Quasiperiodic lattice: Electronic properties, phonon properties, and diffusion

Results of a renormalization-group analysis augmented by numerical calculations are presented for the electronic and phonon properties of a one-dimensional quasiperiodic lattice. Qualitative differences in the electronic and phonon band structure are predicted analytically and confirmed numerically. An exactly evaluated wave function shows a power-law behavior. Results of a calculation of the diffusion coefficient are also presented.