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arXiv · 2208.06667

On the classical reaction rate and the first-time problems of Brownian motion

Aihua Zhang·Sun Choi
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Abstract

We have developed efficient techniques to solve the first-time problems of Brownian motion. Based on a time-scale separation of recrossings, we show that Eyring's transmission coefficient ($\kappa$) equals to the one ($\kappa_\mathrm{V}$) corresponding to an absorbing boundary consistent with the transition state theory, which is greater than the one ($\kappa_\mathrm{K}$) derived by Kramers. We also propose methods for reaction rate determination by analyzing short-time trajectories from the barrier maximum, and discuss the relation to the reactive flux method and the significance of reaction coordinates.

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Aihua Zhang, Sun Choi. 2022-08-13. On the classical reaction rate and the first-time problems of Brownian motion. https://doi.org/10.1016/j.physa.2023.128823

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