arXiv · 2505.11124
Topological Quantum Molecular Dynamics
Abstract
We develop a unified quantum geometric framework to understand reactive quantum dynamics. The critical roles of the quantum geometry of adiabatic electronic states in both adiabatic and non-adiabatic quantum dynamics are unveiled. A numerically exact, divergence-free topological quantum molecular dynamics method is developed through a discrete local trivialization of the projected electronic Hilbert space bundle over the nuclear configuration space. In this approach, the singular electronic quantum geometric tensor-Abelian for adiabatic dynamics and non-Abelian for non-adiabatic dynamics-is fully encoded in the global electronic overlap matrix. With numerical illustrations, it is demonstrated that atomic motion-whether adiabatic or non-adiabatic-is governed not only by the variation in electronic energies with nuclear configurations (potential energy surface) but also by the variation in electronic states (electronic quantum geometry).
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Yujuan Xie, Ruoxi Liu, Bing Gu. 2025-05-16. Topological Quantum Molecular Dynamics. https://arxiv.org/abs/2505.11124
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