Quantum mechanics of a constrained electrically charged particle in the presence of electric currents

Abstract

We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time independent electric currents. Starting from the canonical action in the embedding space we show that a charged particle with charge $q$ couples to a term linear in $q{A}^{3}M$, where $A^3$ is the transverse component of the electromagnetic vector potential and $M$ is the mean curvature in the surface. This term cancels exactly a curvature contribution to the orbital magnetic moment of the particle. It is shown that particles, independently of the value of the charge, in addition to the known couplings to the geometry also couple to the mean curvature in the surface when a Neumann type of constraint is applied on the transverse fluctuations of the wave function. In contrast to a Dirrichlet constraint on the transverse fluctuations a Neumann type of constraint on these degrees of freedom will in general make the equations of motion non separable. The exceptions are the equations of motion for electrically neutral particles on surfaces with constant mean curvature. In the presence of electric currents the equation of motion of a charged particle is generally non separable independently of the coupling to the geometry and the boundary constraints.

to appear in Phys.Rev. A

References in corpus (1)

• Quantum mechanics on curved 2D systems with electric and magnetic fields

Cited by in corpus (16)

• Pauli equation for a charged spin particle on a curved surface in an electric and magnetic field
• Geometric Momentum: the Proper Momentum for a Free Particle on a Two-dimensional Sphere
• Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space
• Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface
• Geometric momentum for a particle constrained on a curved hypersurface
• Geometric effects resulting from square and circular confinements for a particle constrained to a space curve
• Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates
• Hermitian spin-orbit Hamiltonians on a surface in orthogonal curvilinear coordinates: a new practical approach
• Curvature-induced bound states and coherent electron transport on the surface of a truncated cone
• Ballistic Anisotropic Magnetoresistance in Core Shell Nanowires and Rolled-up Nanotubes
• Anomalous phase shift in a twisted quantum loop
• Transmission gaps from corrugations
• Hermitian and Gauge-Covariant Hamiltonians for a particle in a magnetic field on Cylindrical and Spherical Surfaces
• Quantum Scattering of Spinless Particles in Riemannian Manifolds
• Geometric effects on the electronic structure and the bound states in annular corrugated wires
• Spin-deformation coupling in two-dimensional polar materials