Geodesic
On the quasi-classical limit of the quadratic susceptibility
Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 1, pp. 93-104

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For autonomous Hamiltonian systems, the quasi-classical limit ($\hbar\to0$) of the quadratic susceptibility to an external harmonic field is considered. To calculate this limit, the coordinate matrix elements and the quantum transition frequencies are expanded in powers of $\hbar$ up to terms of order $\hbar^2$ based on symmetry relations and sum rules. The quasi-classical limit of the quadratic susceptibility is calculated in terms of classical parameters and can be used to determine the response functions of chaotic systems. 
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     author = {P. V. Elyutin and O. V. Smirnova},
     title = {On the quasi-classical limit of the quadratic susceptibility},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1999_119_1_a7/}
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P. V. Elyutin; O. V. Smirnova. On the quasi-classical limit of the quadratic susceptibility. Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 1, pp. 93-104. http://geodesic.mathdoc.fr/item/TMF_1999_119_1_a7/