Trapping enhanced by noise in nonhyperbolic and hyperbolic chaotic scattering

TL;DR

This paper demonstrates that Gaussian white noise influencing energy, not just variables, can significantly increase trapping times in chaotic scattering, showing a new mechanism for noise-enhanced trapping in Hamiltonian systems.

Contribution

It introduces a novel mechanism where noise affecting energy levels enhances trapping, supported by numerical evidence in the Hénon-Heiles system.

Findings

Noise can decrease particle energy, prolonging trapping times.

Energy-influencing noise enhances trapping in chaotic scattering.

The mechanism is general across different chaotic systems.

Abstract

The noise-enhanced trapping is a surprising phenomenon that has already been studied in chaotic scattering problems where the noise affects the physical variables but not the parameters of the system. Following this research, in this work we provide strong numerical evidence to show that an additional mechanism that enhances the trapping arises when the noise influences the energy of the system. For this purpose, we have included a source of Gaussian white noise in the H\'enon-Heiles system, which is a paradigmatic example of open Hamiltonian system. For a particular value of the noise intensity, some trajectories decrease their energy due to the stochastic fluctuations. This drop in energy allows the particles to spend very long transients in the scattering region, increasing their average escape times. This result, together with the previously studied mechanisms, points out the generality of the noise-enhanced trapping in chaotic scattering problems.