Quantal trajectories for adiabatic and nonadiabatic regimes of vibronic systems

Exact and averaged nuclear pseudo-rotational quantal trajectories are compared for various adiabatic and vibronic states of the Longuet-Higgins E direct product ε Jahn-Teller model. It is argued that the usual averaging over the electronic motion could be understood as being a consequence of ergodicity. The failure of the Born-Oppenheimer factorization to obey the ergodic hypothesis was examined. A quantitative separation of the electronic and nuclear time-scales is, nevertheless, achieved for all regimes. It is shown that the short-time deviations from the global drift of the electronic and nuclear motions are perfectly correlated