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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Large couplings or interactions with low-temperature reservoirs can lead to strong correlations resulting in long memory times and in a failure of the Markov approximation.
“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]
The standard Markov condition alone does not guarantee that the Markovian master equation provides a reasonable description of the dynamics.
“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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Cites
On the generators of quantum dynamical semigroups
Lindblad, G. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01608499 · Cited by 7,548 · see citing works
Theory of open quantum systems
Xu, R., & Yan, Y. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1474579 · Cited by 6,622 · see citing works
The Theory of Open Quantum Systems
Breuer, H.-P., & Petruccione, F. (2007) · doi:10.1093/acprof:oso/9780199213900.001.0001 · Cited by 5,938 · see citing works
Self-citationQuantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
Werner, R. F. (1989) · Physical Review A · doi:10.1103/physreva.40.4277 · Cited by 4,062 · see citing works
Completely positive dynamical semigroups of <i>N</i> -level systems
Gorini, V., Kossakowski, A., & Sudarshan, E. C. G. (1976) · Journal of Mathematical Physics · doi:10.1063/1.522979 · Cited by 3,998 · see citing works
Ensemble Method in the Theory of Irreversibility
Zwanzig, R. W. (1960) · The Journal of Chemical Physics · doi:10.1063/1.1731409 · Cited by 2,366 · see citing works
Statistical Physics II: Nonequilibrium Statistical Mechanics
Kubo, R., Toda, M., & Hashitsume, N. (2003) · Cited by 1,500 · see citing works
On Quantum Theory of Transport Phenomena
Nakajima, S. (1958) · Progress of Theoretical Physics · doi:10.1143/ptp.20.948 · Cited by 1,453 · see citing works
Quantum Brownian motion: The functional integral approach
Grabert, H., Schramm, P., & Ingold, G. (1988) · Physics Reports · doi:10.1016/0370-1573(88)90023-3 · Cited by 1,092 · see citing works
Kinetic equations from Hamiltonian dynamics: Markovian limits
Spohn, H. (1980) · Reviews of Modern Physics · doi:10.1103/revmodphys.52.569 · Cited by 1,013 · see citing works
Hu, B. L., Paz, J. P., & Zhang, Y. (1992) · Physical Review D · doi:10.1103/physrevd.45.2843 · Cited by 996 · see citing works
Positive Functions on C ∗ -Algebras
Stinespring, W. F. (1955) · Proceedings of the American Mathematical Society · doi:10.2307/2032342 · Cited by 753 · see citing works
General state changes in quantum theory
Kraus, K. (1971) · Annals of Physics · doi:10.1016/0003-4916(71)90108-4 · Cited by 749 · see citing works
Properties of quantum Markovian master equations
Gorini, V., Frigerio, A., Verri, M., Kossakowski, A., & Sudarshan, E. C. G. (1978) · Reports on Mathematical Physics · doi:10.1016/0034-4877(78)90050-2 · Cited by 468 · see citing works
A generalized stochastic liouville equation. Non-Markovian versus memoryless master equations
Shibata, F., Takahashi, Y., & Hashitsume, N. (1977) · Journal of Statistical Physics · doi:10.1007/bf01040100 · Cited by 467 · see citing works
Strong damping and low-temperature anomalies for the harmonic oscillator
Haake, F., & Reibold, R. (1985) · Physical Review A · doi:10.1103/physreva.32.2462 · Cited by 412 · see citing works
Gemmer, J., Michel, M., & Mahler, G. (2004) · Lecture notes in physics · doi:10.1007/b98082 · Cited by 355 · see citing works
Chaturvedi, S., & Shibata, F. (1979) · The European Physical Journal B · doi:10.1007/bf01319852 · Cited by 307 · see citing works
Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
Breuer, H., Burgarth, D. K., & Petruccione, F. (2004) · Physical Review B · doi:10.1103/physrevb.70.045323 · Cited by 256 · see citing works
Self-citationExpansion Formulas in Nonequilibrium Statistical Mechanics
Shibata, F., & Arimitsu, T. (1980) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.49.891 · Cited by 253 · see citing works
Schliemann, J., Khaetskii, A. V., & Loss, D. (2003) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/15/50/r01 · Cited by 241 · see citing works
(2018) · Physics Subject Headings (PhySH) · doi:10.29172/8e3130c3-9c84-483a-9907-a9d304524b5d · Cited by 194 · see citing works
Non-Markovian dynamics of a qubit
Maniscalco, S., & Petruccione, F. (2006) · Physical Review A · doi:10.1103/physreva.73.012111 · Cited by 188 · see citing works
Completely positive post-Markovian master equation via a measurement approach
Shabani, A., & Lidar, D. A. (2005) · Physical Review A · doi:10.1103/physreva.71.020101 · Cited by 176 · see citing works
Štelmachovič, P., & Bužek, V. (2001) · Physical Review A · doi:10.1103/physreva.64.062106 · Cited by 173 · see citing works
Genuine quantum trajectories for non-Markovian processes
Breuer, H. (2004) · Physical Review A · doi:10.1103/physreva.70.012106 · Cited by 163 · see citing works
Self-citationNon-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging
Breuer, H.-P., Gemmer, J., & Michel, M. (2006) · Physical Review E · doi:10.1103/physreve.73.016139 · Cited by 134 · see citing works
Self-citationBarnett, S. M., & Stenholm, S. (2001) · Physical Review A · doi:10.1103/physreva.64.033808 · Cited by 126 · see citing works
Schliemann, J., Khaetskii, A. V., & Loss, D. (2003) · University of Regensburg Publication Server (University of Regensburg) · doi:10.5283/epub.28264 · Cited by 125 · see citing works
Fourier’s Law from Schrödinger Dynamics
Michel, M., Mahler, G., & Gemmer, J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.180602 · Cited by 106 · see citing works
Stochastic representation of a class of non-Markovian completely positive evolutions
Budini, A. A. (2004) · Physical Review A · doi:10.1103/physreva.69.042107 · Cited by 102 · see citing works
Horodecki, M., Alber, G., & Beth, T. (2001) · Cited by 99 · see citing works
Budini, A. A. (2006) · Physical Review A · doi:10.1103/physreva.74.053815 · Cited by 83 · see citing works
Quantum master equation for a system influencing its environment
Esposito, M., & Gaspard, P. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.68.066112 · Cited by 79 · see citing works
Unified projection operator formalism in nonequilibrium statistical mechanics
Uchiyama, C., & Shibata, F. (1999) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.60.2636 · Cited by 78 · see citing works
Random Lindblad equations from complex environments
Budini, A. A. (2005) · Physical Review E · doi:10.1103/physreve.72.056106 · Cited by 75 · see citing works
Spin relaxation in a complex environment
Esposito, M., & Gaspard, P. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.68.066113 · Cited by 51 · see citing works
Thermalization of quantum systems by finite baths
Gemmer, J., & Michel, M. (2005) · Europhysics Letters (EPL) · doi:10.1209/epl/i2005-10363-0 · Cited by 46 · see citing works
Štelmachovič, P., & Bužek, V. (2003) · Physical Review A · doi:10.1103/physreva.67.029902 · Cited by 45 · see citing works
Royer, A. (2003) · Physics Letters A · doi:10.1016/s0375-9601(03)01052-1 · Cited by 38 · see citing works
Thermalization of quantum systems by finite baths
Gemmer, J. A., & Michel, M. (2005) · CERN Document Server (European Organization for Nuclear Research) · Cited by 33 · see citing works
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Research works printed but not linked: 2
- [12]F. Haake, Statistical Treatment of Open Systems , Springer Tracts in Modern Physics, Vol. 66 (Springer, Berlin, 1973).
- [29]W. F. Stinespring, Proc. Amer. Math. Soc. 6 , 211 (1955).
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Laine, E.-M., Piilo, J., & Breuer, H. (2010) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/92/60010 · Cited by 158 · see citing works
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Riccati equation and the problem of decoherence
Gardas, B. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3442364 · Cited by 14 · see citing works
Arbitrary spin in a spin bath: Exact dynamics and approximation techniques
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Nonequilibrium Quantum Systems: Divergence between Global and Local Descriptions
Manrique, P. D., Rodríguez, F., Quiroga, L., & Johnson, N. F. (2015) · Advances in Condensed Matter Physics · doi:10.1155/2015/615727 · Cited by 14 · see citing works
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Guff, T., Shastry, C. U., & Rocco, A. (2025) · Scientific Reports · doi:10.1038/s41598-025-87323-x · Cited by 13 · see citing works
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Brasil, C. A., de Castro, L. A., & Napolitano, R. D. J. (2011) · Physical Review A · doi:10.1103/physreva.84.022112 · Cited by 13 · see citing works
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Cusumano, S., & Chiara, G. D. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad202a · Cited by 12 · see citing works
Weak-coupling master equation for arbitrary initial conditions
Halimeh, J. C., & de Vega, I. (2017) · Physical Review A · doi:10.1103/physreva.95.052108 · Cited by 12 · see citing works
Adapted projection operator technique for the treatment of initial correlations
Trevisan, A., Smirne, A., Megier, N., & Vacchini, B. (2021) · Physical Review A · doi:10.1103/physreva.104.052215 · Cited by 11 · see citing works
Vacchini, B. (2009) · Lecture notes in physics · doi:10.1007/978-3-642-02871-7_2 · Cited by 11 · see citing works
Pouthier, V. (2010) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/22/38/385401 · Cited by 11 · see citing works
Pouthier, V. (2011) · Physical Review B · doi:10.1103/physrevb.83.085418 · Cited by 11 · see citing works
Non-Markovianity through multipartite correlation measures
de Paula, F. M., Obando, P. C., & Sarandy, M. S. (2016) · Physical Review A · doi:10.1103/physreva.93.042337 · Cited by 11 · see citing works
Head-Marsden, K., & Mazziotti, D. A. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5100143 · Cited by 11 · see citing works
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Self-citationQuantum jumps in non-Markovian single fluorescent systems
Budini, A. A. (2007) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/40/13/012 · Cited by 11 · see citing works
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Structure-Preserving Numerical Schemes for Lindblad Equations
Cao, Y. H., & Lu, J. (2024) · Journal of Scientific Computing · doi:10.1007/s10915-024-02707-x · Cited by 10 · see citing works
- 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 › Computer Science › Artificial Intelligence › 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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