Geometric effects resulting from square and circular confinements for a particle constrained to a space curve

Abstract

Investigating the geometric effects resulting from the detailed behaviors of the confining potential, we consider square and circular confinements to constrain a particle to a space curve. We find a torsion-induced geometric potential and a curvature-induced geometric momentum just in the square case, while a geometric gauge potential solely in the circular case. In the presence of electromagnetic field, a geometrically induced magnetic moment couples with magnetic field as an induced Zeeman coupling only for the circular confinement, also. As spin-orbit interaction is considered, we find some additional terms for the spin-orbit coupling, which are induced not only by torsion, but also curvature. Moreover, in the circular case, the spin also couples with an intrinsic angular momentum, which describes the azimuthal motions mapped on the space curve. As an important conclusion for the thin-layer quantization approach, some substantial geometric effects result from the confinement boundaries. Finally, these results are proved on a helical wire.

7 pages, 2 figures

References in corpus (7)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited
• Reply to the Comment on "Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited" [PRL 100:232002 (2008)]
• Relativistic electron wave packets carrying angular momentum
• Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space
• Pure Gauge Spin-Orbit Couplings

Cited by in corpus (13)

• Geometrical phase and Hall effect associated with the transverse spin of light
• Pseudo-magnetic field and effective spin-orbit interaction for a spin-1/2 particle confined to a curved surface
• Fermions on a torus knot
• Modifications of electron states, magnetization and persistent current in a quantum dot by controlled curvature
• Schrödinger formalism for a particle constrained to a surface in ${\mathbb{R}}_1^3$
• Effective dynamics for a spin-1/2 particle constrained to a space curve in an electric and magnetic field
• Curved non-interacting two-dimensional electron gas with anisotropic mass
• The geometric potential of a double-frequency corrugated surface
• Dirac equation in curved spacetime: the role of local Fermi velocity
• Geometric effects of a quarter of corrugated torus
• General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere
• Geometry induced quantum Hall effect and Hall viscosity
• Geometric momentum and angular momentum for charge-monopole system