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Electron--electron scattering and conductivity of disordered systems with Galilean-invariant spectrum

The electron--electron scattering does not affect the electrical current in Galilean--invariant systems. We show that nevertheless electron--electron collisions may contribute to the electric resistivity of systems with parabolic spectrum provided that they have multiply connected Fermi surface and there is an additional mechanism of scattering. To this end, we calculate the resistivity of a two-dimensional electron gas with two filled transverse subbands in a presence of electron--electron and impurity scattering. Though the collisions between the electrons do not directly affect the current in such systems, they cause a redistribution of the electrons between the Fermi contours, which results in a noticeable change of resistivity for realistic mechanisms of impurity scattering.