Semiclassical tunneling and magnetic flux effects on the circle

TL;DR

This paper investigates how magnetic fields influence semiclassical tunneling in a double well potential on a circle, revealing oscillatory effects related to magnetic flux in eigenvalue splitting.

Contribution

It introduces a novel analysis of magnetic flux effects on tunneling estimates in a circular double well system, highlighting oscillatory behavior in eigenvalue splitting.

Findings

Oscillating factor in eigenvalue splitting due to magnetic flux

Magnetic field affects tunneling estimates on the circle

Connection of wells via geodesics influences tunneling behavior

Abstract

This paper is devoted to semiclassical tunneling estimates induced on the circle by a double well electric potential in the case when a magnetic field is added. When the two electric wells are connected by two geodesics for the Agmon distance, we highlight an oscillating factor (related to the circulation of the magnetic field) in the splitting estimate of the first two eigenvalues.