Out-of-equilibrium open quantum systems: A comparison of approximate quantum master equation approaches with exact results
Open accessAbstract
We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of noninteracting particles (bosons or fermions) on an arbitrary lattice of $N$ sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the $N=2$ case, we show that RQME gives results which agree with exact analytical results for steady-state properties and with exact numerics for time-dependent properties over a wide range of parameters. In comparison, the Lindblad equations have a limited domain of validity in nonequilibrium. We conclude that it is indeed justified to use microscopically derived full RQME to go beyond the limitations of Lindblad equations in out-of-equilibrium systems. We also derive closed-form analytical results for out-of-equilibrium time dynamics of two-point correlation functions. These results explicitly show the approach to steady state and thermalization. These results are experimentally relevant for cold atoms, cavity QED, and far-from-equilibrium quantum dot experiments.
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For fermionic baths, the analogous local-validity inequalities are usually not fulfilled at low temperatures due to the step-like behavior of the Fermi-Dirac distribution.
“For fermionic baths, equations analogous to equations (17) can be derived.These are usually not fulfilled at low temperatures due to the step-like behavior of the Fermi-Dirac distribution [23,66].”
From Markovian master equations for quantum thermal machines: Local versus global approach (2017) · cites this paper as [23]
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References 57 · Cited by 121
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- Authors
- Purkayastha, A., Dhar, A., & Kulkarni, M.
- Affiliations
- Tata Institute of Fundamental Research (IN)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2016-06-13
- Volume
- 93
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2430536562
- Cited by
- 121
- References
- 57
- Citations by year
- 2026: 2 · 2025: 7 · 2024: 9 · 2023: 10 · 2022: 30 · 2021: 10 · 2020: 14 · 2019: 13 · 2018: 11 · 2017: 12 · 2016: 3
- FWCI
- 7.37
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- City University of New York (68193-0046)
- Topics
- 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
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- open quantum systems, nonequilibrium dynamics, Born-Markov approximation, Lindblad master equation, multiple reservoirs, lattice systems, steady-state characteristics, two-point correlation function, thermalization, cold atoms, cavity quantum electrodynamics, quantum dots
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