Most probable transition path in an overdamped system for a finite transition time

The most probable transition path in a one-dimensional overdamped system is rigorously proved to possess less than two turning points. The proof is valid for any potentials, transition times, initial and final transition points

Adiabatic divergence of the chaotic layer width and acceleration of chaotic and noise-induced transport

SUMMARY We show that, in spatially periodic Hamiltonian systems driven by a time-periodic coordinate-independent (AC) force, the upper energy of the chaotic layer grows unlimitedly as the frequency of the force goes to zero. This remarkable effect is absent in any other physically significant systems. It gives rise to the divergence of the rate of the spatial chaotic transport. We also generalize this phenomenon for the presence of a weak noise and weak dissipation. We demonstrate for the latter case that the adiabatic AC force may greatly accelerate the spatial diffusion and the reset rate at a given threshold

Noise-induced escape flux on time-scales preceding quasistationarity

Noise-induced escape from the metastable part of potential is considered on time scales preceding the formation of quasiequilibrium within that part of the potential. It is shown that, counterintuitively, the escape flux may depend exponentially strongly, and in a complicated manner, on time and friction