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The electron--electron scattering does not affect the electrical current inGalilean--invariant systems. We show that nevertheless electron--electroncollisions may contribute to the electric resistivity of systems with parabolicspectrum provided that they have multiply connected Fermi surface and there isan additional mechanism of scattering. To this end, we calculate theresistivity of a two-dimensional electron gas with two filled transversesubbands in a presence of electron--electron and impurity scattering. Thoughthe collisions between the electrons do not directly affect the current in suchsystems, they cause a redistribution of the electrons between the Fermicontours, which results in a noticeable change of resistivity for realisticmechanisms of impurity scattering.

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