Classical spin and quantum propagation

We consider a classical Brownian motion model of diffusion in two spatial dimensions, where the Brownian particle moves on spiral paths. The classical spin does not change the propagator for the probability density for the position of the particle. However, the subdominant eigenvalues of the classical kernel are simply related to the dominant eigenvalues of the Feynman kernel for an analogous quantum system. The Feynman kernel can be extracted from the classical kernel by coupling to a spin angular momentum of the particle.