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Issue 40, 2018
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The influence of absorbing boundary conditions on the transition path time statistics

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Abstract

We derive an analytical expression for the transition path time (TPT) distribution for a one-dimensional particle crossing a parabolic barrier. The solution is expressed in terms of the eigenfunctions and eigenvalues of the associated Fokker–Planck equation. The particle exhibits anomalous dynamics generated by a power-law memory kernel, which includes memoryless Markovian dynamics as a limiting case. Our result takes into account absorbing boundary conditions, extending existing results obtained for free boundaries. We show that TPT distributions obtained from numerical simulations are in excellent agreement with analytical results, while the typically employed free boundary conditions lead to a systematic overestimation of the barrier height. These findings may be useful in the analysis of experimental results on the transition path time. A web tool to perform this analysis is freely available.

Graphical abstract: The influence of absorbing boundary conditions on the transition path time statistics

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Article information


Submitted
09 Jul 2018
Accepted
04 Sep 2018
First published
04 Sep 2018

Phys. Chem. Chem. Phys., 2018,20, 25676-25682
Article type
Paper

The influence of absorbing boundary conditions on the transition path time statistics

M. Caraglio, S. Put, E. Carlon and C. Vanderzande, Phys. Chem. Chem. Phys., 2018, 20, 25676
DOI: 10.1039/C8CP04322A

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