Geodesic
Quadratic Fermionic Dynamics with Dissipation
Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 908-916

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Gaussian solutions of the Cauchy problem for the GKS-L equation (in the Schrödinger picture) with quadratic fermionic generators are obtained. These Gaussian solutions are represented both as exponentials of quadratic forms in fermionic creation-annihilation operators and by their normal symbols. The coefficients of these forms are represented as algebraic functions of matrices.
Keywords: the Gorini–Kossakowski–Sudarshan equation, the Lindblad equation, quantum dissipation, Gaussian states, completely positive quantum dynamics. 
@article{MZM_2017_102_6_a10,
     author = {A. E. Teretenkov},
     title = {Quadratic {Fermionic} {Dynamics} with {Dissipation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {908--916},
     publisher = {mathdoc},
     volume = {102},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a10/}
}
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A. E. Teretenkov. Quadratic Fermionic Dynamics with Dissipation. Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 908-916. http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a10/