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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, 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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“…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].”
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Metadata
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › 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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