Role of top and under-the-barrier complex transmission poles for the delay time in single barrier tunneling

The transition from time advance to time delay in one-dimensional single barrier tunneling is investigated by considering the trajectories in the complex k plane of the top-barrier transmission poles as a function of the opacity of the barrier. We show that such a transition is linked to the particular event where the first top-barrier transmission pole migrates under the barrier as the opacity of the system diminishes. It is also shown that the above situation has an effect on tunneling dynamics since it governs the presence of transient structures in the time evolution of the probability density.