Explicit volume-preserving numerical schemes for relativistic trajectories and spin dynamics: https://arxiv.org/abs/2012.11652
R. Cabrera, A. G. Campos, D. I. Bondar, S. MacLean, F. Fillion-Gourdeau
A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-BMT equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties: they are energy-conserving, volume-conserving and second order convergent. These properties are analysed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. It is demonstrated that the numerical error in a constant magnetic field remains bounded for long time simulations in contrast to the Boris pusher, whose angular error increases linearly with time. Finally, the intricate spin dynamics of a particle is investigated in a plane wave field configuration.
Comments: 15 pages, 9 figures
И сегодня же - очередная статья Барышевского о динамике спина:
Pseudoscalar corrections to spin motion equation, search for electric dipole moment and muon magnetic (g-2) factor: https://arxiv.org/abs/2012.11751
V. G. Baryshevsky, P. I. Porshnev
The spin dynamics in constant electromagnetic fields is described by the Bargmann-Michel-Telegdi equation which can be upgraded with anomalous magnetic and electric dipole moments. The upgraded equation remains self-consistent, Lorentz-covariant and gauge-invariant. It and its different forms have been confirmed in numerous experiments to high degree of accuracy. We have recently derived the spin motion equation within the Wentzel-Kramers-Brillouin weak-field approximation which adds a pseudoscalar correction to the BMT equation. The upgraded equation is again self-consistent, Lorentz-covariant, gauge-invariant, and free of unwanted artifacts. The pseudoscalar correction is expected to be small, and might become important in hypersensitive experiments, like the measurements of electric dipole moments which are themselves related to pseudoscalar quantities. It also becomes possible to explain why EDMs are so difficult to measure, since this correction term might lead to the effective screening of electric dipole moments. Within the same model, it is possible to explain the discrepancy between experimental and theoretical values of muon magnetic anomaly under assumption that the pseudoscalar correction is the dominant source of this discrepancy.
Comments: 27 pages