Rigorous results for the electrical conductivity due to electron-phonon scattering
Mathematical Physics
2021-03-17 v1 Statistical Mechanics
math.MP
Abstract
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 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.
Keywords
Cite
@article{arxiv.2001.01148,
title = {Rigorous results for the electrical conductivity due to electron-phonon scattering},
author = {J. Amarel and D. Belitz and T. R. Kirkpatrick},
journal= {arXiv preprint arXiv:2001.01148},
year = {2021}
}
Comments
16pp