Geodesic
Diagrammatic technique for calculating nonlinear susceptibilities
Teoretičeskaâ i matematičeskaâ fizika, Tome 20 (1974) no. 2, pp. 265-273

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Rules of a diagrammatic technique are formulated for calculating quadratic susceptibilities at $T=0$ and $T\not=0$. When $T\not=0$, the nonlinear susceptibilities are obtained by analytic continuation of the Matsubara function $K^c(\omega_{n_1},\omega_{n_2})$. Analytic continuation with respect to two frequencies can be made in each diagram as in [1]. Rules of the diagrammatic technique are also formulated for the double spectral densities, which determine all possible constructions of three pairs of operators: three-particle correlation functions, cross sections of three-quantum processes, nonlinear susceptibilities, etc. Unitarity relations for the double spectral densities are obtained. 
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     author = {V. Ya. Demikhovskii and A. P. Kopasov},
     title = {Diagrammatic technique for calculating nonlinear susceptibilities},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {265--273},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a11/}
}
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V. Ya. Demikhovskii; A. P. Kopasov. Diagrammatic technique for calculating nonlinear susceptibilities. Teoretičeskaâ i matematičeskaâ fizika, Tome 20 (1974) no. 2, pp. 265-273. http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a11/