Band-Gap Structure and Singular Character of Bounded One-Dimensional Multibarrier Potentials

Abstract

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.

Note on a Floquet/Bloch-band fusion phenomenon in scattering by truncated periodic multi-well potentials

“…Quantal transmissions through multi-barrier/well systems in one dimension [3]- [12] provide important theoretical notions for analyzing tunneling in solids [13], chemical selection of gas components [14], electronic properties of material structures such as graphene [15]- [20]. Generalizations involve 2D models, relativistic corrections, and spin-coupling effects [21]- [26].…”