%0 Journal Article
%T Complex classical motion in potentials with poles and turning points
%A Carl M. Bender
%A Daniel W. Hook
%J Physics
%D 2014
%I arXiv
%X 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 towards 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.
%U http://arxiv.org/abs/1402.3852v1