Band-gap structure and singular character of bounded one-dimensional multibarrier potential

The bounded one dimensional multibarrier potential shows signs of chaos, phase transition and a transmission probability of unity for certain values of its total length L and the ratio c of total interval to total width. Like the infinite Kronig-Penney system, which is arranged along the whole spatial region, the bounded multibarrier potential has a band-gap structure in its energy spectrum. But unlike the Kronig-Penney system, in which the gaps disappear for large energies, these gaps do not disappear for certain values of L and c. The energy is discontinuous even in parts of the spectrum with no gaps at all. These results imply that the energy spectrum of the bounded multibarrier system is singular. keywords: Band-gap structure, Multibarrier potential, Singular spectrum