Visualizing operators of coupled spin systems

TL;DR

This paper introduces a visualization method for coupled spin system operators using shapes representing spherical harmonics, generalizing Wigner functions and applicable to multiple spins, with transformations under rotations and permutations.

Contribution

It presents a novel visualization approach for coupled spin operators that generalizes Wigner functions and handles multiple spins with natural transformation properties.

Findings

Applicable to arbitrary number of spins

Transforms under rotations and permutations

Illustrated with three spins 1/2 examples

Abstract

The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes representing linear combinations of spherical harmonics. It is applicable to an arbitrary number of spins and can be interpreted as a generalization of Wigner functions. The corresponding visualization transforms naturally under non-selective spin rotations as well as spin permutations. Examples and applications are illustrated for the case of three spins 1/2.