A random-force correlation formula for electrical resistivity, valid for arbitrary frequencies and external magnetic fields, is derived, and its relation to Kubo's formula (1956) for the conductivity and to the fluctuation-dissipation theorem is demonstrated. Several recent papers presenting similar results are shown to be erroneous, principally because of a failure to distinguish the random force from the total fluctuating force on a particle. The authors explain how those erroneous results were able to give the weak scattering limit of the resistivity correctly, even though they will fail in higher orders.
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Ballentine et al. (1974) studied this question.
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