Modification to the pre-factor of the semiclassical propagator

TL;DR

This paper introduces a modified pre-factor for the semiclassical propagator that enhances computational efficiency and convergence, demonstrated through numerical calculations in high-dimensional, unstable orbit systems.

Contribution

The authors propose a new pre-factor for the semiclassical propagator that improves its practical efficiency and applicability to complex high-dimensional systems.

Findings

Faster convergence in numerical calculations

Accurate overlap and spectrum density computations

Effective application to high-dimensional systems with unstable orbits

Abstract

We modify the pre-factor of the semiclassical propagator to improve its efficiency in practical implementations. The new pre-factor represents the smooth portion of an orbit's contribution, and leads to fast convergence in numerical calculations. As an illustration of the accuracy and efficiency of the resultant propagator, we numerically calculate overlaps between quantum and semiclassical wave functions, as well as low-lying spectrum density in a 10-dimensional system contains unstable classical orbits. This sheds light on applying semiclassical propagator to high dimensional systems.