Large fluctuations in multiattractor systems and the generalized Kramers problem

The main subject of the paper is an escape from a multiwell metastable pote ntial on the timescale of the formation of the quasiequilibrium between the wells. Our main attention is devoted to such ranges of friction in which a n external saddle does nor belong to a basin of attraction of an initial at tractor. 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 f lux, the rate on shorter timescales strongly depends on friction: moreover, it may undergo oscillations in the underdamped range and a cutoff in the o verdamped range. A generalization of the results for interattractor transit ions in stable potentials with more than two wells is also presented, and a splitting procedure for a phenomenological description of interattractor t ransitions is suggested. Applications to such problems as the dynamics or e scape on timescales shorter than an optimal fluctuation duration, the prehi story problem, the optimal control of fluctuations, fluctuational transport in ratchets, escapes at a periodic driving, and transitions in biased Jose phson junctions and ionic channels are briefly discussed.