Conductivity of the classical two-dimensional electron gas

We discuss the applicability of the Boltzmann equation to the classical two-dimensional electron gas. We show that in the presence of both electron-impurity and electron-electron scattering an approach which treats the electron-impurity scattering through the scattering integral in the Boltzmann equation can be inapplicable. The correct result for conductivity can be different from the one obtained from the kinetic equation by a logarithmically large factor.