Non-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging
Open accessAbstract
The time-convolutionless (TCL) projection operator technique allows a systematic analysis of the non-Markovian quantum dynamics of open systems. We present a class of projection superoperators that project the states of the total system onto certain correlated system-environment states. It is shown that the application of the TCL technique to this class of correlated superoperators enables the nonperturbative treatment of the dynamics of system-environment models for which the standard approach fails in any finite order of the coupling strength. We demonstrate further that the correlated superoperators correspond to the idea of a best guess of conditional quantum expectations, which is determined by a suitable Hilbert-space average. The general approach is illustrated by means of the model of a spin that interacts through randomly distributed couplings with a finite reservoir consisting of two energy bands. Extensive numerical simulations of the full Schrödinger equation of the model reveal the power and efficiency of the method.
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?
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 [16]
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 [16]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
<i>Quantum Computation and Quantum Information</i>
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895 · see citing works
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,449 · see citing works
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
(2012) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789814374927 · Cited by 2,499 · 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 2,405 · see citing works
Walls, D. F., & Milburn, G. J. (1994) · Springer eBooks · doi:10.1007/978-3-642-79504-6 · Cited by 2,197 · see citing works
Semiconductor Spintronics and Quantum Computation
Awschalom, D. D., Loss, D., & Samarth, N. (2002) · Nanoscience and technology · doi:10.1007/978-3-662-05003-3 · Cited by 1,613 · 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 1,469 · see citing works
Weiß, U. (1999) · Series in modern condensed matter physics · doi:10.1142/4239 · Cited by 1,407 · see citing works
Decoherence and the Appearance of a Classical World in Quantum Theory
Giulini, D., Joos, E., Kiefer, C., Kupsch, J., Stamatescu, I.-O., & Zeh, H. D. (1996) · Springer eBooks · doi:10.1007/978-3-662-03263-3 · Cited by 1,106 · see citing works
Stochastic Liouville Equations
Kubo, R. (1963) · Journal of Mathematical Physics · doi:10.1063/1.1703941 · Cited by 1,019 · 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
Braginsky, V. B., Khalili, F. Y., & Thorne, K. S. (1992) · Cambridge University Press eBooks · doi:10.1017/cbo9780511622748 · Cited by 825 · see citing works
Projection Operator Techniques in Nonequilibrium Statistical Mechanics
Grabert, H. (1982) · Springer tracts in modern physics · doi:10.1007/bfb0044591 · Cited by 531 · see citing works
Nonperturbative decay of an atomic system in a cavity
Garraway, B. M. (1997) · Physical Review A · doi:10.1103/physreva.55.2290 · Cited by 518 · 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
Gemmer, J., Michel, M., & Mahler, G. (2004) · Lecture notes in physics · doi:10.1007/b98082 · Cited by 355 · see citing works
Self-citationA cumulant expansion for stochastic linear differential equations. I
van Kampen, N. G. (1974) · Physica · doi:10.1016/0031-8914(74)90121-9 · Cited by 348 · see citing works
Stochastic wave-function method for non-Markovian quantum master equations
Breuer, H., Kappler, B., & Petruccione, F. (1999) · Physical Review A · doi:10.1103/physreva.59.1633 · Cited by 322 · see citing works
Self-citationChaturvedi, 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
Stochastic wave-function approach to non-Markovian systems
Imamog¯lu, A. (1994) · Physical Review A · doi:10.1103/physreva.50.3650 · Cited by 215 · see citing works
A cumulant expansion for stochastic linear differential equations. II
van Kampen, N. G. (1974) · Physica · doi:10.1016/0031-8914(74)90122-0 · Cited by 214 · see citing works
(2018) · Physics Subject Headings (PhySH) · doi:10.29172/8e3130c3-9c84-483a-9907-a9d304524b5d · Cited by 194 · see citing works
Decay of an atom coupled strongly to a reservoir
Garraway, B. M. (1997) · Physical Review A · doi:10.1103/physreva.55.4636 · Cited by 188 · see citing works
Breuer, H., Kappler, B., & Petruccione, F. (2001) · Annals of Physics · doi:10.1006/aphy.2001.6152 · Cited by 179 · see citing works
Self-citationCompletely 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
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-citationQuantum approach to a derivation of the second law of thermodynamics.
Gemmer, J., Otte, A., & Mahler, G. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.1927 · Cited by 100 · see citing works
Self-citationHorodecki, M., Alber, G., & Beth, T. (2001) · Cited by 99 · see citing works
Cumulant Expansions and Pressure Broadening as an Example of Relaxation
Royer, A. (1972) · Physical Review A · doi:10.1103/physreva.6.1741 · Cited by 97 · see citing works
Gemmer, J., & Mahler, G. (2002) · The European Physical Journal B · doi:10.1140/epjb/e2003-00029-3 · Cited by 81 · see citing works
Self-citationQuantum 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
Chang, T.-M., & Skinner, J. L. (1993) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(93)90489-q · Cited by 52 · see citing works
Gemmer, J., & Mahler, G. (2002) · CERN Document Server (European Organization for Nuclear Research) · Cited by 52 · see citing works
Self-citationThermalization 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
Self-citationRoyer, A. (2003) · Physics Letters A · doi:10.1016/s0375-9601(03)01052-1 · Cited by 39 · see citing works
Decoherence and the Appearance of a Classical World in Quantum Theory, second edition
Joos, E., Zeh, H. D., Kiefer, C., Giulini, D., Kupsch, J., & Stamatescu, I. O. (2003) · Cited by 39 · 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
Self-citationFrom pure Schrödingerian to statistical dynamics
Jochen Gemmer, B., & Mathias Michel, A. (2005) · Physica E Low-dimensional Systems and Nanostructures · doi:10.1016/j.physe.2005.05.011 · Cited by 21 · see citing works
Memory effects in the spin relaxation within and without rotating wave approximation
Blanga, L. D., & Despósito, M. A. (1996) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(95)00472-6 · Cited by 11 · see citing works
Non-Markovian spectral broadening in interacting continuous-wave atom lasers
Breuer, H., Faller, D., Kappler, B., & Petruccione, F. (2001) · Europhysics Letters (EPL) · doi:10.1209/epl/i2001-00222-0 · Cited by 11 · see citing works
Self-citation
Flagged first, then by citations
1 of the 51 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Dynamics of non-Markovian open quantum systems
de Vega, I., & Alonso, D. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.015001 · Cited by 1,227 · see citing works
Entanglement and the foundations of statistical mechanics
Popescu, S., Short, A. J., & Winter, A. (2006) · Nature Physics · doi:10.1038/nphys444 · Cited by 1,058 · see citing works
Foundations and measures of quantum non-Markovianity
Breuer, H.-P. (2012) · Journal of Physics B: Atomic, Molecular and Optical Physics · doi:10.1088/0953-4075/45/15/154001 · Cited by 225 · see citing works
Self-citationNon-Markovian generalization of the Lindblad theory of open quantum systems
Breuer, H.-P. (2007) · Physical Review A · doi:10.1103/physreva.75.022103 · Cited by 196 · see citing works
Self-citationDynamical Typicality of Quantum Expectation Values
Bartsch, C., & Jochen Gemmer, B. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.110403 · Cited by 182 · see citing works
Exact master equations for the non-Markovian decay of a qubit
Vacchini, B., & Breuer, H. (2010) · Physical Review A · doi:10.1103/physreva.81.042103 · Cited by 148 · see citing works
Self-citationFlindt, C., Novotný, T., Braggio, A., & Jauho, A. (2010) · Physical Review B · doi:10.1103/physrevb.82.155407 · Cited by 138 · see citing works
Quantum linear Boltzmann equation
Vacchini, B., & Hornberger, K. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.06.001 · Cited by 133 · see citing works
Breuer, H.-P., & Vacchini, B. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.140402 · Cited by 126 · see citing works
Self-citationEnhancement of low-temperature thermometry by strong coupling
Correa, L. A., Perarnau-Llobet, M., Hovhannisyan, K. V., Hernández-Santana, S., Mehboudi, M., & Sanpera, A. (2017) · Physical Review A · doi:10.1103/physreva.96.062103 · Cited by 104 · see citing works
Smirne, A., & Vacchini, B. (2010) · Physical Review A · doi:10.1103/physreva.82.022110 · Cited by 93 · see citing works
Structure of completely positive quantum master equations with memory kernel
Breuer, H., & Vacchini, B. (2009) · Physical Review E · doi:10.1103/physreve.79.041147 · Cited by 90 · see citing works
Self-citationBudini, A. A. (2006) · Physical Review A · doi:10.1103/physreva.74.053815 · Cited by 83 · see citing works
Correlated projection operator approach to non-Markovian dynamics in spin baths
Fischer, J., & Breuer, H. (2007) · Physical Review A · doi:10.1103/physreva.76.052119 · Cited by 77 · see citing works
Self-citationNon-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
Ferraro, E., Breuer, H.-P., Napoli, A., Jivulescu, M. A., & Messina, A. (2008) · Physical Review B · doi:10.1103/physrevb.78.064309 · Cited by 75 · see citing works
Self-citationInternal dissipation and heat leaks in quantum thermodynamic cycles
Correa, L. A., Palao, J. P., & Alonso, D. (2015) · Physical Review E · doi:10.1103/physreve.92.032136 · Cited by 56 · see citing works
Quantum Systems Correlated with a Finite Bath: Nonequilibrium Dynamics and Thermodynamics
Riera-Campeny, A., Sanpera, A., & Strasberg, P. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010340 · Cited by 48 · see citing works
Quantum dephasing induced by non-Markovian random telegraph noise
Cai, X. (2020) · Scientific Reports · doi:10.1038/s41598-019-57081-8 · Cited by 48 · see citing works
Non-Markovian dynamics for bipartite systems
Vacchini, B. (2008) · Physical Review A · doi:10.1103/physreva.78.022112 · Cited by 40 · see citing works
Quantum discord and non-Markovianity of quantum dynamics
Alipour, S., Mani, A., & Rezakhani, A. T. (2012) · Physical Review A · doi:10.1103/physreva.85.052108 · Cited by 37 · see citing works
On the Structure of Generators for Non-Markovian Master Equations
Kossakowski, A., & Rebolledo, R. (2009) · Open Systems & Information Dynamics · doi:10.1142/s1230161209000190 · Cited by 38 · see citing works
Occurrence of exponential relaxation in closed quantum systems
Bartsch, C., Steinigeweg, R., & Jochen Gemmer, B. (2008) · Physical Review E · doi:10.1103/physreve.77.011119 · Cited by 38 · see citing works
On non-Markovian Time Evolution in Open Quantum Systems
Kossakowski, A., & Rebolledo, R. (2007) · Open Systems & Information Dynamics · doi:10.1007/s11080-007-9051-5 · Cited by 37 · see citing works
Correlation-picture approach to open-quantum-system dynamics
(9646973), S. A., (9646976), A. R., (9646979), A. B., (9646982), K. M., (9646985), M. M., & (3814327), T. A.-N. (2020) · Aaltodoc (Aalto University) · Cited by 36 · see citing works
Correlation-Picture Approach to Open-Quantum-System Dynamics
Alipour, S., Rezakhani, A. T., Babu, A. P., Mølmer, K., Möttönen, M., & Ala-Nissila, T. (2020) · Physical Review X · doi:10.1103/physrevx.10.041024 · Cited by 33 · see citing works
Stochastic wave-function unraveling of the generalized Lindblad master equation
Moodley, M., & Petruccione, F. (2009) · Physical Review A · doi:10.1103/physreva.79.042103 · Cited by 33 · see citing works
Non-Markovian nonstationary completely positive open-quantum-system dynamics
Budini, A. A., & Paolo Grigolini, A. (2009) · Physical Review A · doi:10.1103/physreva.80.022103 · Cited by 33 · see citing works
Some Trends in Quantum Thermodynamics
von Spakovsky, M. R., & Jochen Gemmer, B. (2014) · Entropy · doi:10.3390/e16063434 · Cited by 32 · see citing works
Classicality, Markovianity, and local detailed balance from pure-state dynamics
Strasberg, P., Winter, A., Jochen Gemmer, B., & Wang, J. (2023) · Physical Review A · doi:10.1103/physreva.108.012225 · Cited by 31 · see citing works
Trushechkin, A. S. (2022) · Physical Review A · doi:10.1103/physreva.106.042209 · Cited by 31 · see citing works
Initial correlation in a system of a spin coupled to a spin bath through an intermediate spin
Semin, V., Sinayskiy, I., & Petruccione, F. (2012) · Physical Review A · doi:10.1103/physreva.86.062114 · Cited by 31 · see citing works
Transition from Diffusive to Ballistic Dynamics for a Class of Finite Quantum Models
Steinigeweg, R., Breuer, H., & Jochen Gemmer, B. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.150601 · Cited by 30 · see citing works
Self-citationOpen quantum system approach to single-molecule spectroscopy
Budini, A. A. (2009) · Physical Review A · doi:10.1103/physreva.79.043804 · Cited by 29 · see citing works
Quantum thermalization with couplings
Dong, H., Yang, S., Liu, X. F., & Sun, C. P. (2007) · Physical Review A · doi:10.1103/physreva.76.044104 · Cited by 29 · see citing works
Generalized quantum master equation: A tutorial review and recent advances
Brian, D., & Sun, X. Y. (2021) · Chinese Journal of Chemical Physics · doi:10.1063/1674-0068/cjcp2109157 · Cited by 28 · see citing works
Quantum master equation for the microcanonical ensemble
Esposito, M., & Gaspard, P. (2007) · Physical Review E · doi:10.1103/physreve.76.041134 · Cited by 27 · see citing works
Reduced dynamical maps in the presence of initial correlations
Vacchini, B., & Amato, G. (2016) · Scientific Reports · doi:10.1038/srep37328 · Cited by 26 · see citing works
Finite quantum environments as thermostats: an analysis based on the Hilbert space average method
Gemmer, J., & Michel, M. (2006) · The European Physical Journal B · doi:10.1140/epjb/e2006-00407-3 · Cited by 26 · see citing works
Self-citationOn Completely Positive Non-Markovian Evolution of a d-Level System
Kossakowski, A., & Rebolledo, R. (2008) · Open Systems & Information Dynamics · doi:10.1142/s1230161208000122 · Cited by 25 · see citing works
Characteristics Analysis and State Transfer for Non-Markovian Open Quantum Systems
Cong, S., Long-Zhen, H. U., Yang, F., & Liu, J. (2013) · Acta Automatica Sinica · doi:10.1016/s1874-1029(13)60035-x · Cited by 25 · see citing works
Relaxation, thermalization, and Markovian dynamics of two spins coupled to a spin bath
Raedt, H. A. D., Jin, F., Katsnelson, M. I., & Michielsen, K. F. L. (2017) · Physical review. E · doi:10.1103/physreve.96.053306 · Cited by 25 · see citing works
Operator Correlations and Quantum Regression Theorem in Non-Markovian Lindblad Rate Equations
Budini, A. A. (2008) · Journal of Statistical Physics · doi:10.1007/s10955-007-9476-9 · Cited by 23 · see citing works
Pouthier, V. (2008) · Physical Review E · doi:10.1103/physreve.78.061909 · Cited by 21 · see citing works
Recursive approach for non-Markovian time-convolutionless master equations
Gasbarri, G., & Ferialdi, L. (2018) · Physical Review A · doi:10.1103/physreva.97.022114 · Cited by 21 · see citing works
Stochastic Thermodynamics of a Quantum Dot Coupled to a Finite-Size Reservoir
Moreira, S. V., Samuelsson, P., & Potts, P. P. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.220405 · Cited by 20 · see citing works
Quantum trajectories: Memory and continuous observation
Barchielli, A., Pellegrini, C., & Petruccione, F. (2012) · Physical Review A · doi:10.1103/physreva.86.063814 · Cited by 20 · see citing works
Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
Budini, A. A. (2013) · Physical Review A · doi:10.1103/physreva.88.012124 · Cited by 19 · see citing works
Non-Markovian quantum jump with generalized Lindblad master equation
Huang, X. L., Sun, H., & Yi, X. X. (2008) · Physical Review E · doi:10.1103/physreve.78.041107 · Cited by 19 · see citing works
Noise gates for decoherent quantum circuits
Bassi, A., & Deckert, D.-A. (2008) · Physical Review A · doi:10.1103/physreva.77.032323 · Cited by 18 · see citing works
Open quantum systems coupled to finite baths: A hierarchy of master equations
Riera-Campeny, A., Sanpera, A., & Strasberg, P. (2022) · Physical review. E · doi:10.1103/physreve.105.054119 · Cited by 18 · see citing works
Pouthier, V. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3297947 · Cited by 18 · see citing works
Effective Hamiltonian approach to open systems and its applications
Huang, X. L., Yi, X. X., Wu, C., Feng, X., Yu, S., & Oh, C. H. (2008) · Physical Review A · doi:10.1103/physreva.78.062114 · Cited by 18 · see citing works
Non-Markovian effects on the geometric phase
Huang, X. L., & Yi, X. X. (2008) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/82/50001 · Cited by 18 · see citing works
Finite quantum environments as thermostats: an analysis based on the Hilbert space average method
Jochen Gemmer, B., & Michel, M. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 18 · see citing works
Self-citationJump-diffusion unravelling of a non-Markovian generalized Lindblad master equation
Barchielli, A., & Pellegrini, C. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3514539 · Cited by 17 · see citing works
Quantum thermodynamics under observation: The influence of periodic quantum measurements
Jahnke, T., & Mahler, G. (2010) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/90/50008 · Cited by 16 · see citing works
Dynamics of open quantum spin systems: An assessment of the quantum master equation approach
Zhao, P.-L., Raedt, H. A. D., Miyashita, S., Jin, F., & Michielsen, K. F. L. (2016) · Physical review. E · doi:10.1103/physreve.94.022126 · Cited by 16 · see citing works
Quantum Foundations of Classical Reversible Computing
Frank, M., & Shukla, K. (2021) · Entropy · doi:10.3390/e23060701 · Cited by 17 · see citing works
Pouthier, V. (2009) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/21/18/185404 · Cited by 15 · see citing works
Quantifying non-Markovianity due to driving and a finite-size environment in an open quantum system
Sampaio, R., Suomela, S., Schmidt, R., & Ala-Nissilä, T. (2017) · Physical Review A · doi:10.1103/physreva.95.022120 · Cited by 14 · see citing works
Arbitrary spin in a spin bath: Exact dynamics and approximation techniques
Semin, V., Sinayskiy, I., & Petruccione, F. (2014) · Physical Review A · doi:10.1103/physreva.89.012107 · Cited by 14 · see citing works
Quantum master equation from the eigenstate thermalization hypothesis
O’Donovan, P., Strasberg, P., Modi, K. K., Goold, J., & Mitchison, M. T. (2025) · Physical review. B./Physical review. B · doi:10.1103/kh96-ct3y · Cited by 12 · see citing works
Quantum decoherence in finite size exciton–phonon systems
Pouthier, V. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3566002 · 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
Dynamical and thermodynamical approaches to open quantum systems
Semin, V., & Petruccione, F. (2020) · Scientific Reports · doi:10.1038/s41598-020-59241-7 · 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. (2011) · Physical Review B · doi:10.1103/physrevb.83.085418 · Cited by 11 · see citing works
Non-Markovian Quantum Dynamics and the Method of Correlated Projection Super-Operators
Breuer, H. (2009) · Lecture notes in physics · doi:10.1007/978-3-642-02871-7_5 · Cited by 11 · see citing works
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
Vibron-phonon coupling strength in a finite size lattice of H-bonded peptide units
Pouthier, V. (2010) · Physical Review E · doi:10.1103/physreve.81.031913 · Cited by 10 · see citing works
Santra, S., Cruikshank, B., Balu, R., & Jacobs, K. A. (2017) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aa8777 · Cited by 9 · see citing works
Probing internal bath dynamics by a Rabi oscillator-based detector
Çetinbaş, M., & Wilkie, J. (2007) · Physics Letters A · doi:10.1016/j.physleta.2007.05.075 · Cited by 10 · see citing works
Pouthier, V. (2007) · Physical Review E · doi:10.1103/physreve.75.061910 · Cited by 10 · see citing works
Microscopic modeling of general time-dependent quantum Markov processes
Amato, G., Breuer, H., & Vacchini, B. (2019) · Physical Review A · doi:10.1103/physreva.99.030102 · Cited by 8 · see citing works
Self-citationJochen Gemmer, B., & Breuer, H. (2007) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2007-00357-6 · Cited by 9 · see citing works
Self-citationTypical, finite baths as a means of exact simulation of open quantum systems
Silvestri, L. G., Jacobs, K. A., Dunjko, V., & Olshanii, M. (2014) · Physical Review E · doi:10.1103/physreve.89.042131 · Cited by 8 · see citing works
Information encoding of a qubit into a multilevel environment
Pérez, A. (2010) · Physical Review A · doi:10.1103/physreva.81.052326 · Cited by 8 · see citing works
Pouthier, V. (2009) · Physical Review B · doi:10.1103/physrevb.80.144304 · Cited by 8 · see citing works
Boltzmann-equation approach to transport in finite modular quantum systems
Kadiroḡlu, M., & Jochen Gemmer, B. (2007) · Physical Review B · doi:10.1103/physrevb.76.024306 · Cited by 8 · see citing works
Dephasing Dynamics in a Non-Equilibrium Fluctuating Environment
Meng, X., Sun, Y., Wang, Q., Ren, J., Cai, X.-J., & Czerwiński, A. (2023) · Entropy · doi:10.3390/e25040634 · Cited by 7 · see citing works
Born-Oppenheimer approximation in open systems
Huang, X. L., & Yi, X. X. (2009) · Physical Review A · doi:10.1103/physreva.80.032108 · Cited by 7 · see citing works
Master Equations Versus Keldysh Green’s Functions for Correlated Quantum Systems Out of Equilibrium
Arrigoni, E., & Dorda, A. (2018) · Springer series in solid-state sciences · doi:10.1007/978-3-319-94956-7_4 · Cited by 6 · see citing works
Usui, A., Ptaszyński, K., Esposito, M., & Strasberg, P. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad2895 · Cited by 6 · see citing works
Parametric approximation as an open-quantum-system problem
Karasev, A. Y., & Teretenkov, A. E. (2025) · Physical Review A · doi:10.1103/physreva.111.052203 · Cited by 6 · see citing works
Connecting two jumplike unravelings for non-Markovian open quantum systems
Luoma, K., Suominen, K., & Piilo, J. (2011) · Physical Review A · doi:10.1103/physreva.84.032113 · Cited by 6 · see citing works
Babu, A. P., Alipour, S., Rezakhani, A. T., & Ala-Nissilä, T. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013243 · Cited by 7 · see citing works
Projection operator approach to transport in complex single-particle quantum systems
Steinigeweg, R., Jochen Gemmer, B., Breuer, H., & Schmidt, H. (2009) · The European Physical Journal B · doi:10.1140/epjb/e2009-00143-2 · Cited by 6 · see citing works
Self-citationThermal drag in spin ladders coupled to phonons
Bartsch, C., & Brenig, W. (2013) · Physical Review B · doi:10.1103/physrevb.88.214412 · Cited by 6 · see citing works
Correlated projection superoperators in relaxation and transport investigations
Mathias Michel, A., Steinigeweg, R., & Weimer, H. (2007) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2007-00358-5 · Cited by 6 · see citing works
Transport in anisotropic model systems analyzed by a correlated projection superoperator technique
Weimer, H., Mathias Michel, A., Jochen Gemmer, B., & Günter Mahler, A. (2008) · Physical Review E · doi:10.1103/physreve.77.011118 · Cited by 6 · see citing works
Origin of dissipative dynamics in correlated few electron systems
Nest, M. (2010) · Chemical Physics · doi:10.1016/j.chemphys.2010.02.009 · Cited by 5 · see citing works
On the structure of the master equation for a two-level system coupled to a thermal bath
de Vega, I. (2015) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/48/14/145202 · Cited by 5 · see citing works
Stochastic wave-function unravelling of the generalized Lindblad equation
Semin, V., Semina, I., & Petruccione, F. (2017) · Physical review. E · doi:10.1103/physreve.96.063313 · Cited by 5 · see citing works
Jahnke, T., & Mahler, G. (2011) · Physical Review E · doi:10.1103/physreve.84.011129 · Cited by 5 · see citing works
Meretukov, K. S., & Teretenkov, A. E. (2024) · Proceedings of the Steklov Institute of Mathematics · doi:10.1134/s0081543824010140 · Cited by 4 · see citing works
Bartsch, C., Steinigeweg, R., & Jochen Gemmer, B. (2010) · Physical Review E · doi:10.1103/physreve.81.051115 · Cited by 4 · see citing works
Role of correlations in the thermalization of quantum systems
Smirne, A., Laine, E.-M., Breuer, H., Piilo, J., & Vacchini, B. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/11/113034 · Cited by 4 · see citing works
Self-citationHilbert-space average method and adiabatic quantum search
Pérez, A. (2009) · Physical Review A · doi:10.1103/physreva.79.012314 · Cited by 4 · see citing works
Nonequilibrium aspects of quantum thermodynamics
Mathias Michel, A. (2006) · OPUS Publication Server of the University of Stuttgart (University of Stuttgart) · doi:10.18419/opus-4783 · Cited by 4 · see citing works
- Authors
- Breuer, H.-P., Gemmer, J., & Michel, M.
- Affiliations
- University of Freiburg (DE)
- ORCID
- Breuer, Heinz-Peter
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2006-01-27
- Volume
- 73
- Issue
- 1
- Pages
- 016139-016139
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2089885138
- Cited by
- 134
- References
- 51
- Citations by year
- 2026: 3 · 2025: 4 · 2024: 5 · 2023: 3 · 2022: 3 · 2021: 4 · 2020: 5 · 2019: 3 · 2018: 3 · 2017: 7 · 2016: 2 · 2015: 2 · 2014: 3 · 2013: 4 · 2012: 9
- FWCI
- 11.83
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- FreiDok plus (Universitätsbibliothek Freiburg) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft
- 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 many-body systems
- Keywords
- non-Markovian dynamics, open quantum systems, non-perturbative treatment, random couplings, finite reservoir
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
