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Large Fluctuations in Multiattractor Systems and the Generalized Kramers Problem

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Abstract

The main subject of the paper is an escape from a multiwell metastable potential on the timescale of the formation of the quasiequilibrium between the wells. Our main attention is devoted to such ranges of friction in which an external saddle does not belong to a basin of attraction of an initial attractor. A complete rigorous analysis of the problem for the most probable escape path is presented and a corresponding escape rate is calculated with a logarithmic accuracy. Unlike a conventional rate for a quasistationary flux, the rate on shorter timescales strongly depends on friction, moreover, it may undergo oscillations in the underdamped range and a cutoff in the overdamped range. A generalization of the results for interattractor transitions in stable potentials with more than two wells is also presented, and a splitting procedure for a phenomenological description of interattractor transitions is suggested. Applications to such problems as the dynamics of escape on timescales shorter than an optimal fluctuation duration, the prehistory problem, the optimal control of fluctuations, fluctuational transport in ratchets, escapes at a periodic driving, and transitions in biased Josephson junctions and ionic channels are briefly discussed.

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  1. Institute of Semiconductor Physics, National Ukrainian Academy of Sciences, Kiev, Ukraine

    S. M. Soskin

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Soskin, S.M. Large Fluctuations in Multiattractor Systems and the Generalized Kramers Problem. Journal of Statistical Physics 97, 609–676 (1999). https://doi.org/10.1023/A:1004663224988

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