Semiclassical propagation of coherent states with spin-orbit interaction

We study semiclassical approximations to the time evolution of coherent states for general spin-orbit coupling problems in two different semiclassical scenarios: The limit ~ → 0 is first taken with fixed spin quantum number s and then with ~s held constant. In these two cases different classical spin-orbit dynamics emerge. We prove that a coherent state propagated with a suitable classical dynamics approximates the quantum time evolution up to an error of size √ ~ and identify an Ehrenfest time scale. Subsequently an improvement of the semiclassical error to an arbitray order ~N/2 is achieved by a suitable deformation of the state that is propagated classically. E-mail address: [email protected] E-mail address: [email protected]