Quantum corrections to the conductivity of a two-dimensional disordered system in a strong magnetic field

A system of noninteracting electrons moving in a magnetic field and a field of randomly distributed impurities is considered. An exact expression is obtained for the sum of the series of maximally crossed diagrams; it is valid in an arbitrary magnetic field. It is shown that in the two-dimensional case the relative magnitude of the corrections to the conductivity due to this series reaches 60% in the center of the lower Landau sub-band.