A geometrical approach to the dynamics of spinor condensates II: Collective modes

TL;DR

This paper introduces a symmetry-based, geometrical method to analyze the collective excitations in spinor condensates, linking their modes to molecular vibrations and atomic electron wave functions.

Contribution

It develops a general linearization approach for spinor condensate dynamics using symmetry and stereographic projection, enabling mode extraction without solving complex equations.

Findings

Method to linearize equations based on symmetry

Construction of collective modes from symmetry considerations

Mapping spin-wave modes to atomic electron wave functions

Abstract

In this paper we study the linearized dynamics of spinor condensates using the spin-node formalism developed in arXiv:0812.3403. We provide a general method to linearize the equations of motion based on the symmetry of the mean-field ground state using the local stereographic projection of the spin nodes. We also provide a simple construction to extract the collective modes from symmetry considerations alone akin to the analysis of vibrational excitations of polyatomic molecules. Finally, we will present a mapping between the spin-wave modes, and the wave functions of electrons in atoms, where the spherical symmetry is degraded by a crystal field.