Equivalence of the kinetic and drift-velocity approaches to the Hall conductivity in metals

An analysis of semiclassical velocities of the electron wave packets moving in crystals submitted to a constant magnetic field provides us with the result that the Hall conductivity obtained with the aid of the kinetic theory is inversely proportional to the strength of the magnetic field. But the same behaviour of the Hall conductivity is obtained from the drift-velocity approximation on the basis of the property that a product of the electron gyration frequency and the relaxation time entering the tensor of magnetoconductivity becomes a number dependent solely on the metal band structure but independent of the strength of the applied magnetic field.