High frequency conductivity in the quantum Hall regime

\We have measured the complex conductivity sigma (xx) of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that v,, can be scaled to a single function for different frequencies and several transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length xi. Even for large filling factor distances deltav from the critical point we find xi x deltav(-gamma) with a scaling exponent gamma = 2.3.