New method for obtaining complex roots in the semiclassical coherent-statepropagator formula

A semiclassical formula for the coherent-state propagator requires the dete rmination of specific classical paths inhabiting a complex phase-space and governed by a Hamiltonian flux. Such trajectories are constrained to specia l boundary conditions which render their determination difficult by common methods. In this paper we present a new method based on Runge-Kutta integra tor for a quick, easy and accurate determination of these trajectories. Usi ng nonlinear one dimensional systems we show that the semiclassical formula is highly accurate as compared to its exact counterpart. Further, we clari fy how the phase of the semiclassical approximation is correctly retrieved during the time evolution.