Transcription of Boltzmann Transport - Physics Courses
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Boltzmann Transport - Physics Courses
Chapter 1 Boltzmann References H. Smith and H. H. Jensen, Transport Phenomena N. W. Ashcroft and N. D. Mermin,Solid State Physics , chapter 13. P. L. Taylor and O. Heinonen,Condensed Matter Physics , chapter 8. J. M. Ziman, Principles of the Theory of Solids, chapter IntroductionTransport is the phenomenon of currents flowing in response to applied fields. By current we generally mean an electrical currentj, or thermal currentjq. By applied field wegenerally mean an electric fieldEor a temperature gradient T. The currents and fieldsare linearly related, and it will be our goal to calculate the coefficients (known as transportcoefficients) of these linear relations. Implicit in our discussion is the assumption that weare always dealing with systems near 1. Boltzmann Boltzmann Equation in Semiclassical Dynamics and distribution FunctionsThe semiclassical dynamics of a wavepacket in a solid are described by the equationsdrdt=vn(k) =1~ n(k) k( )dkdt= e~E(r,t) e~cvn(k) B(r,t).
2 CHAPTER 1. BOLTZMANN TRANSPORT 1.3 Boltzmann Equation in Solids 1.3.1 Semiclassical Dynamics and Distribution Functions The semiclassical dynamics of a wavepacket in a solid are described by the equations dr dt = v n(k) = 1 ~ @" n(k) @k (1.1) dk dt = e ~ E(r;t) e ~c v n(k) B(r;t) : (1.2) Here, nis the band index and "n(k) is the dispersion ...
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