I've heard that there is some connection between the GUE and distributions of energy in collections of particles. I was hoping someone who knows the physics can give me a less vague idea on how the GUE relates to the real world.

Keep in mind my physics is pretty lacking :). I'm more interested in the GUE because of it's relation to the riemann zeta function, but I've seen it mentioned several times that the GUE turns up in physics and thought it wouldn't hurt to have some idea how.

cheers