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

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Matematicheskie Zametki, 2008, Volume 84, Issue 1, Pages 108–116
DOI: https://doi.org/10.4213/mzm5193 (Mi mzm5193)

This article is cited in 16 scientific papers (total in 16 papers)

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

F. Fagnola, V. Umanita

Politecnico di Milano

Full-text PDF (485 kB) Citations (16)

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

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.

Received: 19.10.2007

English version:
Mathematical Notes, 2008, Volume 84, Issue 1, Pages 108–115
DOI: https://doi.org/10.1134/S0001434608070092

Bibliographic databases:

UDC: 517.958

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/mzm5193

https://doi.org/10.4213/mzm5193

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This publication is cited in the following 16 articles:

Jinkang Guo, Oliver Hart, Chi-Fang Chen, Aaron J. Friedman, Andrew Lucas, “Designing open quantum systems with known steady states: Davies generators and beyond”, Quantum, 9 (2025), 1612
Dariusz Chruściński, “A Hierarchy of Covariant Generalized Schwarz Maps in M2(ℂ)”, Symmetry, 16:12 (2024), 1655
Chul Ki Ko, Hyun Jae Yoo, “Entropy production of quantum Markov semigroup associated with open quantum walks on the periodic graphs”, Quantum Inf Process, 22:1 (2023)
Wojciech Tarnowski, Dariusz Chruściński, Sergey Denisov, Karol Życzkowski, “Random Lindblad Operators Obeying Detailed Balance”, Open Syst. Inf. Dyn., 30:02 (2023)
Lieu S., McGinley M., Shtanko O., Cooper N.R., Gorshkov V A., “Kramers' Degeneracy For Open Systems in Thermal Equilibrium”, Phys. Rev. B, 105:12 (2022), L121104
Ariane Soret, Vasco Cavina, Massimiliano Esposito, “Thermodynamic consistency of quantum master equations”, Phys. Rev. A, 106:6 (2022)
Bougron J.-F., Bruneau L., “Linear Response Theory and Entropic Fluctuations in Repeated Interaction Quantum Systems”, J. Stat. Phys., 181:5 (2020), 1636–1677
Kirsanskas G., Franckie M., Wacker A., “Phenomenological Position and Energy Resolving Lindblad Approach to Quantum Kinetics”, Phys. Rev. B, 97:3 (2018), 035432
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
Fagnola F., Rebolledo R., “Entropy Production and Detailed Balance For a Class of Quantum Markoy Semigroups”, Open Syst. Inf. Dyn., 22:3 (2015), 1550013
Jaksic V., Pillet C.-A., Westrich M., “Entropic Fluctuations of Quantum Dynamical Semigroups”, J. Stat. Phys., 154:1-2 (2014), 153–187
Horowitz J.M., Parrondo J.M.R., “Entropy Production Along Nonequilibrium Quantum Jump Trajectories”, New J. Phys., 15 (2013), 085028
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
Chetrite R., Mallick K., “Quantum fluctuation relations for the Lindblad master equation”, J. Stat. Phys., 148:3 (2012), 480–501
Fagnola F., Umanita V., “Quantum detailed balance conditions with time reversal: three-level systems”, Stochastics, 84:2-3 (2012), 273–293
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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