Time propagation of constrained coupled Gaussian wave packets.

Area of Science:

• Quantum mechanics
• Computational physics
• Theoretical chemistry

Background:

• Approximating quantum system dynamics often involves time propagation of Gaussian wave packets.
• The time evolution of these wave packets is typically calculated using a time-dependent variational principle, resulting in ordinary differential equations.
• These equations often become ill-behaved in practical applications, necessitating regularization methods.

Purpose of the Study:

• To present a general and effective method for regularizing ill-behaved ordinary differential equations arising from Gaussian wave packet propagation.
• To ensure the stability and well-behaved nature of the equations of motion in complex quantum dynamics simulations.

Main Methods:

• Developed a regularization technique based on applying nonholonomic inequality constraints to the parameters governing wave packet evolution.
• The method ensures that the system's equations of motion remain well-behaved, even with a large number of coupled Gaussian wave packets.
• Tested the method's efficacy on a nonintegrable system with two degrees of freedom.

Main Results:

• The proposed regularization method successfully maintains the well-behaved nature of the ordinary differential equations.
• Demonstrated the method's applicability and power in simulating the dynamics of a complex, nonintegrable quantum system.
• The constraints effectively prevent numerical instabilities during the time evolution calculations.

Conclusions:

• The introduced method provides a robust solution for handling ill-behaved equations in quantum dynamics simulations.
• Nonholonomic inequality constraints offer a powerful tool for regularizing the time evolution of Gaussian wave packets.
• This approach enhances the reliability and applicability of variational methods in studying complex quantum systems.