We present a rigorous solution of the Boltzmann equation for the electron–phonon scattering problem in three spatial dimensions in the limit of low temperatures. The different temperature scaling of the various scattering rates turns the temperature into a control parameter that is not available in classical kinetic theory and allows for a rigorous proof of Bloch’s T⁵ law. The relation between the Boltzmann equation and the Kubo formula is also discussed, as well as implications for the scattering of electrons by excitations other than phonons.

中文翻译：

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由于电子-声子散射而产生的电导率的严格结果

对于低温范围内的三个空间维度的电子-声子散射问题，我们给出了玻尔兹曼方程的严格解。各种散射速率的不同温度比例将温度变成了经典动力学理论中无法获得的控制参数，并为Bloch的T ⁵定律提供了严格的证明。还讨论了玻耳兹曼方程和久保公式之间的关系，以及除声子以外的其他电子对电子散射的影响。