Induced magnetic moment for a spinless charged particle in the thin-layer approach
Instituto de Física, Universidade de São Paulo - São Paulo, Brazil
Received: 1 June 2015
Accepted: 10 September 2015
We determine the effective dynamics for a spinless charged particle, in the presence of electromagnetic fields, constrained to a space curve. We employ the thin-layer procedure and a perturbative expansion for the Schrödinger equation is derived. We find that the first-order term in the perturbative expansion couples the dynamics of the normal and tangent degrees of freedom. However, there is always a gauge transformation that allows to decouple the dynamics. We find that the effective Schrödinger equation in the curve contains an induced Zeeman coupling, independent of the curvature and torsion, which has not been previously reported. This coupling is characteristic of reducing the dimension by two and allows to identify an induced magnetic moment.
PACS: 71.70.Ej – Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect / 73.21.Hb – Quantum wires / 02.40.-k – Geometry, differential geometry, and topology
© EPLA, 2015