The nature of the gaps in the electronic energy spectrum of liquid-like one-dimensional systems

It is shown that the gaps which appear in the energy spectrum of a liquid-like disordered Kronig-Penney model can be explained as the energy intervals in which the phase distributions for the forward and the backward directions are almost or completely non-overlapping. Inasmuch as such a non-overlapping is intimately related to the strong localization of eigenfunctions, this explains at the same time why the wave functions near these gaps are particularly strongly localized.