Quantum tunneling and its absence in deep wells and strong magnetic fields

TL;DR

This paper investigates quantum tunneling in deep potential wells under strong magnetic fields, identifying conditions where tunneling is suppressed or persists, and analyzing the transition of the magnetic ground state symmetry.

Contribution

It constructs specific double well potentials where quantum tunneling is eliminated and studies the transition of the magnetic ground state symmetry.

Findings

Eigenvalue splitting can vanish, eliminating tunneling.

Magnetic ground state symmetry can transition from symmetric to anti-symmetric.

Tunneling persists in typical double wells, with a lower bound for eigenvalue splitting.

Abstract

We present new results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field. We construct a family of double well potentials containing examples for which the low-energy eigenvalue splitting vanishes, and hence quantum tunneling is eliminated. Further, by deforming within this family, the magnetic ground state can be made to transition from symmetric to anti-symmetric. However, for typical double wells in a certain regime, tunneling is not suppressed, and we provide a lower bound for the eigenvalue splitting.