In a quasiperiodic system without de
fects the dissipative part o
f the conductivity is expected to vary as
Reσ0(ω)ω1−2β at low
frequency
ω(0<β<1).
β is the di
ffusion exponent in the per
fect structure such that the spreading o
f wavepackets is
L(t)tβ at large time
t. Under certain conditions disorder induces a current relaxation in a time
τ and we express the conductivity, with de
fects, in terms o
f τ and o
f the conductivity without de
fects,
Reσ0(ω). For AlCuFe and AlPdMn quasicrystals a coherent interpretation o
f the conduction properties is obtained. We extract the values o
f τ and get
β0. It means that quantum di
ffusion is slow or marginal in the per
fect systems.