Zero-frequency anomaly in quasiclassical ac transport:: Memory effects in a two-dimensional metal with a long-range random potential or random magnetic field

We study the low-frequency behavior of the ac conductivity sigma(omega) of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a nonanalytic proportional to \omega \ correction to Re sigma, which corresponds to a 1/t(2) long-time tail in the velocity correlation function. This contribution is induced by return processes neglected in Boltzmann transport theory. The prefactor of this \omega \ term is positive and proportional to (d/l)(2) for the RP, while it is of opposite sign and proportional to d/l in the weak RMF case, where l is the mean free path and d the disorder correlation length. This nonanalytic correction also exists in the strong RMF regime, when the transport is of a percolating nature. The analytical results are supported and complemented by numerical simulations.