Noise activates escapes in closed Hamiltonian systems

In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in finite times. This drastic change in the dynamical behavior turns the bounded motion into a chaotic scattering problem. We analyze the escape dynamics by means of the average escape time, the probability basins and the average escape time distribution. We obtain that the main characteristics of the scattering are different from the case of noisy open Hamiltonian systems. In particular, the noise-enhanced trapping, which is ubiquitous in Hamiltonian systems, does not play the main role in the escapes. On the other hand, one of our main findings reveals a transition in the evolution of the average escape time insofar the noise is increased. This transition separates two different regimes characterized by different algebraic scaling laws. We provide strong numerical evidence to show that the complete destruction of the stickiness of the KAM islands is the key reason under the change in the scaling law. This research unlocks the possibility of modeling chaotic scattering problems by means of noisy closed Hamiltonian systems. For this reason, we expect potential application to several fields of physics such us celestial mechanics and astrophysics, among others. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study reveals a noise-activated escape phenomenon in closed Hamiltonian systems, transforming bounded motion into chaotic scattering. By analyzing average escape time, probability basins, and escape time distribution, it is found that characteristics of scattering in closed systems differ from open systems, with noise-enhanced trapping playing a minor role in escapes and a transition in average escape time evolution with increased noise. This research provides numerical evidence of the destruction of the stickiness of KAM islands as a key factor in changing scaling laws, unlocking the possibility of modeling chaotic scattering problems in noisy closed Hamiltonian systems.