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Quantum Kinetic Theory pp 231–236Cite as

\(*\)Dynamically Screened Ladder Approximation

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Abstract

This chapter contains the most advanced many-body approximation studied in this book—the screened ladder approximation. It combines strong coupling (T-matrix) effects with long-range (dynamical screening) phenomena that were discussed separately in Chaps. 9 and 10, respectively. We present the relevant closure approximation for the BBGKY-hierarchy and the solution for the pair correlation operator and the resulting quantum kinetic equation. We conclude with an alternative idea that allows for an approximate treatment of strong correlations and screening that is due to Gould and DeWitt [301].

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Notes

  1. 1.

    This chapter (as all sections marked with “*") may be skipped on first reading.

  2. 2.

    Recall that the shielded potential contains a Pauli blocking factor, \({\hat{V}}_{ab}=(1\pm F_a\pm F_b)V_{ab}\), see Chap. 3.

  3. 3.

    This approximation is equivalent to the selfconsistent DSLA of Green functions theory where all propagators are renormalized by selfenergies in DSLA, e.g. [31].

  4. 4.

    Since the inhomogeneity in the third hierarchy equation is the same in all approximations for \(\Sigma \), the approximations differ, basically, only in the actual propagators.

  5. 5.

    Notice that this propagator \(U_{12}\) differs from the one used in Chap. 9 by the fact that it obeys a commutator equation. But this equation can be easily transformed into the one used in Chap. 9. The same applies to the Born approximation.

  6. 6.

    A detailed Green functions discussion can be found in [31].

  7. 7.

    It is instructive to consider as an example the equilibrium limit of (11.20) for a non–degenerate plasma, cf. Sect. 56 of [72]. For the distance dependent part, it follows (cf. Sects. 8.3, 9.3.4 and 10.3.2)

    figure a

    where \(V^C\) and \(V^D\) denote the Coulomb and Debye potential, respectively.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Kiel, Kiel, Germany

    Michael Bonitz

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  1. Michael Bonitz
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Correspondence to Michael Bonitz .

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© 2016 Springer International Publishing Switzerland

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Bonitz, M. (2016). \(*\)Dynamically Screened Ladder Approximation. In: Quantum Kinetic Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-24121-0_11

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