Geodesic
Solution of Bloch equation in the Weyl representation
Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 2, pp. 314-319

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The Weyl symbol of the operator exponential $\exp\{-\beta[(2\mu)^{-1}\hat{p^2}+V\hat{(q)}]\}$ is regarded as a solution of the Bloch equation in the phase space. The unperturbed equation is separated in accordance with the $\hbar$ expansion of the product of Weyl symbols. The exact solution and Green's function of the unperturbed Bloch equation are found in analytic form. An iterative procedure for constructing the perturbation-theory series is proposed. 
@article{TMF_1991_88_2_a9,
     author = {V. V. Kudryashov},
     title = {Solution of {Bloch} equation in the {Weyl} representation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {314--319},
     publisher = {mathdoc},
     volume = {88},
     number = {2},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_88_2_a9/}
}
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V. V. Kudryashov. Solution of Bloch equation in the Weyl representation. Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 2, pp. 314-319. http://geodesic.mathdoc.fr/item/TMF_1991_88_2_a9/