Generalized Drude Formula for the Optical Conductivity of Quasicrystals

We derive a generalized Drude formula for the optical conductivity of quasicrystals, assuming a diffusion law in a perfect quasicrystal L(t) approximately t(beta), where L(t) measures the spreading of a wave packet in a time t. We show that the so-called Drude peak in the optical conductivity, characteristic of metals, is strongly modified. If beta<1/2 the Drude peak is even replaced by a dip and the dc conductivity increases when disorder increases. An interpretation of the experimental results on icosahedral and decagonal phases is proposed.