Anomalous Electrical Conduction in Quasicrystals and Fibonacci Lattices

It is shown in perturbation theory that if a dc current is set up in a quasicrystal (or Fibonacci lattice), and then the electric field turned off, the current will decay slowly to zero with an anomalous logarithmic dependence on time. This is most likely due to the extremely long-wavelength Fourier components possessed by a quasiperiodic potential. The calculated electrical conductivity approaches infinity as (frequency)^-1.