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Mat. Zametki, 2008, Volume 84, Issue 1, Pages 108–116 (Mi mz5193)  

This article is cited in 9 scientific papers (total in 9 papers)

Detailed Balance, Time Reversal, and Generators of Quantum Markov Semigroups

F. Fagnola, V. Umanita

Politecnico di Milano

Abstract: We characterize generators $\mathscr L$ of norm continuous quantum Markov semigroups satisfying the quantum detailed balance condition with respect to an antiunitary time reversal in terms of the operators $H$ and $L_k$ in the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) representation $\mathscr L(x)=i[H,x]-(1/2)\sum_k(L^*_kL_kx -2L^*_kxL_k+xL^*_kL_k)$.

Keywords: quantum detailed balance, time reversal, quantum Markov semigroup, Lindblad representation, antiunitary operator

DOI: https://doi.org/10.4213/mzm5193

Full text: PDF file (485 kB)
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English version:
Mathematical Notes, 2008, 84:1, 108–115

Bibliographic databases:

UDC: 517.958
Received: 19.10.2007

Citation: F. Fagnola, V. Umanita, “Detailed Balance, Time Reversal, and Generators of Quantum Markov Semigroups”, Mat. Zametki, 84:1 (2008), 108–116; Math. Notes, 84:1 (2008), 108–115

Citation in format AMSBIB
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\by F.~Fagnola, V.~Umanita
\paper Detailed Balance, Time Reversal, and Generators of Quantum Markov Semigroups
\jour Mat. Zametki
\yr 2008
\vol 84
\issue 1
\pages 108--116
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\crossref{https://doi.org/10.4213/mzm5193}
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\jour Math. Notes
\yr 2008
\vol 84
\issue 1
\pages 108--115
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Fagnola F., Umanità V., “Generators of KMS symmetric Markov semigroups on $\mathscr B(h)$ symmetry and quantum detailed balance”, Comm. Math. Phys., 298:2 (2010), 523–547  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Chetrite R., Mallick K., “Quantum fluctuation relations for the Lindblad master equation”, J. Stat. Phys., 148:3 (2012), 480–501  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Fagnola F., Umanita V., “Quantum detailed balance conditions with time reversal: three-level systems”, Stochastics, 84:2-3 (2012), 273–293  crossref  mathscinet  zmath  isi  scopus
    4. Horowitz J.M., Parrondo J.M.R., “Entropy Production Along Nonequilibrium Quantum Jump Trajectories”, New J. Phys., 15 (2013), 085028  crossref  isi  scopus
    5. Bolanos-Servin J.R., Quezada R., “A Cycle Decomposition and Entropy Production for Circulant Quantum Markov Semigroups”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 16:2 (2013), 1350016  crossref  mathscinet  zmath  isi  elib  scopus
    6. Jaksic V., Pillet C.-A., Westrich M., “Entropic Fluctuations of Quantum Dynamical Semigroups”, J. Stat. Phys., 154:1-2 (2014), 153–187  crossref  mathscinet  zmath  isi  scopus
    7. Fagnola F., Rebolledo R., “Entropy Production and Detailed Balance For a Class of Quantum Markoy Semigroups”, Open Syst. Inf. Dyn., 22:3 (2015), 1550013  crossref  mathscinet  zmath  isi  elib  scopus
    8. Kirsanskas G., Franckie M., Wacker A., “Phenomenological Position and Energy Resolving Lindblad Approach to Quantum Kinetics”, Phys. Rev. B, 97:3 (2018), 035432  crossref  isi  scopus
    9. Ramezani M., Benatti F., Floreanini R., Marcantoni S., Golshani M., Rezakhani A.T., “Quantum Detailed Balance Conditions and Fluctuation Relations For Thermalizing Quantum Dynamics”, Phys. Rev. E, 98:5 (2018), 052104  crossref  isi  scopus
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