I don't have a direct answer to your question but I have observed following.

Most of the heavy quarkonium spectra models are based on spin independent Schrodinger wave equation. To understand spin transport of quarks, a spin dependent heavy quarkonium spectra model could be a first step towards further research. Following article is based on a spin dependent relativistic wave equation for modelling the heavy quarkonium spectra.

Article Quarkonium and hydrogen spectra with spin-dependent relativi...

One of the hot topic at this moment is how the nucleon spin structure is (de)composed. I work on this subject. To study experimentally this phenomenon the so called Deep  Inelastic Scattering (DIS) is used. Term spin transport is not used, normally spin is carried by quarks and gluons. For more info please see my contributions.

This may partially answer your question.  The basic question may be to distinguish spin transport from mass/energy transport or the transport of other quantum numbers.

At the single particle level, or at the level of a small number of particles, one can define the spin vector

(or Pauli-Lyubanski vector) whose equations of motion are given by the Bargmann-Michel-Telegdi equation.

In this sense spin transport is defined; this is what applies to the single proton example.

In a proton-proton collision, at the level of quarks, this is much harder because the parton distribution function must carry the spin transport information. Individual quark trajectories are not meaningful and so any spin transport must be indirectly accounted for. The standard method of separating out the high momentum part

(described by perturbative QCD) from the low momentum part via the operator product expansion then expresses the spin effects in terms of matrix elements of operators which carry spin. Admittedly, this is very indirect.

If one considers something like a quark gluon plasma (or glasma), then a hydrodynamical description may be applicable. In this case, since hydrodynamics can be defined universally in terms of conservation laws, a spin transport equation is possible. (This would be a fluid generalization of the BMT equation.) The following

paper, from which earlier references can be traced, discusses this for a general plasma with Abelian or nonabelian interactions.

`Relativistic Particle and Relativistic Fluids: Magnetic Moment and Spin-Orbit Interactions',

D. Karabali and V.P. Nair, Phys. Rev. D90, 105018 (2014).

dear Churamaini,

what do you mean saying "spin transport'? May be you had in mind a "spin transfer"? These things are very different. The 1-st one implies a medium, while the 2-nd might be related with a particle-particle interaction in an empty space. Please, put your question in a more definite manner!

Dear Churamani!

You say "Spin transport means collective spin motion of nucleons during interactions" and even here you are mixing different things.

Spin of any "elementary" particle is its attribute which cannot be separated from it: the angular momentum which this particle has always, like its electric charge or isospin. You cannot change the spin of a particle. It is valid for quarks and gluons as well. It is valid also for composite particles like nuclei or atoms. We know that the total angular momentum of an atom is a sum of the particlular angular momenta of its constituents (electrons and its nucleus) and the angular momenta of the "orbital movement" of electrons  (relative to the nucleus) in that atom.

If a particle has an angular momentum, i.e. a vector, you can speak about orientation of that vector. It is "_length_" of that vector which is called "spin". When you consider its _orientation_, you speak about a spin-vector (accociated with the particle's total angular momentum) and its averaged value (vector of polarization). Polarization may have any value from 0 to +\- max. possible (the max. value is defined by the spin value).

Despite you cannot change particle spin, you can change orientation of the particle spin-vector relative to a fixed direction in the 3-space (if you succeded in defining that direction somehow) by external instruments. So, the spin of particles  cannot be transferred from one particle to another. But orientation of a particle spin-vector can be changed due to interaction. In this case people speak about "spin transfer" but it is a jargon. Strictly speaking, people should say "polarization transfer". (You cannot transfer spin from nucleon to pion: it is the pion's property that it has spin 0. "Pion" with nonzero spin is not the pion, as well as a "nucleon" with spin different from 1/2 is not a nucleon at all! )

All this is well described in any good textbook on quantum mechanics. Feynmann's "Lectures on physics" is an excellent example. (By the way: BMT (Bargmann-Michel-Telegdi) equation says how the spin-vector changes its orientation when a particle moves in an external magnetic field; the "length" of that spin-vector remains, of course, constant.)

When you speak about "spin transport", "spin waves" etc, this is absolutely different story, specific for systems consisting of many particles (solid state, for example). It is related with description of such systems , which consist of very big (almost infinite) number of the "elementary" constutuents. This is absolutely different topic.

Be accurate using a terminology!