An Initial Value Representation with Complex Trajectories

TL;DR

This paper introduces a novel semiclassical propagator method using complex trajectories, mapping complex phase space to real space, which avoids divergences and enhances accuracy in quantum dynamics simulations.

Contribution

It presents an initial value representation based on complex trajectories that maps to real phase space and automatically eliminates non-contributing paths, improving semiclassical calculations.

Findings

The method avoids divergences caused by caustics.

It provides accurate semiclassical results.

The approach simplifies trajectory selection.

Abstract

We present an Initial Value Representation for the semiclassical coherent state propagator based on complex trajectories. We map the complex phase space into a real phase space with twice as many dimensions and use a simple procedure to automatically eliminate non-contributing trajectories. The resulting semiclassical formulas do not show divergences due to caustics and provide accurate results.