The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Simple derivation of the Lindblad equation
Open accessAbstract
The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is ‘simple’ in that all it uses is the expression of a Hermitian matrix in terms of its orthonormal eigenvectors and real eigenvalues. Thus, it is appropriate for students who have learned the algebra of quantum theory. Where helpful, arguments are first given in a two-dimensional Hilbert space.
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“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 [7]
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“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 [7]
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“Equation (237) has the properties of what is called quantum Markovian master equation : these are master equations where - among other properties which are beyond our scope here - the time-evolution of the system is independent of its past history.”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [7]
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Citations
Cites
On the generators of quantum dynamical semigroups
Lindblad, G. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01608499 · Cited by 7,548
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
General state changes in quantum theory
Kraus, K. (1971) · Annals of Physics · doi:10.1016/0003-4916(71)90108-4 · Cited by 782
Physical Particle Representation and Generalized Transformation Theory
Prigogine, I., George, C., Hénin, F., et al. (1970) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.66.3.709 · Cited by 18
Research works printed but not linked: 2
- d’Espagnat B, 1971, Conceptual Foundations of Quantum Mechanics
- Kraus K, 1983, States, Effects and Operations
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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
Metadata
- Authors
- Pearle, P.
- Affiliations
- Hamilton College (US)
- Corresponding author
- Pearle, Philip
- Venue
- European Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2012-04-27
- Volume
- 33
- Issue
- 4
- Pages
- 805-822
- ISSN
- 0143-0807 (ISSN-L)
- 1361-6404
- OpenAlex
- W2083989927
- Cited by
- 128
- References
- 4
- Citations by year
- 2026: 6 · 2025: 10 · 2024: 37 · 2023: 13 · 2022: 11 · 2021: 11 · 2020: 9 · 2019: 12 · 2018: 7 · 2017: 5 · 2016: 2 · 2014: 4 · 2013: 1
- FWCI
- 0.83
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- European Journal of Physics (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 › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- Lindblad master equation, density matrix, Markovian evolution, completely positive maps, open quantum systems, Hermitian matrices, two-dimensional Hilbert space
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