Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession

TL;DR

This paper compares quantum and classical spin rotations of Dirac particles reflecting off a surface with chiral MIT boundary conditions, revealing similarities in nonrelativistic regimes and discrepancies at ultrarelativistic speeds.

Contribution

It provides a detailed comparison between quantum Dirac spin reflection and classical Thomas precession, highlighting the conditions under which they agree or diverge.

Findings

Spin rotation axes coincide only for zero chiral angle

Rotation angles match in nonrelativistic limit for nonchiral boundary conditions

Quantum rotation angle remains finite at high speeds, classical diverges

Abstract

We consider the reflection of a Dirac plane wave on a perfectly reflecting plane described by chiral MIT boundary conditions and determine the rotation of the spin in the reflected component of the wave. We solve the analogous problem for a classical particle using the evolution of the spin defined by the Thomas precession and make a comparison with the quantum result. We find that the rotation axes of the spin in the two problems coincide only for a vanishing chiral angle, in which case the rotation angles coincide in the nonrelativistic limit, and also remain remarkably close in the relativistic regime. The result shows that in the nonrelativistic limit the interaction between the spin and a reflecting surface with nonchiral boundary conditions is completely contained in the Thomas precession effect, in conformity with the fact that these boundary conditions are equivalent to an infinite repulsive scalar potential outside the boundary. By contrast, in the ultrarelativistic limit the rotation angle in the quantum problem remains finite, while in the classical one the rotation angle diverges. We comment on the possible implications of this discrepancy on the validity of the Mathisson-Papapetrou-Dixon equations at large accelerations.