Time propagation of constrained coupled Gaussian wave packets

TL;DR

This paper introduces a regularization method for the time propagation of coupled Gaussian wave packets in quantum systems, ensuring stable equations of motion through inequality constraints, demonstrated on a complex two-degree system.

Contribution

A novel regularization approach using nonholonomic inequality constraints for stable evolution of coupled Gaussian wave packets in quantum dynamics.

Findings

Method effectively stabilizes equations of motion

Demonstrated on a non-integrable two-degree system

Improves practical applicability of Gaussian wave packet propagation

Abstract

The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be calculated from a set of ordinary differential equations. Unfortunately, the set of equations is ill-behaved in most practical applications, depending on the number of propagated Gaussian wave packets, and methods for regularization are needed. We present a general method for regularization based on applying adequate nonholonomic inequality constraints to the evolution of the parameters, keeping the equations of motion well-behaved. The power of the method is demonstrated for a non-integrable system with two degrees of freedom.