Theory of Transport Coefficients. III. Quantum Statistical Systems

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Abstract
The electrical conductivity of an electron‐phonon system is calculated from Kubo's formula using a perturbation method on the assumptions that the coupling is weak, the system is infinitely large, and that the electrons do not interact between them and obey the Fermi‐Dirac statistics and phonons are in thermodynamic equilibrium. The result is identical with that one would obtain from the usually assumed Boltzmann‐Bloch equation. The calculation is a logical extension of the previous treatment I of the present series, where the same problem is treated on the assumption that the electrons obey the Boltzmann statistics. The relation between the present calculation and the derivation of master equation is critically discussed. A brief sketch is given for the calculation of the viscosity coefficient of a dilate quantum statistical gas.