Induced magnetic moment for a spinless charged particle in the thin-layer approach

Abstract

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 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.

7 pages. To be published in Europhysics Letters

References in corpus (5)

• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Cylindrical Two-Dimensional Electron Gas in a Transverse Magnetic Field
• Persistent and radiation-induced currents in distorted quantum rings
• Bilayer graphene Origami: curvature-induced p-n junctions
• Curvature induced quantum potential on deformed surfaces

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• Effective dynamics for a spin-1/2 particle constrained to a space curve in an electric and magnetic field
• Quantum mechanics of fermion confined to a curved surface in Foldy-Wouthuysen representation
• Geometric effects of a quarter of corrugated torus
• General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere
• Spin-deformation coupling in two-dimensional polar materials
• Geometric scattering in the presence of line defects