Transient capture of electrons in magnetic fields, or: comets in the restricted three-body problem

TL;DR

This paper explores the analogy between celestial and atomic systems, analyzing how objects like comets or electrons can be transiently captured by a central body before escaping, highlighting classical-quantum parallels.

Contribution

It introduces a framework for understanding transient capture phenomena in celestial and atomic systems, linking classical trajectories with quantum states.

Findings

Objects can be temporarily trapped near a central body.

The dynamics resemble quantum eigenstates in atomic systems.

Escape occurs after multiple revolutions around the center.

Abstract

The motion of celestial bodies in astronomy is closely related to the orbits of electrons encircling an atomic nucleus. Bohr and Sommerfeld presented a quantization scheme of the classical orbits to analyze the eigenstates of the hydrogen atom. Here we discuss another close connection of classical trajectories and quantum mechanical states: the transient dynamics of objects around a nucleus. In this setup a comet (or an electron) is trapped for a while in the vicinity of an parent object (Jupiter or an atomic nucleus), but eventually escapes after many revolutions around the center of attraction.