Abstract
The basic perturbation theoretic method for dealing with non-equilibrium quantum statistical mechanical problems has been known for years. The theory discussed here evolved from the work of Schwinger and was developed further by Kadanoff and Baym1. In fact virtually all the theory discussed here is contained in Kadanoff’s and Baym’s book. Essentially the same theory was developed independently by Keldysh2 who even anticipates a rather useful addendum by Craig3.
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References
L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics, W. A. Benjamin, Inc., New York, 1962.
L. V. Keldysh, J. Exptl. Theoret. Phys. (U.S.S.R.) 47, 1515 (1964) [English Translation: Soviet Physics JETP 20, 1018 (1965)].
R. A. Craig, J. Math. Phys. 9, 605 (1968).
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See for example D. Pines, The Many-Body Problem, W. A. Benjamin, Inc., New York, 1961, p. 41, Eq. (2.49).
The derivation of the identities given here is taken from D. C. Langreth and J. W. Wilkins, Phys. Rev. 6, 3189 (1972).
R. E. Prange and L. P. Kadanoff 134, A566 (1964).
D. C. Langreth, Phys. Rev. 159, 717 (1967).
D. C. Langreth, D. L. Cowan and J. W. Wilkins, Solid State Commun. 6, 131 (1968);
D. C. Langreth and J. W. Wilkins, Phys. Rev. 6, 3189 (1972)
J. Sweer, D. C. Langreth and J. W. Wilkins, Phys. Rev. (to appear).
This work was reviewed by D. C. Langreth in Nobel Symposia — Medicine and Natural Sciences, Academic Press, New York and London, Vol. 24, p. 210, 1973.
J. T. Yue and S. Doniach, Phys. Rev. B8, 4578 (1973).
T. McMullen and B. Bergersen, Can. J. Phys. 50, 1002 (1972).
P. Nozieres and E. Abrahams, Phys. Rev. B10, 3099 (1974).
For the band case where ε2 p p /2m see D. C. Langreth, Phys. Rev. 148, 707 (1966).
D. C. Langreth, Phys. Rev. Lett. 26, 1229 (1971); see Eq. (8).
J. J. Chang and D. C. Langreth, Phys. Rev. B5, 3512 (1972).
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C. Caroli, D. Lederer-Rozenblatt , B. Roulet and S. Saint-James, Phys. Rev. B8, 4552 (1973).
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Langreth, D.C. (1976). Linear and Nonlinear Response Theory with Applications. In: Devreese, J.T., van Doren, V.E. (eds) Linear and Nonlinear Electron Transport in Solids. NATO Advanced Study Institutes Series, vol 17. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0875-2_1
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