Global dynamical analysis of an electronic spin–orbit coupling system

Abstract

By means of a canonical generalized momentum and a canonical conjugate spin variable, a complete canonical Hamiltonian formalism is designed to describe a coulomb field with electronic spin–orbit coupling in a semi-classical and non-relativistic way. After this operation, unlike the existing Lagrange formulation, the concepts of hidden momentum, hidden angular momentum and spin kinetic energy are not used in the canonical formalism. Besides, it is easy to find that there are four first integrals involving the conserved total energy and the conserved total angular momentum vector in an 8-dimensional phase space of the system. In this sense, the global dynamics is typically integrable, regular and non-chaotic, and each orbit in the phase space is a quasi-periodic 4-dimensional Kolmogorov-Arnold-Moser(KAM) torus.