Quantum Kinetic Theory by Michael Bonitz

Author:Michael Bonitz
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(9.44)

Gradient expansion of . To evaluate expression (9.44), we need the expansion of which follows from (9.26), and we have, up to first order in ,

(9.45)

If, furthermore, the damping in the propagators is being neglected, we obtain, after Fourier transformation and using (D.22) and (D.23), of Appendix D, the result for the gradient expansion of

(9.46)

where we recall that is the two–particle energy ( denotes the principal value. Finally, we write down the gradient expansion of the binary density operator, up to the first order in the retardation,

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