Inert states of spin-S systems

TL;DR

This paper introduces a geometric method to identify inert states in spin-S systems, applicable to any spin value, by representing pure states with points on a sphere, aiding in understanding ground states of spinor Bose-Einstein condensates.

Contribution

The paper presents a novel geometric approach for determining inert states in arbitrary spin systems, simplifying analysis of their ground states.

Findings

Method successfully identifies inert states for various spin values.

Application to spinor Bose-Einstein condensates demonstrates practical utility.

Provides a visual and analytical tool for spin state analysis.

Abstract

We present a simple but efficient geometrical method for determining the inert states of spin-S systems. It can be used if the system is described by a spin vector of a spin-S particle and its energy is invariant in spin rotations and phase changes. Our method is applicable to an arbitrary S and it is based on the representation of a pure spin state of a spin-S particle in terms of 2S points on the surface of a sphere. We use this method to find candidates for some of the ground states of spinor Bose-Einstein condensates.