Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system
Open accessAbstract
We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The system considered includes the damped and undamped Jaynes-Cummings model. The result is obtained by exploiting an expression of quantum maps in terms of matrices and a simple relation between the time evolution map and the time-convolutionless generator as well as the Nakajima-Zwanzig memory kernel. This nonperturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time-dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that, depending on the state of the environment, the operator structures of the two sets of equations of motion can exhibit important differences.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The statistical operator of a quantum system provides different, and generally incompatible, classical probability densities for different observables, as a typical feature of quantum probability with respect to classical probability [41,42].
“on the other hand the statistical operator of a quantum systems provide different, and generally incompatible, classical probability densities for different observables, as a typical feature of quantum probability with respect to classical probability [41, 42].”
From Markovianity and non-Markovianity in quantum and classical systems (2011) · cites this paper as [42]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
The citation lists haven’t been fetched yet
References 44 · Cited by 93
Research works printed but not linked: 1
- E.-M. Laine, J. Piilo, and H.-P. Breuer, e-print arXiv:1004.2184v1. · arXiv
- Authors
- Smirne, A., & Vacchini, B.
- Affiliations
- University of Milan (IT)
- Corresponding author
- Smirne, Andrea
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2010-08-18
- Volume
- 82
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1983511478
- Cited by
- 93
- References
- 44
- Citations by year
- 2026: 8 · 2025: 12 · 2024: 4 · 2023: 7 · 2022: 10 · 2021: 9 · 2020: 6 · 2019: 4 · 2018: 5 · 2017: 4 · 2016: 4 · 2015: 4 · 2014: 2 · 2013: 3 · 2012: 6
- FWCI
- 2.40
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Ministero dell’Istruzione, dell’Università e della Ricerca (PRIN 2008)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- 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 optics and atomic interactions
- Keywords
- Nakajima-Zwanzig equation, time-convolutionless master equation, non-Markovian dynamics, two-level system, bosonic reservoir, Jaynes-Cummings model, quantum maps, memory kernel, reduced dynamics, 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 ›
Are you an author, or do you see a problem with this page? Request a review
