Development of the path-integral methodologies for non-adiabatic dynamics
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Cao, Ziying
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Abstract
This thesis presents the development of path-integral methodologies for non-adiabatic dynamics, which are crucial for accurately describing systems with energetically close electronic states. In such systems, the Born-Oppenheimer approximation often fails, necessitating a more comprehensive approach that includes both nuclear and electronic degrees of freedom will a complete description. The path-integral framework for nuclear degrees of freedom is employed due to its success in capturing nuclear quantum effects in ground-state problems.
Extending the path-integral treatment of nuclei to multi-state systems requires a semi-classical or mixed quantum-classical treatment for the electronic states. Two key methods are explored and tested in this thesis: Non-adiabatic Ring Polymer Molecular Dynamics (NRPMD), which combines path-integral nuclei with Meyer-Miller-Stock-Thoss (MMST) mapping for the electronic states, and the Ring Polymer Mapping Approach to Surface Hopping (RP-MASH), an extension of the deterministic quasi-classical surface hopping method. These methods allow for the treatment of nuclei and electronic states in a classically isomorphic manner, ensuring that all degrees of freedom are consistently represented. This uniform approach enables the use of classical computational techniques, such as molecular dynamics, to simulate electronically non-adiabatic dynamics while preserving important nuclear quantum effects. The performance of these methods on model systems, such as spin-boson and linear vibronic models, demonstrates their promise for more complex systems including realistic conical intersections.
However, while the methods show great promise, challenges remain. For example, the treatment of decoherence effects and the precise handling of frustrated hops during non-adiabatic transitions still require further refinement of RP-MASH. Future developments will focus on improving the accuracy of these methods, particularly by incorporating decoherence effects and refining the treatment of multi-state systems. There is also potential for extending these methods to account for quantum light-matter interactions, such as polaritons, which could open up new avenues in the study of complex quantum systems.
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2025-12
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Dissertation (PhD)