Classical Wigner model based on a Feynman path integral open polymer

Area of Science:

• Quantum mechanics
• Computational physics
• Nuclear dynamics

Background:

• The classical Wigner model approximates quantum dynamics of atomic nuclei.
• Accurate sampling of the initial quantum mechanical distribution is crucial for the Wigner model.

Purpose of the Study:

• To introduce and test a novel method for sampling the initial quantum mechanical distribution for the classical Wigner model.
• To evaluate the performance of the new method for various potentials and system dimensions.

Main Methods:

• Developed and tested two versions of a new sampling method.
• Applied the method to one-dimensional quartic oscillators, double well potentials, and multi-dimensional systems coupled to harmonic baths.
• Compared results with the Feynman-Kleinert linearized path integral method.

Main Results:

• Both versions of the new method consistently converge towards the classical Wigner limit.
• Effective convergence was achieved for one-dimensional systems.
• Approximating harmonic bath sampling with classical mechanics significantly enhanced numerical performance for multi-dimensional systems.
• The new method outperformed the Feynman-Kleinert method in reproducing exact classical Wigner results for the double well potential.

Conclusions:

• The new sampling method is a potentially useful tool for approximating quantum nuclear dynamics using the classical Wigner model.
• The method demonstrates good performance, especially for one-dimensional systems, and shows advantages over existing techniques for specific cases.
• Further investigation on other correlation functions and systems is warranted.