Abstract
For pt.II see ibid., vol.10, p.2131 (1977). It is shown that, when a random substitutional alloy has a small carrier density, a large cancellation occurs between two terms of its electrical conductivity in the quantum transport theory. This cancellation must be treated carefully when the reduction of some quantum transport theory to the Boltzmann transport theory is made in the weak-scattering or the dilute limit. It is shown that the quantum transport theory in the coherent-potential approximation is consistent with the Ward identity and a similar identity and that this consistency is essential to obtaining the correct result in that reduction.
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