Jens Bolte and Rainer Galser
Semiclassical propagation of coherent states with spin-orbit interaction
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ABSTRACT. We study semiclassical approximations to the time evolution of coherent
states for general spin-orbit coupling problems in two different
semiclassical scenarios: The limit \hbar to zero is first taken with
fixed spin quantum number s and then with \hbar*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 \sqrt{\hbar} and
identify an Ehrenfest time scale. Subsequently an improvement of the
semiclassical error to an arbitray order \hbar^{N/2} is achieved by a
suitable deformation of the state that is propagated classically.