GAP-LABELING PROPERTIES OF THE ENERGY-SPECTRUM FOR THE ON-SITE MODEL OF ONE-DIMENSIONAL FIBONACCI QUASI-LATTICES

We study the gap-labelling properties of the energy spectrum for the o n-site model of one-dimensional Fibonacci quasi-periodic lattices; we have obtained the occupation probabilities on subbands of the hierarch ical energy spectrum and the step heights of the integrated density of states. It is analytically proved that the step height is equal to {m tau}, where the braces denote the fractional part, and m is an integer which can be used to label the corresponding energy gap. Numerical si mulations confirm these results.