Quantum Tunneling and the Aharonov-Bohm effect

TL;DR

This paper analyzes the quantum effects of an Aharonov-Bohm vector potential on a Hamiltonian with radial potential wells, deriving semi-classical asymptotics for energy level splitting and highlighting the dominance of potential wells over flux effects.

Contribution

It provides the first semi-classical asymptotic analysis of energy splitting in a system with Aharonov-Bohm flux and symmetric potential wells.

Findings

Energy splitting asymptotics derived for the system.

Flux effects are lower order compared to potential well contributions.

Symmetry assumption simplifies the analysis.

Abstract

We investigate a Hamiltonian with radial potential wells and an Aharonov-Bohm vector potential with two poles. Assuming that the potential wells are symmetric, we derive the semi-classical asymptotics of the splitting between the ground and second state energies. The flux effects due to the Aharonov-Bohm vector potential are of lower order compared to the contributions coming from the potential wells.