This is the main point of a nice article by Roald Hoffmann, that I posted about in the early days of this blog.
I experienced this a few weeks ago. I have been working on a paper with my postdoc Nandan Pakhira about the viscosity of strongly correlated fermion fluids, focussing on the Hubbard model. A basic issue I got quite confused about is the relation between the momentum, Bloch wave vector, and velocity of an electron in a Bloch state. Yet, I when I taught this to my solid state physics class I was reminded of the correct result.
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I have a naive question about the viscosity. The mechanical momentum is no longer conserved when a lattice is present. In this case, is viscosity still a well defined concept at low energy?
ReplyDeleteHi Yuan Wan,
DeleteThank you for your question. I don't think it is naive, but rather profound.
I think the viscosity is well-defined in a lattice system for the same reason that any "low-energy" macroscopic transport coefficient quantity (cf. conductivity) that is actually defined in a long-wavelength (i.e. continuum) limit.
But, I may be missing something.
Nandan and I are trying to make this clear in the paper we are finishing.