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Article Dans Une Revue Journal of Chemical Physics Année : 2022

Non-adiabatic mapping dynamics in the phase space of the SU ( N ) Lie group

Résumé

We present the rigorous theoretical framework of the generalized spin mapping representation for non-adiabatic dynamics. Our work is based upon a new mapping formalism recently introduced by Runeson and Richardson [J. Chem. Phys. 152, 084110 (2020)], which uses the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space. Following this interesting idea, the Stratonovich–Weyl transform is used to map an operator in the Hilbert space to a continuous function on the SU(N) Lie group, i.e., a smooth manifold which is a phase space of continuous variables. We further use the Wigner representation to describe the nuclear degrees of freedom and derive an exact expression of the time-correlation function as well as the exact quantum Liouvillian for the non-adiabatic system. Making the linearization approximation, this exact Liouvillian is reduced to the Liouvillian of several recently proposed methods, and the performance of this linearized method is tested using non-adiabatic models. We envision that the theoretical work presented here provides a rigorous and unified framework to formally derive non-adiabatic quantum dynamics approaches with continuous variables and connects the previous methods in a clear and concise manner.
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Dates et versions

hal-04197996 , version 1 (06-09-2023)

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Duncan Bossion, Wenxiang Ying, Sutirtha Chowdhury, Pengfei Huo. Non-adiabatic mapping dynamics in the phase space of the SU ( N ) Lie group. Journal of Chemical Physics, 2022, 157 (8), ⟨10.1063/5.0094893⟩. ⟨hal-04197996⟩

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