Noise-enhanced trapping in chaotic scattering

TL;DR

This paper demonstrates that noise can increase the trapping time of trajectories in chaotic scattering systems, affecting decay rates and phase-space dynamics, with implications for experiments and quantum systems.

Contribution

It reveals that noise can enhance trapping in chaotic and Hamiltonian scattering systems, a phenomenon previously unrecognized, with detailed analysis and confirmation in the Henon map.

Findings

Noise decreases decay rates in chaotic systems.

Noise causes slower algebraic decay in mixed phase space.

Enhanced trapping mechanisms are likely in most scattering systems.

Abstract

We show that noise enhances the trapping of trajectories in scattering systems. In fully chaotic systems, the decay rate can decrease with increasing noise due to a generic mismatch between the noiseless escape rate and the value predicted by the Liouville measure of the exit set. In Hamiltonian systems with mixed phase space we show that noise leads to a slower algebraic decay due to trajectories performing a random walk inside Kolmogorov-Arnold-Moser islands. We argue that these noise-enhanced trapping mechanisms exist in most scattering systems and are likely to be dominant for small noise intensities, which is confirmed through a detailed investigation in the Henon map. Our results can be tested in fluid experiments, affect the fractal Weyl's law of quantum systems, and modify the estimations of chemical reaction rates based on phase-space transition state theory.