A comparison between the sensitivity behavior of direct and long-lived classical trajectories and quantum wave packets

We compare the sensitivities to initial conditions for both direct (regular) and long-lived (chaotic) trajectories in classical scattering calculations with the corresponding properties of trajectories of position and momentum expectation values for quantum wave packets. The collinear H + H ₂ reaction is used as an example. The results show that the high sensitivity seen in chaotic trajectories is not reflected in the quantum dynamics. We conclude that it is possible for a classical ensemble consisting of only regular trajectories to respond trajectory by trajectory to perturbations in much the same way as a quantum wave packet. (There will of course be cases that are exceptions to this rule.) The response of an ensemble consisting of chaotic trajectories may on the average be similar to that of a wave packet, but not at the level of individual trajectories. In addition, the sensitivities of these trajectories to variations in the potential are analyzed. We conclude that the large contributions to the sensitivities from particular long-lived trajectories must approximately cancel when an exact ensemble average is taken. An algorithm is presented to smoothly account for the contributions to the sensitivities from these trajectories.