Noise activates escapes in closed Hamiltonian systems

TL;DR

This paper demonstrates that noise can induce escape in closed Hamiltonian systems by opening isopotential curves, transforming bounded motion into chaotic scattering, and reveals a transition in escape dynamics with increasing noise.

Contribution

It introduces the concept of noise-activated escape in closed Hamiltonian systems and analyzes the resulting chaotic scattering behavior and transition in escape time scaling laws.

Findings

Noise causes energy fluctuations that open isopotential curves.

A transition in escape time scaling occurs with increased noise.

Destruction of KAM island stickiness explains the change in scaling laws.

Abstract

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.