New method for obtaining complex roots in semiclassical coherent-state propagator formula

A semiclassical formula for the coherent-state propagator requires the determination of specific classical paths inhabiting a complex phase-space and governed by a Hamiltonian flux. Such trajectories are constrained to special boundary conditions which render their determination difficult by common methods. In this paper we present a new method based on Runge-Kutta integrator for a quick, easy and accurate determination of these trajectories. Using nonlinear one dimensional systems we show that the semiclassical formula is highly accurate as compared to ots exact counterpart. Further, we clarify how the phase of the semiclassical approximation is correctly retrieved during the time evolution. (author)