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Non-Markovian generalization of the Lindblad theory of open quantum systems
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A systematic approach to the non-Markovian quantum dynamics of open systems is given by the projection operator techniques of nonequilibrium statistical mechanics. Combining these methods with concepts from quantum information theory and from the theory of positive maps, we derive a class of correlated projection superoperators that take into account in an efficient way statistical correlations between the open system and its environment. The result is used to develop a generalization of the Lindblad theory to the regime of highly non-Markovian quantum processes in structured environments.
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“However, large couplings or interactions with lowtemperature reservoirs can lead to strong correlations resulting in long memory times and in a failure of the Markov approximation.”
From Foundations and measures of quantum non-Markovianity (2012) · cites this paper as [17]
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“Moreover, the standard Markov condition (34) alone does not guarantee, in general, that the Markovian master equation provides a reasonable description of the dynamics, a situation which can occur, for example, for finite and/or structured reservoirs [16, 17].”
From Foundations and measures of quantum non-Markovianity (2012) · cites this paper as [17]
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Metadata
- Authors
- Breuer, H.-P.
- Affiliations
- University of Freiburg (DE)
- Corresponding author
- Breuer, Heinz-Peter
- ORCID
- Breuer, Heinz-Peter
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2007-02-15
- Volume
- 75
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2085891404
- Cited by
- 196
- References
- 40
- Citations by year
- 2026: 8 · 2025: 10 · 2024: 8 · 2023: 2 · 2022: 9 · 2021: 11 · 2020: 6 · 2019: 10 · 2018: 3 · 2017: 7 · 2016: 5 · 2015: 7 · 2014: 10 · 2013: 7 · 2012: 16
- FWCI
- 13.87
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- FreiDok plus (Universitätsbibliothek Freiburg) (submittedVersion)
- arXiv (Cornell University)
- 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 Information and Cryptography
- Keywords
- non-Markovian dynamics, open quantum systems, Lindblad master equation, projection operator method, positive maps, system-environment correlations, structured environments, quantum information
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