Simulated annealing algorithm for finding periodic orbits of multi-electron atomic systems

TL;DR

This paper adapts the simulated annealing algorithm to identify periodic orbits in classical multi-electron atomic systems, demonstrating its effectiveness on the helium atom across different dimensions and analyzing the system's dynamics.

Contribution

It introduces a novel application of simulated annealing for finding periodic orbits in multi-electron atomic systems, linking the method to dynamical structure analysis.

Findings

Feasibility of the method demonstrated on helium atom

Identified periodic orbits in 1-3 dimensions

Connected orbit structure to system dynamics

Abstract

We adapt the simulated annealing algorithm to the search of periodic orbits for classical multi-electron atomic systems. This is done by minimizing the n-th return distance to the initial position on a Poincare surface of section under an energy constraint. Here we give evidence of the feasibility of the method by applying it to the helium atom in the ground state for one to three spatial dimensions. We examine the structure of the dynamics and connect its organization to the periodic orbits we have found.