## Exact formulas for the electrical resistivity: heating of an electron gas by an electric field: a long time scale perturbation solution of the Boltzmann equation |

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### Contents

INTRODUCTION TO PART I | 2 |

REVIEW OF THE CONDUCTIVITY AND RESISTIVITY | 6 |

B Derivation of the Resistivity Formula | 13 |

14 other sections not shown

### Common terms and phrases

Appendix assumptions Boltzmann equation boundary conditions Chapter classical system constant energy constant relaxation defined density derive describes the evolution electric field electrical conductivity electrical resistivity electron gas electron's energy equation for f evaluate evolution of f EXACT FORMULAS expand f expansion of f f in powers Fermi distribution Fermi energy harmonic of order initial value integral Joule heating limit of weak linear response theory Liouville equation long time limit long time scale lowest order term Maxwell-Boltzmann distribution mean energy mean velocity momentum scale Ap Note number of electrons obtain one-dimensional system operator perturbation expansion quantum mechanics quantum system random fixed impurities resistivity formula response theory formula scale perturbation solution scale perturbation theory scale solution scattered by random scattering is uniform scattering potential solution for f solved spherical harmonics standard perturbation theory Substituting surfaces of constant thermodynamic limit typical value uniform over surfaces valid weak scattering