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Title: An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials
Authors: Gray, Thomas H.
Yong, Ee Hou
Keywords: Science::Physics
Issue Date: 2021
Source: Gray, T. H. & Yong, E. H. (2021). An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials. Journal of Chemical Physics, 154(8), 084103-.
Project: 04INS000175C230
Journal: Journal of Chemical Physics
Abstract: Thermally activated escape processes in multi-dimensional potentials are of interest to a variety of fields, so being able to calculate the rate of escape-or the mean first-passage time (MFPT)-is important. Unlike in one dimension, there is no general, exact formula for the MFPT. However, Langer's formula, a multi-dimensional generalization of Kramers's one-dimensional formula, provides an approximate result when the barrier to escape is large. Kramers's and Langer's formulas are related to one another by the potential of mean force (PMF): when calculated along a particular direction (the unstable mode at the saddle point) and substituted into Kramers's formula, the result is Langer's formula. We build on this result by using the PMF in the exact, one-dimensional expression for the MFPT. Our model offers better agreement with Brownian dynamics simulations than Langer's formula, although discrepancies arise when the potential becomes less confining along the direction of escape. When the energy barrier is small our model offers significant improvements upon Langer's theory. Finally, the optimal direction along which to evaluate the PMF no longer corresponds to the unstable mode at the saddle point.
ISSN: 0021-9606
DOI: 10.1063/5.0040071
Rights: © 2021 Author(s). All rights reserved. This paper was published by AIP Publishing in Journal of Chemical Physics and is made available with permission of Author(s).
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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