Eur. Phys. J. Plus (2020) 135: 731
https://doi.org/10.1140/epjp/s13360-020-00752-7

Regular Article

Transition path dynamics across rough inverted parabolic potential barrier

¹ Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi’an, China
² MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, 710072, Xi’an, China
³ Center for Mathematical Sciences & School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074, Wuhan, China
⁴ Institute for Physics & Astronomy, University of Potsdam, 14476, Potsdam-Golm, Germany

^b hsux3@nwpu.edu.cn

Received: 22 July 2020
Accepted: 3 September 2020
Published online: 15 September 2020

Abstract

Transition path dynamics have been widely studied in chemical, physical, and technological systems. Mostly, the transition path dynamics is obtained for smooth barrier potentials, for instance, generic inverse-parabolic shapes. We here present analytical results for the mean transition path time, the distribution of transition path times, the mean transition path velocity, and the mean transition path shape in a rough inverted parabolic potential function under the driving of Gaussian white noise. These are validated against extensive simulations using the forward flux sampling scheme in parallel computations. We observe how precisely the potential roughness, the barrier height, and the noise intensity contribute to the particle transition in the rough inverted barrier potential.