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Statistical theory of electron transport in open electron-phonon systems

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  • Möbius, A.
  • Vojta, G.

Abstract

Within the framework of general statistical mechanics of irreversible processes the electrical resistivity of an open electron-phonon system is calculated. By means of the projection operator technique an evolution equation for coupled subsystems in a heat bath is derived and specialized for electrons and longitudinal phonons, the latter being coupled to a bath of transverse phonons. The influence of heating of the electron-phonon system is investigated and the question of validity of the linear response theory with or without inclusion of a dissipative mechanism is discussed. In the balance equation for the total electron momentum, terms of only third (and higher) order in the electrical field strength and the current density appear; consequently, the transverse phonons act only as a “momentum bath”. A general resistivity formula is derived containing the Bloch-Grüneisen law as a special case and including corrections due to phonon drag up to infinite order without a partial summation.

Suggested Citation

  • Möbius, A. & Vojta, G., 1978. "Statistical theory of electron transport in open electron-phonon systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 94(2), pages 321-338.
    • Handle: RePEc:eee:phsmap:v:94:y:1978:i:2:p:321-338
    DOI: 10.1016/0378-4371(78)90102-4
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