Systematic elimination of Stokes divergences emanating from complex phase space caustics

TL;DR

This paper presents a rigorous method to eliminate unphysical divergences caused by Stokes phenomena near phase space caustics, improving wavepacket reconstruction accuracy in quantum systems.

Contribution

It introduces a novel approach based on deviations from second order to precisely identify Stokes lines and remove unphysical divergences in complex trajectory analyses.

Findings

Accurate wavepacket reconstruction for Morse, Quartic, Coulomb, and Eckart systems.

Effective elimination of Stokes divergences near phase space caustics.

Enhanced understanding of asymptotic expansions in complex phase space.

Abstract

Stokes phenomenon refers to the fact that the asymptotic expansion of complex functions can differ in different regions of the complex plane, and that beyond the so-called Stokes lines has an unphysical divergence. An important special case is when the Stokes lines emanate from phase space caustics of a complex trajectory manifold. In this case, symmetry determines that to second order there is a double coverage of the space, one portion of which is unphysical. Building on the seminal but laconic findings of Adachi, we show that the deviation from second order can be used to rigorously determine the Stokes lines and therefore the region of the space that should be removed. The method has applications to wavepacket reconstruction from complex valued classical trajectories. With a rigorous method in hand for removing unphysical divergences, we demonstrate excellent wavepacket reconstruction for the Morse, Quartic, Coulomb and Eckart systems.