Amorphous substances and liquids—the existence of energy gaps in their one-dimensional analogs

Abstract

The model of a one-dimensional liquid or amorphous material is represented by a linear chain of symmetric, localized, but otherwise arbitrary, potential cells, each of which consists of a central core, the same in all cells, surrounded by two regions of zero potential of varying extent. The physical restriction that cell sizes are bounded is applied. The present article gives the proof for the existence of gaps in such a model. It is also hinted that the proof can be generalized to the real situation where the central core potentials may be slightly different from one another.