The band-gap structure and the singular character of the bounded large array of potential barriers

Details The band-gap structure and the singular character of the bounded large array of potential barriers The band-gap structure and the singular character of the bounded large array of potential barriers

2003-06-08

arxiv.org/abs/quant-ph/0306060v3

IJTP, 44, 1281-1302 (2005)

Physics

Quantum Physics

22 pages, 7 PS figures, former text removed and a new one inserted

Scientific paper

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.

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