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Proceedings Paper

Noise-induced transitions in overdamped systems: short times
Author(s): Slanislav M. Soskin; Valentin I. Sheka; Tatiana L. Linnik; Riccardo Mannella
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Paper Abstract

In the problem of the activation energy for a noise-induced transition over a finite given time in an arbitrary overdamped one-dimensional potential system, we find and classify all extremal paths and provide a simple algorithm to explicitly select which is the most probable transition path (MPTP). The activation energy is explicitly expressed in quadratures. For the transition beyond the top of the barrier, the MPTP does not possess turning points and the activation energy is a monotonously decreasing function of the transition time. For transitions between points lying on one and the same slope of the potential well, which may be relevant e.g. for the problem of the tails of the prehistory probability density, the situation is more complicated: the activation energy is a non-monotonous function of time and, most important, may possess bends corresponding to jump-wise switches in the topology of the MPTP; it can be proved also that the number of turning points in the MPTP is necessarily less than two. The prefactor is calculated numerically using the scheme suggested by Lehmann, Reimann and Hanggi, PRE 55, 419 (1998). The theory is compared with simulations.

Paper Details

Date Published: 7 May 2003
PDF: 12 pages
Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); doi: 10.1117/12.498532
Show Author Affiliations
Slanislav M. Soskin, Institute of Semiconductor Physics (Ukraine)
Lancaster Univ. (United Kingdom)
Valentin I. Sheka, Institute of Semiconductor Physics (Ukraine)
Tatiana L. Linnik, Institute of Semiconductor Physics (Ukraine)
Riccardo Mannella, Lancaster Univ. (United Kingdom)
Univ. degli Studi di Pisa (Italy)

Published in SPIE Proceedings Vol. 5114:
Noise in Complex Systems and Stochastic Dynamics
Lutz Schimansky-Geier; Derek Abbott; Alexander Neiman; Christian Van den Broeck, Editor(s)

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