Dirac Particles in Twisted Tubes

TL;DR

This paper explores the behavior of relativistic Dirac particles in twisted tubes, revealing nontrivial spin dynamics and modifications to effective potentials not predicted by nonrelativistic models.

Contribution

It introduces a relativistic analysis of Dirac particles in twisted geometries, showing spin effects and potential modifications absent in nonrelativistic theories.

Findings

Relativistic particles can acquire angular momentum components opposite to initial polarization.

The effective potential in relativistic theory differs from the nonrelativistic case.

Spin eigenstates exhibit nontrivial behavior during propagation.

Abstract

We consider the dynamics of a relativistic Dirac particle constrained to move in the interior of a twisted tube by confining boundary conditions, in the approximation that the curvature of the tube is small and slowly varying. In contrast with the nonrelativistic theory, which predicts that a particle's spin does not change as the particle propagates along the tube, we find that the angular momentum eigenstates of a relativistic spin-1/2 particle may behave nontrivially. For example, a particle with its angular momentum initially polarized in the direction of propagation may acquire a nonzero component of angular momentum in the opposite direction on turning through 2 \pi radians. Also, the usual nonrelativistic effective potential acquires an additional factor in the relativistic theory.