Transition events in one dimension
- 12 January 2004
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 69 (1), 012101
- https://doi.org/10.1103/physreve.69.012101
Abstract
The instanton or stationary-phase formula has received much attention recently as a way of determining transition paths in reacting systems. In this paper, we analyze the instanton approach for some one-dimensional problems and compare the results it gives with data from a numerical simulation. We show that a proper comparison of the analytic and numerical results must take into account the boundary conditions used in the numerical simulations and also suggest values for the integration constant in the instanton formula that gives the best agreement with the simulated results.Keywords
This publication has 9 references indexed in Scilit:
- Transition events in butane simulations: Similarities across modelsThe Journal of Chemical Physics, 2002
- Efficient dynamic importance sampling of rare events in one dimensionPhysical Review E, 2000
- Anomalous diffusion and the first passage time problemPhysical Review E, 2000
- Temperature dependent reaction coordinatesThe Journal of Chemical Physics, 2000
- Intrawell relaxation of overdamped Brownian particlesPhysical Review E, 1999
- Intrawell Relaxation Time: The Limit of the Adiabatic ApproximationPhysical Review Letters, 1999
- Stochastic Calculus: Application to Dynamic Bifurcations and Threshold CrossingsJournal of Statistical Physics, 1998
- δ‐function perturbations and boundary problems by path integrationAnnalen der Physik, 1993
- Reaction-rate theory: fifty years after KramersReviews of Modern Physics, 1990