Sensitivity to initial conditions in quantum dynamics: an analytical semiclassical expansion

Given a quantum Hamiltonian of point particles and angular momenta, we give a procedure to define a corresponding semiclassical dynamics with essentially classical content, around which the quantum dynamics can be expanded. The modulus of the quantum overlap of coherent states, evolved with the semiclassical Hamiltonian, naturally introduces a classical distance between classical phase points. Using this fact we analytically show that the time rate of change (trc) of two neighboring classical trajectories is directly proportional to the trc of quantum correlations. Coherence loss and nonlocality effects appear as corrections to semiclassical dynamics and we show that they can be perturbatively given in terms of classical trajectories and generalized actions. We apply the results to the nonintegrable (classically chaotic) version of the N-atom Jaynes-Cummings model