Random spin distributions and the diffusion equation

TL;DR

This paper demonstrates that the probability distribution of a fully random spin system obeys a diffusion equation with a spin-dependent coefficient, and introduces a bosonization scheme for total spin operators.

Contribution

It shows the diffusion-like behavior of spin distributions and provides a bosonization method for total spin operators, advancing understanding of spin dynamics.

Findings

Probability distribution satisfies a diffusion equation.

Diffusion coefficient is S(S+1)/6.

Bosonization scheme for total spin operators introduced.

Abstract

We show that the probability distribution corresponding to a fully random tracial state of a system of spin-S particles satisfies a diffusion-like equation. The diffusion coefficient turns out to be equal to $S(S+1)/6$, where $S$ is the magnitude of the spin of each particle. We also present a bosonization scheme for the lowering and raising total spin operators.