The localization of electrons in ordered and disordered systems I. Percolation of classical particles

The localization of `classical electrons' in disordered materials (e.g. liquid metals) is studied with the aid of percolation theory. It is shown that the transition from localized to delocalized states occurs over a fairly narrow range of energy, but is not mathematically discontinuous except in the one-dimensional case. Some implications for the theory of this transition for real quantum-mechanical electrons are suggested.