Basin Entropy, a Measure of Final State Unpredictability and Its Application to the Chaotic Scattering of Cold Atoms

Abstract

Basins of attraction take its name from hydrology, and in dynamical systems they refer to the set of initial conditions that lead to a particular final state. When different final states are possible, the predictability of the system depends on the structure of these basins. We introduce the concept of basin entropy, that aims to quantify the final state unpredictability associated to the basins. Using several paradigmatic examples from nonlinear dynamics, we dissect the meaning of this new quantity and suggest some useful applications such as the basin entropy parameter set. Then, we explain how it is possible to apply this concept to experiments with cold atoms. Previous works pointed out that chaotic dynamics could be at the heart of some interesting regimes found in the scattering of cold atoms. Here, we detail how one of the hallmarks of chaos, the appearance of fractal structures in phase space, can be detected directly from experimental measurements thanks to the basin entropy.