What happens to the electron density in a metal during an electric discharge? Suppose we are able to see into a grain of metal at the boundary between the grain and air (perhaps along one of the faces of this cube):

(Source: Wikimedia Commons.)
This image does not show the electron density, but maybe we can imagine it being vaguely similar to what is shown in the image, but more diffuse.
What happens when an electric arc discharges into the grain from outside?  Specifically, what happens to the electron density? Do the electrons in the arc pass through the voids, do they pass through the lattice sites, or do they do something else? What is the name of the subfield that studies this kind of nonequilibrium phenomenon?
 A: Electrons in a metal behave 'very strongly' according to quantum mechanics. This means that unlike classical objects, their position and velocity cannot be defined precisely. With that said, you can expect a shift in the electron density - a shift which resembles a sort of electron fluid flowing out of the conductor, and becoming a part of the arc. But NOTE that this electron fluid is more accurately the probability density, not a classical charge density.
You can relate more to the problem by studying the way a single electron would move around an obstacle. For instance, quite astoundingly, in the hydrogen atom, there is a non-zero probability that the electron would be inside the nucleus! In a nutshell, we can only study the movement of the probability current for the electrons, rather than a classical charge density. Nevertheless, approximately, this situation would equal a moving charge density.
The field that studies such dynamic phenomenon is Plasma physics. Many people think that a plasma is just a very hot gas, but technically even the electron gas in a metal at normal temperatures is a type of plasma.
