Refined approach to cellularization: going from Heller's thawed Gaussian approximation to the Herman--Kluk propagator

TL;DR

This paper introduces a refined cellularization scheme for the Herman--Kluk propagator that improves phase space sampling and converges to both the original and simplified approximations depending on the number of trajectories used.

Contribution

The authors develop a new cellularization method employing the inverse Weierstrass transform and optimal cell scaling, bridging the gap between thawed Gaussian and Herman--Kluk approximations.

Findings

Converges to Herman--Kluk result with many trajectories.

Reduces to thawed Gaussian approximation with a single trajectory.

Effective in modeling both integrable and chaotic systems.

Abstract

We present a refined cellularization (Filinov filtering) scheme for the semiclassical Herman--Kluk propagator, which employs the inverse Weierstrass transform and optimal scaling of the cell's size with the number of cells, and was previously used only in the context of the dephasing representation. In the new methodology, the sampling density for the cell centers correlates with the cell size, allowing for an effective sampling of the phase space covered by the initial state of the system. The main advantage of the presented approach is that, unlike the standard cellularization, it converges to the original Herman--Kluk result in the limit of an infinite number of trajectories and to the thawed Gaussian approximation when a single trajectory is used. We illustrate the performance of the refined cellularization scheme by calculating autocorrelation functions and spectra of both integrable and chaotic model systems.