For example, such a one-dimensional model, in which the particle is a movable ring on the torus, and the spatial coordinate is the irrational winding of the torus, suitable for the role of the pre-quant model? Even not to mention the random walk of the ring as a quantum behavior of the particle, we can talk about the uniform motion of the ring along the helical lines of the torus, which will immediately give an interpretation of the spin of the particle as the direction of rotation of the ring.
It is about such models that I tried to speak in the article about the application of local algebras of vector fields to the modeling of physical phenomena.
Article Applications of the local algebras of vector fields to the m...