  We consider conductivities of two-dimensional lattice electrons in a magnetic
field. We focus on systems where the flux per plaquette $\phi$ is irrational
(incommensurate flux). To realize the system with the incommensurate flux, we
consider a series of systems with commensurate fluxes which converge to the
irrational value. We have calculated a real part of the longitudinal
conductivity $\sigma_{xx}(\omega)$. Using a scaling analysis, we have found
$\Re\sigma_{xx}(\omega)$ behaves as $1/\omega ^{\gamma}$ \,$(\gamma =0.55)$
when $\phi =\tau,(\tau =\frac{\sqrt{5}-1}{2})$ and the Fermi energy is near
zero. This behavior is closely related to the known scaling behavior of the
spectrum.
