Low-frequency anomalies and scaling of the dynamic conductivity in the quantum Hall effect

A numerical study of the dynamic conductivity sigma(xx)(omega) in the lowest Landau level for a quantum Hall system with short-range and long-range disorder potentials is performed. In the latter case two distinct types of low-frequency anomalies are observed: a scaling regime with an anomalous diffusion exponent of eta=0.36+/-0.06 independent of the potential correlation range lambda and a semiclassical regime giving evidence of the existence of long time tails in the velocity correlation decaying proportional to t(-2). The range of validity of this behavior increases with increasing lambda. The universal value of the critical conductivity is sigma(xx)(c)=(0.5+/-0.02)e(2)/h for lambda=0 to 2 magnetic lengths.