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Transition-event durations in one-dimensional activated processes.

Bin W Zhang¹, David Jasnow, Daniel M Zuckerman

¹Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.

The Journal of Chemical Physics

|March 3, 2007

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This study analyzes transition event durations in systems with Langevin dynamics. We provide a theoretical framework and simulations to understand these short, crucial events, revealing their dependence on system potential details.

Area of Science:

Statistical Mechanics
Physical Chemistry
Computational Physics

Background:

Transition events are critical in activated processes but their durations are not well understood theoretically.
Existing models often focus on first passage times, neglecting shorter transition event durations.

Purpose of the Study:

To theoretically investigate the distribution of transition event durations over a potential barrier.
To develop a framework for analyzing short-time dynamics in activated processes.

Main Methods:

Utilized overdamped Langevin dynamics and a Fokker-Planck equation with absorbing boundary conditions.
Derived analytic expressions for short-time and long-time behaviors of transition event durations.
Employed transition-path-sampling simulations for validation.

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Main Results:

Obtained the universal analytic form of short-time transient behavior, independent of the potential.
Identified the first nonuniversal correction to estimate a key physical time scale.
Developed a recursive method for calculating moments and approximations for the duration distribution.
Found that mean event duration depends on potential details, not just barrier curvature.

Conclusions:

The theoretical framework accurately describes transition event durations.
Results are validated by novel transition-path-sampling simulations.
Discussed the generalizability of findings to more complex systems.