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In the book "Introduction to Many-Body Physics" by Piers Coleman, it is argued (page 406) that a momentum supercurrent (superflow) corresponds to sheer stress in a crystal. What would be a simple example to understand this?

I can easily imagine a charge supercurrent in a superconductor due to an electric field.

I also understand the fact that it is a "supercurrent", as otherwise there would be a plastic deformation involved.

However, I have trouble coming up with a simple example which shows momentum superflow.

For example, if I have a glass rod which is being compressed from both sides, what is the direction of momentum superflow?

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  • $\begingroup$ well at first glance and without thinking of it: if you prescribe a momentum on one side of a crystal the whole crystal will eventually move with the same velocity (note that your example leads to compressive stress not shear stress). That is different from a liquid, where you (idealized) have no shear stress that will restore the shape. $\endgroup$
    – Bort
    Sep 23, 2016 at 13:05
  • $\begingroup$ Thanks, Bort! I have found some references, which basically go in the same direction as your comment but are more complete. I've posted them as an answer to my own question. $\endgroup$
    – jarm
    Oct 5, 2016 at 6:18

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It turns out that answers to these questions have been elaborated in a series of articles by Friedrich Herrmann from Karlsruhe and his collaborators. The first article on the subject is "Statics in the momentum current picture" (paywalled).

Examples illustrating application of this technique to bodies under tension or compression are given in "Momentum flow diagrams for just-rigid static structures" (also paywalled, but available from the website of the author as a pdf). See in particular the paragraph under Fig. 2.

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