Semiclassics and propagation of coherent states for spin-orbit coupling problems

Marcel Novaes

Bailey C. Hsu, Jean-François S. Van Huele

A. D. Ribeiro, Marcus A. M. de Aguiar, A. F. R. de Toledo Piza

We derive the semiclassical limit of the coherent state propagator for systems with two degrees of freedom of which one degree of freedom is canonical and the other a spin. Systems in this category include those involving spin–orbit interactions and the Jaynes–Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. We construct a path integral representation for the propagator of such systems and derive its semiclassical limit. As special cases we consider separable systems, the limit of very large spins and the case of spin-1/2.

George A. Hagedorn

Mikhail Pletyukhov

The problem of an origin of the Solary-Kochetov extra-phase contribution to the naive semiclassical form of a generalized phase-space propagator is addressed with the special reference to the su(2) spin case which is the most important in applications. While the extra-phase correction to a flat phase-space propagator can straightforwardly be shown to appear as a difference between the principal and the Weyl symbols of a Hamiltonian in the next-to-leading order expansion in the semiclassical parameter, the same statement for the semiclassical spin coherent-state propagator holds provided the Holstein-Primakoff representation of the su(2) algebra generators is employed.

Carol Braun, Anupam Garg

We obtain the semiclassical coherent-state propagator for a many-spin system with an arbitrary Hamiltonian.