov–Bohm phase, from which general degeneracy conditions depending on the magnetic flux is obtained. We apply these results to the spin tunneling in a spin system with N-fold rotational symmetry around a hard axis.

Y. Imry, R. A. Webb

Chris Philippidis, David Böhm, R.D. Kaye

A. Cano, Indranil Paul

The scattering of electrons with inhomogeneities produces modulations in the local density of states of a metal. We show that electron interference contributions to these modulations are affected by the magnetic field via the Aharonov-Bohm effect. This can be exploited in a simple scanning-tunneling-microscopy setup that serves as an Aharonov-Bohm interferometer at the nanometer scale.

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.

M. Y. Choi, Minchul Lee