A short introduction to the Lindblad master equation
Open accessAbstract
The theory of open quantum systems is one of the most essential tools for the development of quantum technologies. Furthermore, the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) master equation plays a key role as it is the most general generator of Markovian dynamics in quantum systems. In this paper, we present this equation together with its derivation and methods of resolution. The presentation tries to be as self-contained and straightforward as possible to be useful to readers with no previous knowledge of this field.
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The equations of motion for the density matrix for relaxation processes are often linear but often not amenable to easy resolution.
“the equations of motion for the density matrix for such relaxation processes are often linear in the former, they are often not amenable to easy resolution.”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [5]
For ρ(t) defined on a finite-dimensional state space of dimension d, the GKSL equation reads [5,6,7,8] (191).
“For ρ ( t ) defined on a finite-dimensional state space of dimension d , the GKSL equation reads [5, 6, 7, 8]”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [5]
|ρ(∞)〉〉 is a linear combination of those {|ζ_k〉〉} with Re[λ_k]=0.
“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 [5]
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Cites
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“In this case the most general quantum dynamics is generated by the Lindblad equation (also called Gorini-Kossakowski-Sudarshan-Lindblad equation) [4, 5].”
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Cited by
Sorted by citations
Fundamentals of quantum mechanics in Liouville space
Gyamfi, J. A. (2020) · European Journal of Physics · doi:10.1088/1361-6404/ab9fdd · Cited by 77 · see citing works
Patwa, H., Babcock, N. S., & Kurian, P. (2024) · Frontiers in Physics · doi:10.3389/fphy.2024.1387271 · Cited by 20 · see citing works
- Authors
- Manzano, D.
- Affiliations
- Universidad de Granada (ES)
- Corresponding author
- Manzano, Daniel
- ORCID
- Manzano, Daniel
- Venue
- AIP Advances
- Publisher
- AIP Publishing
- Published
- 2020-02-01
- Volume
- 10
- Issue
- 2
- ISSN
- 2158-3226 (ISSN-L)
- OpenAlex
- W2952169450
- Cited by
- 714
- References
- 25
- Citations by year
- 2026: 147 · 2025: 160 · 2024: 133 · 2023: 111 · 2022: 83 · 2021: 69 · 2020: 10 · 2019: 1
- FWCI
- 27.77
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- AIP Advances (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- Institutional Repository of the University of Granada (University of Granada) (submittedVersion, cc-by)
- LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Agencia Española de Investigación (FIS2017-84256-P)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- Lindblad master equation, open quantum systems, Markovian dynamics, quantum master equation, solution methods
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