An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Gray, Thomas H., Yong, Ee Hou
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2021
Subjects:
Online Access:https://hdl.handle.net/10356/153611
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-153611
record_format dspace
spelling sg-ntu-dr.10356-1536112023-02-28T19:36:20Z An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials Gray, Thomas H. Yong, Ee Hou School of Physical and Mathematical Sciences Division of Physics and Applied Physics Science::Physics Physical Chemistry Physics 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. Nanyang Technological University Published version T.H.G. acknowledges support from the EPSRC, and E.H.Y. acknowledges support from Nanyang Technological University Singapore, under its Start-Up Grant Scheme (Grant No. 04INS000175C230). 2021-12-10T06:08:53Z 2021-12-10T06:08:53Z 2021 Journal Article 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-. https://dx.doi.org/10.1063/5.0040071 0021-9606 https://hdl.handle.net/10356/153611 10.1063/5.0040071 33639738 2-s2.0-85101376795 8 154 084103 en 04INS000175C230 Journal of Chemical Physics © 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). application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Physics
Physical Chemistry
Physics
spellingShingle Science::Physics
Physical Chemistry
Physics
Gray, Thomas H.
Yong, Ee Hou
An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Gray, Thomas H.
Yong, Ee Hou
format Article
author Gray, Thomas H.
Yong, Ee Hou
author_sort Gray, Thomas H.
title An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials
title_short An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials
title_full An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials
title_fullStr An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials
title_full_unstemmed An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials
title_sort effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials
publishDate 2021
url https://hdl.handle.net/10356/153611
_version_ 1759854025896886272