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I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf j_{\pm} = n_{\pm} \mathbf V_{\pm} - D \nabla n_{\pm},$$ where $n$ is the number of spins(up/down).

Now the second term is clear, as this one comes from Fick's first law, but the first one is strange. He claims that $\mathbf V_{\pm}$ is the velocity of positively(negatively) oriented spins (he restricts himself to spin 1/2). Does anybody know what this drift velocity could mean?

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  • $\begingroup$ Could you send the paper somehow? I am unable to access it. $\endgroup$ – Yuzuriha Inori Mar 10 '18 at 7:43
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Drift velocity means velocity due to the magnetic field gradient acting upon the particle having the spin.

This reference may be helpful: http://people.duke.edu/~ad159/files/p142/4.pdf

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I haven't read the paper but I can speculate...

One possible reason for drift is a very obvious one: If the nuclei are drifting, then they will carry their spins with them. For example, if the nucleon is part of a molecule in blood, and the blood is flowing down an artery, then the spin will flow down the artery too.

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