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9, 605 (1968). 3. R. Mills, unpublished first, then Propagators for Many-Particle Systems (Gordon and Breach, New York, 1969). 4. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]. 5. -C. -B. -L. Hao, and L. Yu, Phys. Rep. 118, 1 (1985). 6. E. Calzetta and B. L. Hu, Phys. Rev. D 37, 2878 (1988). 7. P. Danielewicz, Ann. Phys. 152, 239 (1984). 8. L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962). 9. S. Fujita, Introduction to Nonequilibrium Quantum Statistical Mechanics (Saunders, Philadelphia, 1966), and papers.

The equilibrium result for time-ordered quantities is well-known (Eq. 30)), Σ(p, ω) = ni V0 + ni d3 q |Vp−q |2 G(q, ω) (2π)3 54 3 Applications where Vk is the Fourier transform of the impurity scattering potential and ni is the density of impurities. Since diagrammatic perturbation theory is formally the same in or out of equilibrium, the relation still holds for the Keldysh contour-ordered functions and the real-time components follow by the usual analytic continuation (which is trivial here since there are no products of contour-ordered quantities): d3 q |Vp−q |2 G<,> (q, ω, R, T ) (2π)3 Σ <,> (p, ω, R, T ) = ni Substituting into the collision term Eq.

16. J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986). ˇ cka, and B. Velick´ 17. P. Lipavsk´ y, V. Spiˇ y, Phys. Rev. B 34, 6933 (1986). 18. D. C. Langreth and J. W. Wilkins, Phys. Rev. B 6, 3189 (1972). 19. D. C. Langreth, in Linear and Nonlinear Electron Transport in Solids (Plenum Press, New York, 1976), vol. 17 of NATO Advanced Study Institute, Series B: Physics, edited by J. T. Devreese and V. E. van Doren. 20. J. M. Luttinger and J. C. Ward, Phys. Rev. 118, 1417 (1960). 21. G. Baym and L.

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