Quantum toroidal moments of an elliptic toroidal helix in a constant magnetic field

TL;DR

This paper develops an effective Schrödinger equation for a particle on a toroidal helix in a magnetic field, analyzing how magnetic flux and geometry influence toroidal moments, with implications for quantum magnetic properties.

Contribution

It introduces a one-dimensional quantum model for a particle on a toroidal helix in a magnetic field, including curvature effects to ensure Hermiticity.

Findings

Toroidal moments depend strongly on magnetic flux and field orientation.

Moment magnitude varies with coil eccentricity.

Field-curvature coupling terms are essential for a Hermitian Hamiltonian.

Abstract

An effective one-dimensional Schr\"odinger equation for a spinless particle constrained to motion near a toroidal helix immersed in an arbitrarily oriented constant magnetic field is developed. The dependence of the induced toroidal moments on the magnetic flux through the helix is presented. The magnitude of the moments depend strongly on the component of the field normal to the toroidal plane. A strong dependence on coil eccentricity is also indicated. It is also shown that field-curvature coupling potential terms are necessary to preserve the Hermiticity of the minimal prescription Hamiltonian.