Nearly real trajectories in complex semiclassical dynamics

Abstract

We introduce a very general approximation to the quantum propagator that is based on the assumption that the most important contributions to the complex semiclassical propagator evolve from real classical trajectories that almost satisfy the desired boundary conditions. Our results for two systems --- the autocorrelation function for the quartic anharmonic oscillator and the photodissociation spectrum of ${\mathrm{CO}}_{2}$ --- show that these nearly real contributions yield an excellent approximation to the quantum propagator for quite long times. The approach taken here is applicable to problems with many (e.g., several hundred) degrees of freedom, and hence promises to provide an accurate and useful representation of the quantum dynamics for a wide variety of physically interesting systems.