The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
On the product of semi-groups of operators
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“The key ingredient of TEBD-based methods is a Lie-Trotter-Suzuki [16,17] splitting of the Schrödinger equation according to the individual terms ĥi of the Hamiltonian Ĥ = i ĥi .”
From Unifying time evolution and optimization with matrix product states (2016) · cites this paper as [16]
In the citing paper
“For this type of differential equation consisting of a sum of integrable parts, it is very natural to use a Lie-Trotter splitting approach [16,29,30], where one evolves according to each integrable part for a small time t.”
From Unifying time evolution and optimization with matrix product states (2016) · cites this paper as [16]
In the citing paper
“If this is true, then the operator e -iHt can be implemented in terms of the corresponding operators for every term in the Hamiltonian, using the Trotter-Suzuki formula [164]:”
From The prospects of quantum computing in computational molecular biology (2021) · cites this paper as [164]
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Citations
Cites
Functional Analysis and Semi-groups
Hille, E., & Phillips, R. (1996) · Colloquium Publications - American Mathematical Society/Colloquium Publications · doi:10.1090/coll/031 · Cited by 4,047
Approximation of semi-groups of operators
Trotter, H. F. (1958) · Pacific Journal of Mathematics · doi:10.2140/pjm.1958.8.887 · Cited by 459
Self-citationOn the Generation of Unbounded Semi-Groups of Bounded Linear Operators
Feller, W. (1953) · Annals of Mathematics · doi:10.2307/1969826 · Cited by 62
Dye, H. A., & Phillips, R. S. (1956) · Canadian Journal of Mathematics · doi:10.4153/cjm-1956-055-1 · Cited by 4
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Imada, M., Fujimori, A., & Tokura, Y. (1998) · Reviews of Modern Physics · doi:10.1103/revmodphys.70.1039 · Cited by 7,671
Reversible multiple time scale molecular dynamics
Tuckerman, M. E., Berne, B. J., & Martyna, G. J. (1992) · The Journal of Chemical Physics · doi:10.1063/1.463137 · Cited by 3,623
The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323
Path integrals in the theory of condensed helium
Ceperley, D. M. (1995) · Reviews of Modern Physics · doi:10.1103/revmodphys.67.279 · Cited by 2,482
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
Moler, C., & Van Loan, C. (2003) · SIAM Review · doi:10.1137/s00361445024180 · Cited by 2,357
Metadata
- Authors
- Trotter, H. F.
- Corresponding author
- Trotter, H. F.
- Venue
- Proceedings of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1959-08
- Volume
- 10
- Issue
- 4
- Pages
- 545-551
- ISSN
- 0002-9939 (ISSN-L)
- 1088-6826
- OpenAlex
- W1997126380
- Cited by
- 2,282
- References
- 4
- Citations by year
- 2026: 114 · 2025: 175 · 2024: 147 · 2023: 150 · 2022: 124 · 2021: 102 · 2020: 98 · 2019: 97 · 2018: 90 · 2017: 67 · 2016: 71 · 2015: 55 · 2014: 71 · 2013: 50 · 2012: 46
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Proceedings of the American Mathematical Society (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Banach Space Theory
- Physical Sciences › Mathematics › Applied Mathematics › Holomorphic and Operator Theory
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Keywords
- operator semigroups
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