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Generalized Gaussian wave packet dynamics: Integrable and chaotic systems.

Harinder Pal¹, Manan Vyas¹, Steven Tomsovic²

¹Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, USA and Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México - C.P. 62210 Cuernavaca, México.

Physical Review. E

|February 13, 2016

Summary

This summary is machine-generated.

Generalized Gaussian wave packet dynamics (GGWPD) is made more practical by connecting it to linearized methods. This approach uses real trajectories to find complex saddle-point trajectories for improved semiclassical wave packet propagation.

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Area of Science:

Quantum dynamics
Computational chemistry
Statistical mechanics

Background:

Semiclassical wave packet propagation is crucial for understanding molecular dynamics.
Generalized Gaussian wave packet dynamics (GGWPD) is a powerful but complex technique.
Existing linearized methods offer practical alternatives but may lack full accuracy.

Purpose of the Study:

To develop a more practical implementation of GGWPD.
To connect GGWPD with existing linearized wave packet dynamics methods.
To improve the accuracy of semiclassical wave packet propagation.

Main Methods:

Established a connection between GGWPD and linearized wave packet dynamics using off-center, real trajectories.
Employed a multidimensional Newton-Raphson root search to find complex saddle-point trajectories.
Utilized the correspondence between real and saddle-point trajectories for practical GGWPD implementation.

Main Results:

Demonstrated a one-to-one correspondence between off-center real trajectories and complex saddle-point trajectories.
Showcased the ability to accurately capture dynamical transport in both integrable and chaotic systems.
Applied the method to the kicked rotor model, showing accuracy improvements with decreasing Planck's constant (ℏ).

Conclusions:

The developed method provides a practical pathway for implementing GGWPD.
The use of saddle-point trajectories significantly enhances the accuracy of semiclassical wave packet propagation.
This approach offers a more accessible tool for studying complex quantum dynamical systems.