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Symmetries and conserved quantities in Lindblad master equations
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This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations of unitary quantum mechanics, extending the intuition of symmetries and conserved quantities to the dissipative case. We combine and apply various results to obtain an exhaustive characterization of the infinite-time behavior of Lindblad evolution, including both the structure of the infinite-time density matrix and its dependence on initial conditions. The effect of the environment in the infinite-time limit can therefore be tracked exactly for arbitrary state initialization and without knowledge of dynamics at intermediate time. As a consequence, sufficient criteria for determining the steady state of a Lindblad master equation are obtained. These criteria are knowledge of the initial state, a basis for the steady-state subspace, and all conserved quantities. We give examples of two-qubit dissipation and single-mode $d$-photon absorption where all quantities are determined analytically. Applications of these techniques to quantum information, computation, and feedback control are discussed.
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“For many complex problems in quantum mechanics, the Liouville space formalism turns out to be very effective in finding solutions or mathematically characterizing the problem.”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [2]
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“This means that | ρ ( ∞ ) 〉 〉 is a linear combination of those {| ζ k 〉 〉} with Re[ λ k ] = 0 [2, 5, 48].”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [2]
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Cites
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500
On the generators of quantum dynamical semigroups
Lindblad, G. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01608499 · Cited by 7,548
Theory of open quantum systems
Xu, R., & Yan, Y. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1474579 · Cited by 6,622
The Theory of Open Quantum Systems
Breuer, H.-P., & Petruccione, F. (2007) · doi:10.1093/acprof:oso/9780199213900.001.0001 · Cited by 5,938
Decoherence, einselection, and the quantum origins of the classical
Zurek, W. H. (2003) · Reviews of Modern Physics · doi:10.1103/revmodphys.75.715 · Cited by 4,295
Principles of Nuclear Magnetic Resonance in One and Two Dimensions
Ernst, R. R., Bodenhausen, G., Wokaun, A. J., & Redfield, A. G. (1989) · Physics Today · doi:10.1063/1.2811094 · Cited by 4,202
Completely positive dynamical semigroups of N -level systems
Gorini, V., Kossakowski, A., & Sudarshan, E. C. G. (1976) · Journal of Mathematical Physics · doi:10.1063/1.522979 · Cited by 3,998
Quantum Measurement and Control
Wiseman, H. M., & Milburn, G. J. (2009) · Cambridge University Press eBooks · doi:10.1017/cbo9780511813948 · Cited by 2,280
Decoherence-Free Subspaces for Quantum Computation
Lidar, D. A., Chuang, I. L., & Whaley, K. B. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.2594 · Cited by 1,818
Quantum computation and quantum-state engineering driven by dissipation
Verstraete, F., Wolf, M. M., & Ignacio Cirac, J. (2009) · Nature Physics · doi:10.1038/nphys1342 · Cited by 1,570
Research works printed but not linked: 1
- M. Petkovsek, 1997, A=B
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Buča, B., Tindall, J., & Jaksch, D. (2019) · Nature Communications · doi:10.1038/s41467-019-09757-y · Cited by 329
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Variational Neural-Network Ansatz for Steady States in Open Quantum Systems
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Larson, J., & Irish, E. K. T. (2017) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aa65dc · Cited by 121
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Lieu, S., Belyansky, R., Young, J. T., Lundgren, R., Albert, V. V., & Gorshkov, A. V. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.240405 · Cited by 126
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de Groot, C., Turzillo, A., & Schuch, N. (2022) · Quantum · doi:10.22331/q-2022-11-10-856 · Cited by 112
Holonomic Quantum Control with Continuous Variable Systems
Albert, V. V., Shu, C., Krastanov, S., Shen, C., Liu, R., Yang, Z., Schoelkopf, R. J., Mirrahimi, M., Devoret, M., & Jiang, L. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.140502 · Cited by 121
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Candia, R. D., Minganti, F., Petrovnin, K. V., Paraoanu, G. S., & Felicetti, S. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00690-z · Cited by 122
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Azses, D., Haenel, R., Naveh, Y., Raussendorf, R., Sela, E., & Dalla Torre, E. G. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.120502 · Cited by 108
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Li, L., Zou, C., Albert, V. V., Muralidharan, S., Girvin, S. M., & Jiang, L. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.030502 · Cited by 112
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Vitale, V., Elben, A., Kueng, R., Neven, A., Carrasco, J. A., Kraus, B., Zoller, P., Calabrese, P., Vermersch, B., & Dalmonte, M. (2022) · SciPost Physics · doi:10.21468/scipostphys.12.3.106 · Cited by 105
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Altland, A., Fleischhauer, M., & Diehl, S. (2021) · Physical Review X · doi:10.1103/physrevx.11.021037 · Cited by 108
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Liu, J., Segal, D., & Hanna, G. (2019) · The Journal of Physical Chemistry C · doi:10.1021/acs.jpcc.9b06373 · Cited by 100
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Longhi, S. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.201103 · Cited by 92
Qin, W., Miranowicz, A., Jing, H., & Nori, F. (2021) · arXiv (Cornell University) · doi:10.1103/physrevlett.127.093602 · Cited by 88
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Albert, V. V., Mundhada, S., Grimm, A., Touzard, S., Devoret, M., & Jiang, L. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/ab1e69 · Cited by 96
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Manzano, D., & Hurtado, P. I. (2014) · Physical Review B · doi:10.1103/physrevb.90.125138 · Cited by 80
Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
Kawabata, K., Kulkarni, A., Li, J., Numasawa, T., & Ryu, S. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.030328 · Cited by 90
Dissipation-driven quantum phase transitions and symmetry breaking
Hannukainen, J. D., & Larson, J. (2018) · Physical Review A · doi:10.1103/physreva.98.042113 · Cited by 85
Dissipative time crystal in an asymmetric nonlinear photonic dimer
Seibold, K., Rota, R., & Savona, V. (2020) · Physical Review A · doi:10.1103/physreva.101.033839 · Cited by 79
Fundamentals of quantum mechanics in Liouville space
Gyamfi, J. A. (2020) · European Journal of Physics · doi:10.1088/1361-6404/ab9fdd · Cited by 77
Asymptotic Floquet states of open quantum systems: the role of interaction
Hartmann, M., Poletti, D., Ivanchenko, M., Denisov, S., & Peter Hänggi, A. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa7ceb · Cited by 77
Non-stationarity and dissipative time crystals: spectral properties and finite-size effects
Booker, C., Buča, B., & Jaksch, D. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ababc4 · Cited by 80
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Flynn, V. P., Cobanera, E., & Viola, L. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.245701 · Cited by 77
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Nigro, D. (2019) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ab0c1c · Cited by 73
Can, T. (2019) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab4d26 · Cited by 72
Arkhipov, I. I., Miranowicz, A., Minganti, F., & Nori, F. (2020) · Physical Review A · doi:10.1103/physreva.101.013812 · Cited by 69
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Driven Bose-Hubbard dimer under nonlocal dissipation: A bistable time crystal
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Thingna, J., Manzano, D., & Cao, J. (2016) · Scientific Reports · doi:10.1038/srep28027 · Cited by 61
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Symmetries and conserved quantities of boundary time crystals in generalized spin models
Piccitto, G., Wauters, M. M., Nori, F., & Shammah, N. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.014307 · Cited by 57
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Guarnieri, G., Morrone, D., Çakmak, B., Plastina, F., & Campbell, S. (2020) · Physics Letters A · doi:10.1016/j.physleta.2020.126576 · Cited by 55
Metastability in an open quantum Ising model
Rose, D. C., Macieszczak, K., Lesanovsky, I., & Garrahan, J. P. (2016) · Physical review. E · doi:10.1103/physreve.94.052132 · Cited by 59
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Hilbert space fragmentation in open quantum systems
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Beaulieu, G., Minganti, F., Frasca, S., Savona, V., Felicetti, S., Candia, R. D., & Scarlino, P. (2025) · Nature Communications · doi:10.1038/s41467-025-56830-w · Cited by 59
Open quantum generalisation of Hopfield neural networks
Rotondo, P., Marcuzzi, M., Garrahan, J. P., Lesanovsky, I., & Müller, M. (2018) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aaabcb · Cited by 54
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Mittnenzweig, M., & Mielke, A. (2017) · Journal of Statistical Physics · doi:10.1007/s10955-017-1756-4 · Cited by 48
Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver
Lotem, M., Weichselbaum, A., von Delft, J., & Goldstein, M. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043052 · Cited by 48
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Zhou, Y., Yu, X.-D., Wu, C.-W., Li, X.-Q., Zhang, J., Li, W., & Chen, P. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.043036 · Cited by 47
Lieb-Schultz-Mattis Theorem in Open Quantum Systems
Kawabata, K., Sohal, R., & Ryu, S. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.070402 · Cited by 52
Stationary state degeneracy of open quantum systems with non-abelian symmetries
Zhang, Z., Tindall, J., Mur-Petit, J., Jaksch, D., & Buča, B. (2020) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab88e3 · Cited by 47
Quantum behavior of the Duffing oscillator at the dissipative phase transition
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Symmetry-protected topological phases at finite temperature
Viyuela, O., Rivas, A., & Martin-Delgado, M. A. (2015) · 2D Materials · doi:10.1088/2053-1583/2/3/034006 · Cited by 49
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Kawabata, K., Kulkarni, A., Li, J., Numasawa, T., & Ryu, S. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.075110 · Cited by 45
Unconditional preparation of nonclassical states via linear-and-quadratic optomechanics
Brunelli, M., Houhou, O., Moore, D. W., Nunnenkamp, A., Paternostro, M., & Ferraro, A. (2018) · Physical Review A · doi:10.1103/physreva.98.063801 · Cited by 45
Nonlinear semiclassical dynamics of the unbalanced, open Dicke model
Stitely, K. C., Giraldo, A., Krauskopf, B., & Parkins, S. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033131 · Cited by 43
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Kleinherbers, E., Szpak, N., König, J., & Schützhold, R. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.125131 · Cited by 39
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Garbe, L., Wade, P., Minganti, F., Shammah, N., Felicetti, S., & Nori, F. (2020) · Scientific Reports · doi:10.1038/s41598-020-69704-6 · Cited by 38
Dissipative quantum dynamics, phase transitions, and non-Hermitian random matrices
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Metadata
- Authors
- Albert, V. V., & Jiang, L.
- Affiliations
- Yale University (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2014-02-21
- Volume
- 89
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2044042033
- Cited by
- 448
- References
- 117
- Citations by year
- 2026: 56 · 2025: 72 · 2024: 60 · 2023: 44 · 2022: 43 · 2021: 39 · 2020: 49 · 2019: 29 · 2018: 19 · 2017: 11 · 2016: 12 · 2015: 8 · 2014: 6
- FWCI
- 6.14
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (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 › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- Lindblad master equation, steady state, first integrals, quantum symmetries, dissipative quantum systems, quantum feedback control, quantum information
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