Measurement of three-body chaotic absorptivity predicts chaotic outcome distribution

TL;DR

This paper validates a flux-based statistical theory for three-body chaotic systems by measuring the absorptivity function through simulations, confirming the predicted chaotic outcome distribution with high accuracy.

Contribution

It provides the first direct measurement of the tri-variate absorptivity function, confirming the flux-based theory and reducing computational effort in predicting chaotic outcomes.

Findings

Good agreement between predicted and measured chaotic outcome distribution.

Successful measurement of the tri-variate absorptivity function.

Confirmation of the flux-based statistical theory for three-body chaos.

Abstract

The flux-based statistical theory of the non-hierarchical three-body system predicts that the chaotic outcome distribution reduces to the chaotic emissivity function times a known function, the asymptotic flux. Here, we measure the chaotic emissivity function (or equivalently, the absorptivity) through simulations. More precisely, we follow millions of scattering events only up to the point when it can be decided whether the scattering is regular or chaotic. In this way, we measure a tri-variate absorptivity function. Using it, we determine the flux-based prediction for the chaotic outcome distribution over both binary binding energy and angular momentum, and we find good agreement with the measured distribution. This constitutes a detailed confirmation of the flux-based theory, and demonstrates a considerable reduction in computation to determine the chaotic outcome distribution.