Quantum Theory of Electrical Transport Phenomena. II

Phys. Rev. 109, 1892 – Published 15 March 1958
J. M. Luttinger and W. Kohn

Abstract

In a previous paper we have developed a theory of electrical transport phenomena for a simple quantum-mechanical model. That treatment was based on an expansion in powers of the strength of the scattering mechanism. In the present paper we consider the same model, but obtain the transport equation in powers of the density of scatterers without restricting ourselves to weak scattering potentials. The expansion involves scattering operators for single centers, pairs of centers, etc., in a manner in many ways analogous to the virial expansion of equilibrium properties. The lowest order terms yield the usual Boltzmann equation. The first correction, in density, to this equation is explicitly given. For the case of spherically symmetric scatterers the solutions of these equations are also obtained.

DOI: http://dx.doi.org/10.1103/PhysRev.109.1892

  • Received 13 September 1957
  • Published in the issue dated March 1958

© 1958 The American Physical Society

Authors & Affiliations

J. M. Luttinger

  • University of Michigan, Ann Arbor, Michigan

W. Kohn

  • Carnegie Institute of Technology, Pittsburgh, Pennsylvania

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