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

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 $qA^3M$, 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.Comment: to appear in Phys.Rev.

Quantum anticentrifugal potential in a bent waveguide

We show the existence of an anticentrifugal force for a quantum particle in a bent waveguide. This counterintuitive force due to dimensionality was shown to exist in a flat $R^2$ space but there it needs an additional $\delta$-like potential at the origin in order to brake the translational invariance and to exhibit localized states. In the case of the bent waveguide there is no need of any additional potential since here the boundary conditions break the symmetry. The effect may be observed in interference experiments which are sensitive to the additional phase of the wavefunction gained in the bent regions and can find application in distinguishing between straight and bent geometries

An Exactly Solvable Case for a Thin Elastic Rod

We present a new exact solution for the twist of an asymmetric thin elastic rods. The shape of such rods is described by the static Kirchhoff equations. In the case of constant curvatire and torsion the twist of the asymmetric rod represents a soliton lattice.Comment: 6 pages, title changed, revised versio

Quantum Hall-like effect on strips due to geometry

In this Letter we present an exact calculation of the effective potential which appears on a helicoidal strip. This potential leads to the appearance of lcalized states at a distance \xi_0 from the central axis. The twist \omega of the strip plays the role of a magnetic field and is responsable for the appearance of these localized states and an effective transverse electric field thus this is reminiscent of the quantum Hall effect. At very low temperatures the twisted configuration of the strip may be stalilized by the electronic states.Comment: 3 page