具有极点和转向点的势场中的复经典运动
Complex classical motion in potentials with poles and turning points
摘要：
研究了H=p^n+V（x）形式的哈密顿量的复轨线。对于n=2，时间反演对称性防止轨迹交叉。然而，对于n>2，轨迹确实可以交叉，因此，这种哈密顿量的复杂轨迹具有丰富和精细的结构。在过去对复杂经典轨迹的研究中，人们观察到转折点起着吸引子的作用;它们拉动复杂的轨迹，使它们转向转折点。本文证明了V（x）的极点具有相反的作用--它们使轨迹偏转和排斥。此外，极点屏蔽和屏蔽了转折点的影响。
英文摘要：
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.
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