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. 
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/
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[1] F. A. Berezin, Metod vtorichnogo kvantovaniya, Nauka, M., 1986 | MR | Zbl

[2] V. V. Dodonov, V. I. Manko, Invarianty i evolyutsiya nestatsionarnykh kvantovykh sistem, Tr. FIAN, 183, Nauka, M., 1987

[3] A. S. Chirkin, M. Yu. Saigin, “Statistic and information characterization of tripartite entangled states”, J. Russian Laser Research, 28:5 (2007), 505–515 | DOI

[4] T. V. Tlyachev, A. M. Chebotarev, A. S. Chirkin, “Canonical transformations and multipartite coupled parametric processes”, Phys. Scr., T160 (2014), 014041 | DOI

[5] A. S. Kholevo, Kvantovye sistemy, kanaly, informatsiya, MTsNMO, M., 2010

[6] A. E. Teretenkov, “Kvadratichnaya dissipativnaya evolyutsiya gaussovskikh sostoyanii”, Matem. zametki, 100:4 (2016), 636–640 | DOI | MR | Zbl

[7] A. E. Teretenkov, “Quadratic dissipative evolution of Gaussian states with drift”, Math. Notes, 101:2 (2017), 341–351 | DOI | MR | Zbl

[8] L. Accardi, Y. G. Lu, I. V. Volovich, Quantum Theory and Its Stochastic Limit, Springer-Verlag, Berlin, 2002 | MR | Zbl

[9] A. M. Basharov, “A theory of open systems based on stochastic differential equations”, Opt. Spectrosc., 116:4 (2014), 495–503 | DOI

[10] A. S. Trushechkin, “Ob obschem opredelenii proizvodstva entropii v markovskikh otkrytykh kvantovykh sistemakh”, Kvantovye vychisleniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 138, VINITI RAN, M., 2017, 82–98

[11] V. Gorini, A. Kossakowski, E. C. G. Sudarshan, “Completely positive dynamical semigroups of $N$-level systems”, J. Math. Phys., 17:5 (1976), 821–825 | MR

[12] G. Lindblad, “On the generators of quantum dynamical semigroups”, Commun. Math. Phys., 48:2 (1976), 119–130 | MR | Zbl

[13] L. A. Takhtadzhyan, Kvantovaya mekhanika dlya matematikov, RKhD, M.–Izhevsk, 2011

[14] T. Prosen, B. Žunkovič, “Exact solution of Markovian master equations for quadratic Fermi systems: thermal baths, open XY spin chains and non-equilibrium phase transition”, New J. Phys., 12 (2010), 025016 | MR | Zbl

[15] S. R. Clark, J. Prior, M. J. Hartmann, D. Jaksch, M. B. Plenio, “Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain”, New J. Phys., 12 (2010), 025005 | MR | Zbl

[16] R. Alicki, K. Lendi, Quantum Dynamical Semigroups and Applications, Lecture Notes in Phys., 717, Springer-Verlag, Berlin, 2007 | MR | Zbl

[17] E. Greplova, Quantum Information with Fermionic Gaussian States, Master of Science Thesis, 2013 http://www2.mpq.mpg.de/Theorygroup/CIRAC/wiki/images/9/9f/Greplova_Master_thesis_2013.pdf

[18] A. M. Chebotarev, A. E. Teretenkov, “Operatornye ODU i formula Feinmana”, Matem. zametki, 92:6 (2012), 943–948 | DOI | MR | Zbl