Topological Quantum Molecular Dynamics

2025/05/16 by Yujuan Xie, Xie, Yujuan, Ruoxi Liu +3 · 2 citations
Physics and Astronomy · #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.2505.11124

openalex publication_date 2025/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Citations

• Path-ordered linked product approximation to the global electronic overlap matrix
• Dynamics of the molecular geometric phase
• Recent developments in the PySCF program package
• A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the cases of Trivial & Near Trivial Crossings
• Quantal phase factors accompanying adiabatic changes
• Zur Quantentheorie der Molekeln

Cited by

• Exponential convergence of the local diabatic representation for nonadiabatic models
• Geometric phase-induced nuclear quantum interference is robust against quantum dissipation

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