Short-time dynamics of noise-induced escapes and transitions in overdamped systems

Using the path-integral approach, we have developed a general solution of the problem of a noise-induced escape or transition of the overdamped one-dimensional potential system at time scales of the order of dynamic relaxation time. The results strongly differ from those obtained before by other methods. Computer simulations confirm the validity of our theory in the relevant time range. The obtained results may be of interest in studies of Josephson junctions, levitating nanoparticles in optical traps, ionic channels, chemical reactions and chemical-physical systems.