Quasiclassical memory effects: anomalous transport properties of two-dimensional electrons and composite fermions subject to a long-range disorder

We have studied the ac response and magnetoresistance of a two-dimensional electron gas in high-mobility samples in the presence of smooth disorder, with emphasis on the composite-fermion description of a half-filled Landau level. We have found that the low-$\omega$ behavior of the ac conductivity $\sigma(\omega)$ is governed by memory effects associated with return processes that are neglected in Boltzmann transport theory: the return-induced correction to $\mathrm{Re}\,\sigma$ exhibits a kink $\propto|\omega|$. It is shown that the non-Markovian quasiclassical kinetics leads to a strong magnetoresistance $\Delta\rho_{xx}$. We argue that the quasiclassical memory effects account for the positive $\Delta\rho_{xx}$ observed at small deviations from half-filling. At a larger deviation, the positive magnetoresistance is followed by a sharp falloff of $\rho_{xx}$.