Identifying the Stern-Gerlach force of classical electron dynamics

TL;DR

This paper compares classical models of electron spin dynamics with quantum predictions, highlighting the limitations of existing models and identifying the more accurate Foldy-Wouthuysen approach in high-intensity fields.

Contribution

It benchmarks classical models against the Dirac equation, revealing the Foldy-Wouthuysen model's superior agreement for spin-dependent forces in strong fields.

Findings

Foldy-Wouthuysen model aligns better with Dirac theory

Frenkel model shows significant deviations in predictions

Classical models' validity depends on electromagnetic field strength

Abstract

Different classical theories are commonly applied in various branches of physics to describe the relativistic dynamics of electrons by coupled equations for the orbital motion and spin precession. Exemplarily, we benchmark the Frenkel model and the classical Foldy-Wouthuysen model with spin-dependent forces (Stern-Gerlach forces) to the quantum dynamics as predicted by the Dirac equation. Both classical theories can lead to different or even contradicting predictions how the Stern-Gerlach forces modify the electron's orbital motion, when the electron moves in strong electromagnetic field configurations of emerging high-intensity laser facilities. In this way, one may evaluate the validity and identify the limits of these classical theories via a comparison with possible experiments to provide a proper description of spin-induced dynamics. Our results indicate that the Foldy-Wouhuysen model is qualitatively in better agreement with the Dirac theory than the widely used Frenkel model.