Adiabatic and nonadiabatic dynamics in classical mechanics for coupled fast and slow modes: sudden transition caused by the fast mode against the slaving principle

ABSTRACT

Adiabatic and nonadiabatic dynamics in classical systems composed of fast and slow modes are formulated. Theoretical consequences from both adiabatic and nonadiabatic dynamics are discussed. In particular, we aim to identify a possible physical origin for drastic change of the slow dynamics to be induced by instability that happens to emerge in the fast mode. The Haken slaving principle and other theories like the adiabatic elimination method focus on the order formation led by the growth of the slow modes, with slaving the fast modes so as to faithfully follow the system dynamics. In this context, the fast modes are quite often regarded as ‘noise’ or a factor of small fluctuation. However, in molecular nonadiabatic dynamics, due to the breakdown of the Born–Oppenheimer approximation, the roles of the fast mode (due to electron dynamics) is far from that of ‘noise’, and sometimes bring about a qualitative bifurcation of the dynamics of the slow subsystem, which we usually refer to as nonadiabatic transition. We show the similar sudden change can be caused by the fast mode in classical mechanics too. The similarity and difference between quantum and classical nonadiabatic dynamics will be discussed.

GRAPHICAL ABSTRACT

KEYWORDS:

• Nonadiabatic dynamics
• classical mechanics
• sudden transition
• Liouville dynamics
• fast and slow modes

Acknowledgments

This work was supported in part by Japan Society for the Promotion of Science with the grant number 15H05752.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Japan Society for the Promotion of Science [grant number 15H05752].