Local versus global master equation with common and separate baths: Superiority of the global approach in partial secular approximation
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Abstract Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, showing that they intrinsically depend on the way we apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born–Markov approximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach.
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In the dressed picture, local baths on each buffer spin become global baths acting collectively on the dressed buffer spins.
“In the dressed picture, the separate baths acting locally on each buffer spins become global baths [102,103] acting collectively on the dressed buffer spins.”
From Quantum Models of Consciousness from a Quantum Information Science Perspective (2025) · cites this paper as [102]
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Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics
Cattaneo, M., Chiara, G. D., Maniscalco, S., Zambrini, R., & Giorgi, G. L. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.130403 · Cited by 100 · see citing works
“…promises to be particularly valuable to deal with the microscopic description of multipartite open systems, where global master equations are needed [59] and one cannot always rely on local descriptions, that may display fundamental differences e.g. from the thermodynamic point of view [60, 61].”
BackgroundMethodTrushechkin, A. S. (2021) · Physical Review A · doi:10.1103/physreva.103.062226 · Cited by 105 · see citing works
Quantum engines and refrigerators
Cangemi, L. M., Bhadra, C., & Levy, A. (2024) · Physics Reports · doi:10.1016/j.physrep.2024.07.001 · Cited by 100 · see citing works
Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths
Tupkary, D., Dhar, A., Kulkarni, M., & Purkayastha, A. (2022) · Physical Review A · doi:10.1103/physreva.105.032208 · Cited by 82 · see citing works
A thermodynamically consistent Markovian master equation beyond the secular approximation
Potts, P. P., Kalaee, A. A. S., & Wacker, A. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac3b2f · Cited by 72 · see citing works
Combining Critical and Quantum Metrology
Hotter, C., Ritsch, H., & Gietka, K. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.060801 · Cited by 66 · see citing works
Quantum thermodynamically consistent local master equations
Hewgill, A., Chiara, G. D., & Imparato, A. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.013165 · Cited by 61 · see citing works
“[52] M.”
BackgroundMpemba Effects in Open Nonequilibrium Quantum Systems
Nava, A. K., & Egger, R. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.136302 · Cited by 65 · see citing works
“(6) only connect states in different parity sectors, {| 0 ⟩ , | d ⟩} ↔ {| 1 ⟩ , | 2 ⟩} .”
Implications of gauge freedom for nonrelativistic quantum electrodynamics
Stokes, A., & Nazir, A. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.045003 · Cited by 62 · see citing works
Superconducting microwave cavities and qubits for quantum information systems
Krasnok, A., Dhakal, P., Fedorov, A., Frigola, P., Kelly, M. J., & Kutsaev, S. (2024) · Applied Physics Reviews · doi:10.1063/5.0155213 · Cited by 62 · see citing works
Many-body open quantum systems
Fazio, R., Keeling, J., Mazza, L., & Schirò, M. (2025) · SciPost Physics Lecture Notes · doi:10.21468/scipostphyslectnotes.99 · Cited by 57 · see citing works
Boosting the performance of small autonomous refrigerators via common environmental effects
Manzano, G., Giorgi, G. L., Fazio, R., & Zambrini, R. (2019) · New Journal of Physics · doi:10.1088/1367-2630/ab5c58 · Cited by 49 · see citing works
“Furthermore, as the coupling among the three qubits is assumed to be weak (g Ei), a local approach can be taken such that the dissipative part of the master equation can be calculated neglecting the interqubit coupling, which would only enter in the coherent part of the evolution [65–69].”
BackgroundMethodLiu, J., & Segal, D. (2021) · Physical review. E · doi:10.1103/physreve.103.032138 · Cited by 50 · see citing works
Quantum Simulation of Dissipative Collective Effects on Noisy Quantum Computers
Cattaneo, M., Rossi, M. A. C., García-Pérez, G., Zambrini, R., & Maniscalco, S. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.010324 · Cited by 51 · see citing works
“(23)] can be derived from a microscopic model with two identical two-level atoms dissipatively coupled in a symmetric way to the same common bath at zero temperature [44].”
BackgroundInfluentialCritical heat current for operating an entanglement engine
Khandelwal, S., Palazzo, N., Brunner, N., & Haack, G. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab9983 · Cited by 46 · see citing works
Dissipation as a resource for Quantum Reservoir Computing
Sannia, A., Martínez‐Peña, R., Soriano, M. C., Giorgi, G. L., & Zambrini, R. (2024) · Quantum · doi:10.22331/q-2024-03-20-1291 · Cited by 46 · see citing works
“…dissipation leading to local losses (i.e. independent losses at each of the N reservoir nodes) modeled by N jump operators We notice that this model adequately accounts for Markovian dissipation in independent baths whenever the interaction between reservoir nodes is weak (for a more accurate…”
BackgroundLocal master equations bypass the secular approximation
Scali, S., Anders, J., & Correa, L. A. (2021) · Quantum · doi:10.22331/q-2021-05-01-451 · Cited by 45 · see citing works
Nonequilibrium thermodynamics of quantum friction
Reiche, D., Intravaia, F., Hsiang, J.-T., Busch, K., & Hu, B. L. (2020) · Physical Review A · doi:10.1103/physreva.102.050203 · Cited by 39 · see citing works
Symmetry and block structure of the Liouvillian superoperator in partial secular approximation
Cattaneo, M., Giorgi, G. L., Maniscalco, S., & Zambrini, R. (2020) · Physical Review A · doi:10.1103/physreva.101.042108 · Cited by 37 · see citing works
Thermodynamics of optical Bloch equations
Elouard, C., Herrera-Martí, D. A., Esposito, M., & Auffèves, A. (2020) · New Journal of Physics · doi:10.1088/1367-2630/abbd6e · Cited by 39 · see citing works
Synchronization and non-Markovianity in open quantum systems
Karpat, G., Yalçınkaya, İ., Çakmak, B., Giorgi, G. L., & Zambrini, R. (2021) · Physical Review A · doi:10.1103/physreva.103.062217 · Cited by 39 · see citing works
“Assuming that the qubit-qubit coupling λ is either larger than the system-bath interaction strength or smaller than the absolute value of the detuning |∆| = |ω1 − ω2|, the open-system dynamics can be described employing a full secular approximation [44].”
BackgroundEngineering Dissipation with Resistive Elements in Circuit Quantum Electrodynamics
Cattaneo, M., & Paraoanu, G. S. (2021) · Advanced Quantum Technologies · doi:10.1002/qute.202100054 · Cited by 38 · see citing works
Heat rectification by two qubits coupled with Dzyaloshinskii-Moriya interaction
Upadhyay, V., Naseem, M. T., Marathe, R., et al. (2021) · Physical review. E · doi:10.1103/physreve.104.054137 · Cited by 35 · see citing works
Open system dynamics from thermodynamic compatibility
Dann, R., & Kosloff, R. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.023006 · Cited by 33 · see citing works
Cattaneo, M., Giorgi, G. L., Maniscalco, S., et al. (2021) · Annalen der Physik · doi:10.1002/andp.202100038 · Cited by 34 · see citing works
Critical heat current for operating an entanglement engine
Khandelwal, S., Palazzo, N., Brunner, N., et al. (2020) · Archive ouverte UNIGE (University of Geneva) · Cited by 31 · see citing works
Local master equations bypass the secular approximation
(16204319), S. S., (19928142), J. A., & Correa, L. A. (2025) · Figshare · Cited by 31 · see citing works
Krasnok, A., & Alù, A. (2022) · ACS Photonics · doi:10.1021/acsphotonics.1c00968 · Cited by 31 · see citing works
D’Abbruzzo, A., & Rossini, D. (2021) · Physical Review A · doi:10.1103/physreva.103.052209 · Cited by 29 · see citing works
“If they do occur, a more general partial secular approximation needs to be invoked [52]: without it, non-physical results may emerge (as the absence of heat transport between different temperature reservoirs—see Ref.”
BackgroundRole of coherence and degeneracies in quantum synchronization
Solanki, P., Jaseem, N., Hajdušek, M., & Vinjanampathy, S. (2022) · Physical Review A · doi:10.1103/physreva.105.l020401 · Cited by 29 · see citing works
Optimal nonequilibrium thermometry in Markovian environments
Sekatski, P., & Perarnau-Llobet, M. (2022) · Quantum · doi:10.22331/q-2022-12-07-869 · Cited by 31 · see citing works
Timofeev, G. M., & Trushechkin, A. S. (2022) · International Journal of Modern Physics A · doi:10.1142/s0217751x22430217 · Cited by 27 · see citing works
“It can be written in the following GKLS-like form [41,42]: ρ̇(t) = −i[HLS, ρ(t)] + ∑”
BackgroundMinimal two-body quantum absorption refrigerator
Bhandari, B., & Jordan, A. N. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.075442 · Cited by 25 · see citing works
Lyapunov equation in open quantum systems and non-Hermitian physics
Purkayastha, A. (2022) · Physical Review A · doi:10.1103/physreva.105.062204 · Cited by 25 · see citing works
Continuous measurement boosted adiabatic quantum thermal machines
Bhandari, B., & Jordan, A. N. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033103 · Cited by 25 · see citing works
“[62] Marco Cattaneo, Gian Luca Giorgi, Sabrina Maniscalco, and Roberta Zambrini, “Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation,” 21, 113045 (2019).”
BackgroundQuantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
Lacerda, A. M., Purkayastha, A., Kewming, M. J., Landi, G. T., & Goold, J. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.195117 · Cited by 25 · see citing works
Transient Synchronization in Open Quantum Systems
Giorgi, G. L., Cabot, A., & Zambrini, R. (2019) · Springer proceedings in physics · doi:10.1007/978-3-030-31146-9_6 · Cited by 23 · see citing works
Going beyond local and global approaches for localized thermal dissipation
Farina, D., Filippis, G. D., Cataudella, V., Polini, M., & Giovannetti, V. (2020) · Physical Review A · doi:10.1103/physreva.102.052208 · Cited by 22 · see citing works
Zarei, M., Bartolo, N., Bertacca, D., Matarrese, S., & Ricciardone, A. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.083508 · Cited by 22 · see citing works
“If there exist values of ω′ and ω in equation (10) being coarse-grained in time as from [4] ∃ t∗ such that ∣∣ω′ − ω∣∣−1 t∗ τS = O(g−2) , (11) then the terms in equation (10) oscillating with frequency ω′ − ω will not give any significant contribution to the system evolution.”
A Brief Journey through Collision Models for Multipartite Open Quantum Dynamics
Cattaneo, M., Giorgi, G. L., Zambrini, R., & Maniscalco, S. (2022) · Open Systems & Information Dynamics · doi:10.1142/s1230161222500159 · Cited by 22 · see citing works
Response theory for nonequilibrium steady states of open quantum systems
Levy, A., Rabani, E., & Limmer, D. T. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.023252 · Cited by 21 · see citing works
Bernardis, D. D., Mercurio, A., & Liberato, S. D. (2024) · Journal of the Optical Society of America B · doi:10.1364/josab.522786 · Cited by 21 · see citing works
“04 have been assumed. master equations [130] explicitly taking these degeneracies account and leading to correct results Although the dressed and the”
Synchronization and coalescence in a dissipative two-qubit system
Cabot, A., Giorgi, G. L., & Zambrini, R. (2021) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2020.0850 · Cited by 20 · see citing works
“Finally, an important remark on the parameter values is that we consider them to follow a hierarchy given by ω0 δ, γ , s12, w and w, δ, s12 ∼ γ , as is the usual requirement for this kind of phenomenological models to have a microscopic origin [19,62], while mutual dependencies between the values of these parameters a…”
BackgroundGerry, M., & Segal, D. (2023) · Physical review. E · doi:10.1103/physreve.107.054115 · Cited by 20 · see citing works
Two-Time Weak-Measurement Protocol for Ergotropy Protection in Open Quantum Batteries
Malavazi, A. H. A., Sagar, R., Ahmadi, B., & Dieguez, P. R. (2025) · PRX Energy · doi:10.1103/bv4w-jr6q · Cited by 19 · see citing works
“We adopt a local master equation derived under standard Born-Markov approximations with a common environment [59, 146].”
Subdiffusive Phases in Open Clean Long-Range Systems
Purkayastha, A., Saha, M., & Agarwalla, B. K. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.240601 · Cited by 18 · see citing works
Operational nonclassicality in minimal autonomous thermal machines
Brask, J. B., Clivaz, F., Haack, G., & Tavakoli, A. (2022) · Quantum · doi:10.22331/q-2022-03-22-672 · Cited by 18 · see citing works
“jump operators acting locally onto each qubit separately [9, 11, 19, 21, 34, 37].”
BackgroundVaaranta, A., Cattaneo, M., & Lake, R. E. (2022) · Physical Review A · doi:10.1103/physreva.106.042605 · Cited by 18 · see citing works
“The derivation of the master equation along with a careful consideration of the secular approximation [35] is discussed in Appendix D.”
BackgroundMethodInfluentialBath-assisted transport in a three-site spin chain: Global versus local approach
Benatti, F., Roberto Floreanini, B., & Memarzadeh, L. (2020) · Physical Review A · doi:10.1103/physreva.102.042219 · Cited by 17 · see citing works
Local master equations may fail to describe dissipative critical behavior
Konopik, M., & Lutz, E. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.013171 · Cited by 18 · see citing works
Unique Steady-State Squeezing in a Driven Quantum Rabi Model
Gietka, K., Hotter, C., & Ritsch, H. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.223604 · Cited by 17 · see citing works
Harnessing coherence generation for precision single- and two-qubit quantum thermometry
Aiache, Y., Allati, A. E., & Anouz, K. E. (2024) · Physical Review A · doi:10.1103/physreva.110.032605 · Cited by 17 · see citing works
“According to references [35, 36], the local master equations remain valid when the connection between subsystems is weak.”
Validity of Born-Markov master equations for single- and two-qubit systems
Vadimov, V., Tuorila, J., Orell, T., Stockburger, J. T., Ala-Nissilä, T., Ankerhold, J., & Möttönen, M. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.214308 · Cited by 17 · see citing works
Steady state entanglement of distant nitrogen-vacancy centers in a coherent thermal magnon bath
Ullah, K., Köse, E., Yagan, R., et al. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023221 · Cited by 15 · see citing works
“In a more rigorous partial secular approximation, some time dependent terms are kept in such a way that the dynamical hierarchy of dissipation terms are respected [81].”
BackgroundBettmann, L. P., Kewming, M. J., & Goold, J. (2023) · Physical review. E · doi:10.1103/physreve.107.044102 · Cited by 15 · see citing works
Sudden death of entanglement induced by a minimal thermal environment
Deçordi, G. L., & Vidiella-Barranco, A. (2020) · Optics Communications · doi:10.1016/j.optcom.2020.126233 · Cited by 15 · see citing works
Quantum-enhanced performance in superconducting Andreev reflection engines
Manzano, G., & López, R. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.043041 · Cited by 14 · see citing works
Blasi, G., Khandelwal, S., & Haack, G. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.043091 · Cited by 14 · see citing works
Detuning effects for heat-current control in quantum thermal devices
Malavazi, A. H. A., Ahmadi, B., Mazurek, P., & Mandarino, A. (2024) · Physical review. E · doi:10.1103/physreve.109.064146 · Cited by 13 · see citing works
“The equation of motion of the system was obtained under the usual assumptions for deriving a global master equation, which provides the appropriate formalism for considering strong internal couplings [52, 54, 74].”
MethodDephasing-assisted entanglement in a system of strongly coupled qubits
Vovcenko, I. V., Shishkov, V. Y., & Andrianov, E. S. (2021) · Optics Express · doi:10.1364/oe.417294 · Cited by 13 · see citing works
Ultrasensitive Calorimetric Detection of Single Photons from Qubit Decay
Pekola, J. P., & Karimi, B. (2022) · Physical Review X · doi:10.1103/physrevx.12.011026 · Cited by 13 · see citing works
“[49] Marco Cattaneo, Gian Luca Giorgi, Sabrina Maniscalco,”
BackgroundQuantum Models of Consciousness from a Quantum Information Science Perspective
Gassab, L., Pusuluk, O., Cattaneo, M., & Müstecaplıoğlu, Ö. E. (2025) · Entropy · doi:10.3390/e27030243 · Cited by 14 · see citing works
“In the dressed picture, the separate baths acting locally on each buffer spins become global baths [102, 103] acting collectively on the dressed buffer spins.”
Learning the best nanoscale heat engines through evolving network topology
Ashida, Y., & Sagawa, T. (2021) · Communications Physics · doi:10.1038/s42005-021-00553-z · Cited by 12 · see citing works
Winczewski, M., Mandarino, A., Suárez, G., Alicki, R., & Horodecki, M. (2024) · Physical review. E · doi:10.1103/physreve.110.024110 · Cited by 16 · see citing works
Vovchenko, I. V., Shishkov, V. Y., Zyablovsky, A. A., & Andrianov, E. S. (2021) · Journal of Experimental and Theoretical Physics Letters · doi:10.1134/s0021364021130099 · Cited by 12 · see citing works
Exact Steady State of the Open X X -Spin Chain: Entanglement and Transport Properties
Benatti, F., Roberto Floreanini, B., & Memarzadeh, L. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.030344 · Cited by 12 · see citing works
Dicke superradiant heat current enhancement in circuit quantum electrodynamics
Andolina, G. M., Erdman, P. A., Noé, F., Pekola, J. P., & Schirò, M. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.043128 · Cited by 11 · see citing works
Environment-assisted strong coupling regime
Sergeev, T. T., Vovchenko, I. V., Zyablovsky, A. A., & Andrianov, E. S. (2022) · Quantum · doi:10.22331/q-2022-04-13-684 · Cited by 11 · see citing works
“(39) This approximation is called semisecular [83].”
Quantum Mpemba effect in dissipative spin chains at criticality
Wei, Z., Xu, M., Jiang, X.-P., et al. (2026) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-025-2878-4 · Cited by 10 · see citing works
Sequential-measurement thermometry with quantum many-body probes
Yang, Y., Montenegro, V., & Bayat, A. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.22.024069 · Cited by 10 · see citing works
Microscopic and phenomenological models of driven systems in structured reservoirs
Giorgi, G. L., Saharyan, A., Guérin, S., Sugny, D., & Bellomo, B. (2020) · Physical Review A · doi:10.1103/physreva.101.012122 · Cited by 10 · see citing works
Engineered common environmental effects on multitransistor systems
Ekanayake, U. N., Gunapala, S. D., & Premaratne, M. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.075440 · Cited by 10 · see citing works
Quantum thermal diode dominated by pure classical correlation via three triangular-coupled qubits
Yang, Y., Liu, Y., & Yu, C. (2023) · Physical review. E · doi:10.1103/physreve.107.064125 · Cited by 10 · see citing works
Dorn, G., Arrigoni, E., & von der Linden, W. (2020) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/abd736 · Cited by 10 · see citing works
Nefedkin, N. E., Alù, A., & Krasnok, A. (2021) · Advanced Quantum Technologies · doi:10.1002/qute.202000121 · Cited by 10 · see citing works
Topological signatures in a weakly dissipative Kitaev chain of finite length
D’Abbruzzo, A., & Rossini, D. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.115139 · Cited by 10 · see citing works
Enhanced thermal rectification in coupled qutrit–qubit quantum thermal diode
Rajapaksha, A., Gunapala, S. D., & Premaratne, M. (2024) · APL Quantum · doi:10.1063/5.0237842 · Cited by 10 · see citing works
Yang, Y., Liu, Y., & Yu, C. (2022) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ac8bb4 · Cited by 9 · see citing works
Time dependent Markovian master equation beyond the adiabatic limit
Meglio, G. D., Plenio, M. B., & Huelga, S. F. (2024) · Quantum · doi:10.22331/q-2024-11-21-1534 · Cited by 10 · see citing works
Coupling of two autonomous quantum refrigerators: Collective and relative performances
Chakour, M. H. B. A., Allati, A. E., & Hassouni, Y. (2022) · Physics Letters A · doi:10.1016/j.physleta.2022.128410 · Cited by 9 · see citing works
Magazzù, L., Paladino, E., & Grifoni, M. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.085419 · Cited by 8 · see citing works
“(42) splits into the set of equations Within this partial secular approximation [38, 83–85], the surviving coherences at the steady state are those associated to the sub-spaces defined by the indices n, m of the small transition frequencies.”
BackgroundPotential renormalisation, Lamb shift and mean-force Gibbs state – to shift or not to shift?
Correa, L. A., & Glatthard, J. (2025) · Quantum · doi:10.22331/q-2025-09-30-1868 · Cited by 10 · see citing works
“[18, 27, 32]), where the Hamiltonian correction › ∆H is › ∆H =− i 2 ∫ ∞”
A multifunctional quantum thermal device: With and without inner coupling
Huangfu, Y., Qi, S.-F., & Jing, J. (2021) · Physics Letters A · doi:10.1016/j.physleta.2021.127172 · Cited by 8 · see citing works
Strain-spectroscopy of strongly interacting defects in superconducting qubits
Santos-Sánchez, O. D. L., & Román-Ancheyta, R. (2021) · Superconductor Science and Technology · doi:10.1088/1361-6668/ac4150 · Cited by 8 · see citing works
“Customarily, one would describe the system’s open dynamics under study by establishing a fitting local [42], or global [43], master equation.”
Exploring quantum synchronization with a composite two-qubit oscillator
Vaidya, G. M., Mamgain, A., Hawaldar, S., Hahn, W., Kaubruegger, R., Suri, B., & Shankar, A. (2024) · Physical Review A · doi:10.1103/physreva.109.033718 · Cited by 8 · see citing works
“Writing the spectral decomposition ˆ ρ u = 4 j =1 λ j | λ j ⟩ ⟨ λ j | , the global U (1) symmetry implies that each | λ j ⟩ is an eigenstate of the operator ˆ S z = ˆ S zA + ˆ S zB .”
BackgroundInfluentialSemi-empirical Haken–Strobl model for molecular spin qubits
Aruachan, K., Colón, Y. J., Aravena, D., et al. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acf2bd · Cited by 7 · see citing works
Does canonical quantization lead to GKSL dynamics?
Tomoi Koide, C., & Nicacio, F. (2023) · Physics Letters A · doi:10.1016/j.physleta.2023.129277 · Cited by 7 · see citing works
Dynamics of the nonequilibrium spin-boson model: A benchmark of master equations and their validity
Suárez, G., Łobejko, M., & Horodecki, M. (2024) · Physical Review A · doi:10.1103/physreva.110.042428 · Cited by 7 · see citing works
“…equation being a CPTP map make it a good alternative to simulate open quantum systems in the weak coupling regime, specially with respect to the several efforts to make the Bloch-Redfield equation completely positive [28–30] From this section forward all simulations shown in plots have ρ (0) = 0 .”
MethodDynamics of Microscale and Nanoscale Systems in the Weak-Memory Regime
Brandner, K. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.037101 · Cited by 7 · see citing works
Geometry-based circulation of local thermal current in quantum harmonic and Bose-Hubbard systems
Dugar, P., & Chien, C.-C. (2022) · Physical review. E · doi:10.1103/physreve.105.064111 · Cited by 7 · see citing works
Thermodynamics of the Coarse-Graining Master Equation
Schaller, G., & Ablaßmayer, J. (2020) · Entropy · doi:10.3390/e22050525 · Cited by 8 · see citing works
Leveraging Collective Effects for Thermometry in Waveguide Quantum Electrodynamics
Sharafiev, A., Juan, M. L., Cattaneo, M., & Kirchmair, G. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.213602 · Cited by 6 · see citing works
“Then, we can introduce the lowering operators: j +1 ,j are the jump operators [17, 46] of the local master equation, respectively associated with the jump frequencies ω ( α ) j and − ω ( α ) j .”
InfluentialQuantum consensus dynamics by entangling Maxwell demon
Ryu, S., López, R., & Toral, R. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac57ea · Cited by 6 · see citing works
“The bit-flip noise can be realized when (a) each qubit observable Xi is weakly coupled to the bosonic bath [38], and (b) the interaction between the qubits is weak J Γflip [4].”
BackgroundParticle and thermal transport through one dimensional topological systems via Lindblad formalism
He, Y., & Chien, C.-C. (2023) · Physics Letters A · doi:10.1016/j.physleta.2023.128826 · Cited by 6 · see citing works
Angeletti, J., Zippilli, S., & Vitali, D. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/acd4e3 · Cited by 6 · see citing works
Vovchenko, I. V., Zyablovsky, A. A., Pukhov, A. A., & Andrianov, E. S. (2023) · Journal of the Optical Society of America B · doi:10.1364/josab.499439 · Cited by 6 · see citing works
Effect of Inter-System Coupling on Heat Transport in a Microscopic Collision Model
Tian, F., Zou, J., Li, L., Li, H., & Shao, B. (2021) · Entropy · doi:10.3390/e23040471 · Cited by 6 · see citing works
“For two coupled qubits interacting with common and separate baths, it was shown that the global approach with partial secular rather than full secular approximation always provides the most accurate choice for the master equation [24].”
Background
- Authors
- Cattaneo, M., Giorgi, G. L., Maniscalco, S., & Zambrini, R.
- Affiliations
- Consejo Superior de Investigaciones Científicas (ES)
- University of Turku (FI)
- Corresponding author
- Cattaneo, Marco
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2019-11-01
- Volume
- 21
- Issue
- 11
- Pages
- 113045
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2952234744
- Semantic Scholar
- 28c3c80a750a8d571ed3e459850f32da0a76ce16
- Cited by
- 169
- References
- 105
- Citations by year
- 2026: 14 · 2025: 31 · 2024: 30 · 2023: 19 · 2022: 28 · 2021: 33 · 2020: 12 · 2019: 2
- FWCI
- 8.46
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- New Journal of Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (acceptedVersion)
- Aaltodoc (Aalto University) (submittedVersion, cc-by)
- UTUPub (University of Turku) (submittedVersion)
- UTUPub (University of Turku) (submittedVersion, cc-by)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Ministerio de Econom??a y Competitividad
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- coupled qubits, Born-Markov approximation, Markovian dynamics, pure dephasing, energy dissipation, entanglement dynamics, spontaneous synchronization, open quantum systems
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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