HOPPING CONDUCTIVITY OF THE FIBONACCI-CHAIN QUASI-CRYSTAL

We present an exact calculation of the ac conductivity of a one-dimensional quasicrystal at all frequencies of the driving electric field. Our model is one of electrons tightly bound around identical atomic centers, with both the rates for hopping between adjacent sites and the distances between the sites varying quasiperiodically. The equations governing this system are the Miller-Abrahams equations, which we solve by a real-space renormalization-group method. We present results for the particular case of the "Fibonacci-chain" quasicrystal. Despite the strong similarity between the Miller-Abrahams equations and the equations previously used by other workers to find the electron and phonon spectra of similar systems, our results show none of the self-similar aspects displayed by those spectra. However, our results do corroborate earlier analytical results for the low- and high-frequency forms of the conductivity.