Noise-induced transitions in overdamped systems: short times

Slanislav M. Soskin; Valentin I. Sheka; Tatiana L. Linnik; Riccardo Mannella

doi:10.1117/12.498532

7 May 2003 Noise-induced transitions in overdamped systems: short times

Slanislav M. Soskin, Valentin I. Sheka, Tatiana L. Linnik, Riccardo Mannella

Proceedings Volume 5114, Noise in Complex Systems and Stochastic Dynamics; (2003) https://doi.org/10.1117/12.498532
Event: SPIE's First International Symposium on Fluctuations and Noise, 2003, Santa Fe, New Mexico, United States

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.

Citation Download Citation

Slanislav M. Soskin, Valentin I. Sheka, Tatiana L. Linnik, and Riccardo Mannella "Noise-induced transitions in overdamped systems: short times", Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); https://doi.org/10.1117/12.498532

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