Quantum Theory of Electrical Transport Phenomena

Phys. Rev. 108, 590 – Published 1 November 1957
W. Kohn and J. M. Luttinger


The usual theories of electrical conductivity suffer from a number of weaknesses. This paper attempts, on the basis of a simple model, to put the theory on as rigorous a basis as possible. A technique is developed which gives the entire density matrix of the system of charge carriers in the steady state. Our model consists of noninteracting free (or Bloch) electrons being scattered by "random" rigid impurity centers. The density matrix is developed in ascending powers of the strength of the scattering potential. The familiar Boltzmann transport equation represents an approximation valid in the limiting cases of very weak or very dilute scatterers. Higher order corrections are given.

DOI: http://dx.doi.org/10.1103/PhysRev.108.590

  • Received 28 March 1957
  • Published in the issue dated November 1957

© 1957 The American Physical Society

Authors & Affiliations

W. Kohn

  • Carnegie Institute of Technology, Pittsburgh, Pennsylvania

J. M. Luttinger

  • The University of Michigan, Ann Arbor, Michigan

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