Complex Classical Mechanics of a QES Potential

We study a combined parity (P) and time reversal (T) invariant non-Hermitian quasi-exactly solvable (QES) potential, which exhibits PT phase transition, in the complex plane classically to demonstrate different quantum effects. The particle with real energy makes closed orbits around one of the periodic wells of the complex potential depending on the initial condition. However interestingly the particle escapes to an open orbits even with real energy if it is placed beyond a certain distance from the center of the well. On the other hand when the particle energy is complex the trajectory is open and the particle tunnels back and forth between two wells which are separated by a classically forbidden path. The tunneling time is calculated for different pair of wells and is shown to vary inversely with the imaginary component of energy. Our study reveals that spontaneous PT symmetry breaking does not affect the qualitative features of the particle trajectories in the analogous complex classical model.