| 概 要 |
Nonadiabatic dynamics means transitions of quantum population over the multiple potential energy surfaces and is one of the universal quantum phenomena in coupled systems with fast and slow degrees of freedom, e.g., electrons and nuclei. Particularly, in molecular systems, the nonadiabatic transitions are caused frequently by nuclear dynamics on adiabatic surfaces corresponding to electronic excited states and are known as an important factor to predict product states in photo chemical processes. Besides, the nonadiabatic transitions in energy conversion process like organic solar cells and photocatalysis are also recognized recently.
To analyze the nonadiabatic dynamics, we introduce new theoretical framework based on the path integral picture, which differs from other quasi-classical methods like Tully's surface hopping and Ehrenfest dynamics. This nonadiabatic path integral requires no derivative couplings and reveals that the nonadiabatic transition can be formulated by overlap integrals of electronic eigenstates between different nuclear coordinates.
In this talk, I first present the basic and general framework of the nonadiabatic path integral. Then, thermal averages of physical quantities in nonadiabatic systems [1] and semiclassical nonadiabatic dynamics including quantum effects of nuclei [2] are presented. Finally, a semiclassical quantization condition, i.e., quantum–classical correspondence, for steady states of nonadiabatic systems is presented by extending Gutzwiller’s trace formula to a nonadiabatic form. In the course of finding the correspondence concretely, symbolic dynamics is introduced to extract a countably infinite set of "hopping periodic orbits" from an uncountably infinite set of "hopping trajectories".
References:
[1] J. R. Schmidt and J. C. Tully, J. Chem. Phys. 127, 094103(2007).
[2] M. Fujii, J. Chem. Phys. 135, 114102 (2011)
[3] M. Fujii and K. Yamashita, arXiv:1406.3769 (accepted to be published in JCP)
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