Kim, W.K. and Netz, R.R. (2015) The mean shape of transition and firstpassage paths. The Journal of Chemical Physics, 143 (224108).

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Official URL: http://dx.doi.org/10.1063/1.4936408
Abstract
Based on the onedimensional FokkerPlanck equation in an arbitrary free energy landscape including a general inhomogeneous diffusivity profile, we analytically calculate the mean shape of transition paths and firstpassage paths, where the shape of a path is defined as the kinetic profile in the plane spanned by the mean time and the position. The transition path ensemble is the collection of all paths that do not revisit the start position xA and that terminate when first reaching the final position xB. In contrast, a firstpassage path can revisit its start position xA before it terminates at xB. Our theoretical framework employs the forward and backward FokkerPlanck equations as well as firstpassage, passage, lastpassage, and transitionpath time distributions, for which we derive the defining integral equations.We show that the mean shape of transition paths, in other words the mean time at which the transition path ensemble visits an intermediate position x, is equivalent to the mean firstpassage time of reaching the position xA when starting from x without ever visiting xB. The mean shape of firstpassage paths is related to the mean shape of transition paths by a constant time shift. Since for a large barrier height U, the mean firstpassage time scales exponentially in U, while the mean transition path time scales linearly inversely in U, the time shift between firstpassage and transition path shapes is substantial. We present explicit examples of transition path shapes for linear and harmonic potentials and illustrate our findings by trajectories obtained from Brownian dynamics simulations.
Item Type:  Article 

Subjects:  Physical Sciences Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
ID Code:  1891 
Deposited By:  Ulrike Eickers 
Deposited On:  16 Mar 2016 19:28 
Last Modified:  03 Mar 2017 14:42 
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