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Universalities in One-electron Properties of Limit Quasi-periodic Lattices

Rihei Endou·Komajiro Niizeki·Nobuhisa Fujita
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Abstract

We investigate one-electron properties of one-dimensional self-similar structures called limit quasi-periodic lattices. The trace map of such a lattice is nonconservative in contrast to the quasi-periodic case, and we can determine the structure of its attractor. It allows us to obtain the three new features of the present system: 1) The multi-fractal characters of the energy spectra are {\it universal}. 2) The supports of the $f(α)$-spectra extend over the whole unit interval, $[0, 1]$. 3) There exist marginal critical states.

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Rihei Endou, Komajiro Niizeki, Nobuhisa Fujita. 2003-10-20. Universalities in One-electron Properties of Limit Quasi-periodic Lattices. https://doi.org/10.1088/0305-4470%2F37%2F13%2Fl01

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