Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics

TL;DR

This paper develops a comprehensive framework for the time evolution of single spins in continuous phase spaces using star products and spin-weighted spherical harmonics, enabling efficient analysis of large spin systems.

Contribution

It introduces a simplified method to explicitly determine star products for arbitrary spin numbers, connecting phase spaces to the quantum-optical limit and facilitating large spin approximations.

Findings

Explicit star products for general spins derived

Efficient large spin approximations developed

Phase-space representations of complex quantum states improved

Abstract

We study continuous phase spaces of single spins and develop a complete description of their time evolution. The time evolution is completely specified by so-called star products. We explicitly determine these star products for general spin numbers using a simplified approach which applies spin-weighted spherical harmonics. This approach naturally relates phase spaces of increasing spin number to their quantum-optical limit and allows for efficient approximations of the time evolution for large spin numbers. We also approximate phase-space representations of certain quantum states that are challenging to calculate for large spin numbers. All of these applications are explored in concrete examples and we outline extensions to coupled spin systems.