Comments on Eigenvalue Problems on the Fibonacci Quasicrystals

Tomonari Dotera

(Proceedings of China-Japan seminars) Quasicrystals,

K. H. Kuo and T. Ninomiya eds. World Scientific (1991), pp.316-323


We review our recent development for electronic problems on the Fibonacci quasicrystal. Our method relies on transfer matrix method in terms of a new set of self-similar polynomials, a quasiperiodic generalization of the Chebyshev polynomials of the first kind. We discuss physical meaning with recourse to the polynomials, which clarifies the relation between the lattice and spectrum.


phase transformations, polymers, quasicrystals, self-assembly, specific heat