I'm reading this paper and it has the line (end of 3rd paragraph, page 2):
It turns out that the simple fact that electrons are diffusive instead of freely propagating leads to a profound modification of the traditional view based on the Fermi-liquid theory of metals.
So it kind of suggests it means something that's not freely propagating, like bound I guess?
No, it does not mean bound. It has to do with the amount of scattering: diffusive is the opposite of ballistic. Let's talk semi-classically so that the concept of a mean free path makes sense.
In the totally ballistic limit, the electron would go about its business, without being scattered into a different state. This limit is often approached if the electron doesn't have very far to go -- for example, if it just has to go through a short channel. Here, the mean free path is longer than whatever system you want to study.
In the diffusive limit, the electron is scattering very frequently, to the extent that it's basically doing a random walk. If you apply an electric field -- on average -- the electron will follow the electric field, but it will spend a lot of time going the "wrong way". Here, the mean free path is much shorter than the system you want to study.
