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The Boltzmann Equation in Solid State Physics

  • Ryogo Kubo
Part of the Acta Physica Austriaca book series (FEWBODY, volume 10/1973)

Abstract

The Boltzmann equation has been used successfully in solving a number of problems in solid state physics. This paper presents a historical review of such applications and further a brief review of some recent developments which go beyond the limitations of its applicability. The first use of a Boltzmann equation goes back to Lorentz (1905) who formulated the Drude theory of metallic electrons as a kinetic theory. Sommerfeld (1928) rewrote the Lorentz theory introducing the Fermi statistics. This was immediately followed by the work of Bloch who opened the new era of the quantum theory of solids. The Boltzmann-Bloch equation was a great success to elucidate the problem of metallic conduction. The phonon transport theory was established by Peierls in 1929. Between 1928 and the mid-fifties the progress had been more or less along the line set up by these pioneers. The soil of solid state physics became exceedingly rich after the war mainly because of rapid growth on the experimental side, for example in semiconductor physics. After the mid-fifties, however, there has been a remarkable progress on the theoretical side. Quantum-statistical theories of many-body systems developed various new methods and new concepts, which cover not only many-body systems in thermal equilibrium but also those in non-equilibrium. Thus they necessarily have some connection with the Boltzmann equation approach. They should be able to provide a satisfactory foundation of a Boltzmann equation if it is really to be justified, or they should provide us with a better method to approach reality when a naive kinetic approach is not legitimate. It should be remembered that the gas-like particles in solid states are only quasi-particles representing some sort of excitation modes, which are by no means elementary objects like real gas particles. Thus, we need a more sophisticated approach to understand transport phenomena in a condensed matter like a solid.

Keywords

Boltzmann Equation Collision Term Linear Response Theory Phonon Transport Relaxation Time Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Ryogo Kubo
    • 1
  1. 1.Department of PhysicsUniversity of TokyoJapan

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