Complex trajectories for Hamiltonians of the form H = p~n + V(x) are studied. For n = 2, time-reversal symmetry prevents trajectories from crossing. However, for n > 2 trajectories may indeed cross, and as a result, the complex trajectories for such Hamiltonians have a rich and elaborate structure. In past work on complex classical trajectories, it has been observed that turning points act as attractors; they pull on complex trajectories and make them veer toward the turning point. In this paper, it is shown that the poles of V(x) have the opposite effect—they deflect and repel trajectories. Moreover, poles shield and screen the effect of turning points.
展开▼
