Some elementary questions in the theory of quasiperiodic heterostructures

The characterization of the spectrum of eigenstates of quasiperiodic heterostructures is discussed by focusing on three questions. Arguments are advanced to justify the often indiscriminate use of different approximants in the calculation of the eigenvalue spectra. It is stressed that the calculation of the fractal dimension may be rather inaccurate if the high eigenvalue range is not included, even if physically the interest is limited to the low range. The question of self-similarity is critically examined and found to have a very limited range of validity in practice. The unique properties of the Rudin-Shapiro sequence are also stressed.