The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
Lattice Boltzmann equation for quantum mechanics
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Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Schemes using this strategy can be found in [, ] and in [] for higher order splittings.”
From Quantum lattice Boltzmann is a quantum walk (2015) · cites this paper as [18]
In the citing paper
“This Dirac QW [4-6] models the + (2 1)-dimensional Dirac equation.”
From The Dirac equation as a quantum walk: higher dimensions, observational convergence (2014) · cites this paper as [4]
Citations
Cites
Use of the Boltzmann Equation to Simulate Lattice-Gas Automata
McNamara, G. R., & Zanetti, G. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2332 · Cited by 2,096
The lattice Boltzmann equation: theory and applications
Benzi, R., Succi, S., & Vergassola, M. (1992) · Physics Reports · doi:10.1016/0370-1573(92)90090-m · Cited by 2,089
Self-citationDodd, J. E., & Gripaios, B. M. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108616270.006 · Cited by 1,098
Boltzmann Approach to Lattice Gas Simulations
Higuera, F. J., & Jiménez, J. L. (1989) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/9/7/009 · Cited by 881
Lattice Gas Models for 3D Hydrodynamics
d’Humières, D., Lallemand, P., & Frisch, U. (1986) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/2/4/006 · Cited by 395
Hyperbolic evolution system for numerical relativity
Bona, C., & Massó, J. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.1097 · Cited by 101
Dürr, D., & Lazarovici, D. (2020) · Springer eBooks · doi:10.1007/978-3-030-40068-2_11 · Cited by 30
Research works printed but not linked: 3
- Madelung, 1926, Z. Phys., 40, 332
- 1991, Comput. Phys. Commun., 63
- Frisch, 1986, Phys. Rev. Lett., 56, 15
Cited by
Sorted by citations
Items 201–217 of 217
Stochastic evolution equations within the context of both the Hamiltonian and Lagrangian formalisms
Costanza, G. (2014) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2014.08.058
Bisio, A., D’Ariano, G. M., Perinotti, P., & Tosini, A. (2015)
Numerical Evidence of Sinai Diffusion of Random-Mass Dirac Particles
null, S. P., & Sauro Succi, A. (2018) · Communications in Computational Physics · doi:10.4208/cicp.oa-2016-0239
A Lattice Boltzmann Model for the Steady State Compressible Flows
闫, 铂. (2017) · International Journal of Fluid Dynamics · doi:10.12677/ijfd.2017.51002
A Lattice Runge-Kutta-Boltzmann Model for the Reaction Diffusion Equation
闫, 铂. (2017) · Advances in Applied Mathematics · doi:10.12677/aam.2017.63047
Moment Independent Expansion for Fourth-Order Corrections in Lattice Boltzmann MethodsPreprint
Strand, K. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1710.11261
Quantum Lattice Boltzmann (QLB)
Sauro Succi, A. (2018) · doi:10.1093/oso/9780199592357.003.0032
QLB for Quantum Many-Body and Quantum Field Theory
Sauro Succi, A. (2018) · doi:10.1093/oso/9780199592357.003.0033
Landau levels in wrinkled and rippled graphene sheets
Flouris, K., Jimenez, M. M., & Herrmann, H. J. (2019) · International Journal of Modern Physics C · doi:10.1142/s0129183119410067
Analysis of Carlemann Linearization of Lattice BoltzmannPreprint
Itani, W., & Sauro Succi, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.11327
Sauro Succi, A., & Licata, I. (2016) · MDPI eBooks · doi:10.3390/books978-3-03842-307-2
Sauro Succi, A., Marco Lauricella, A., & Tiribocchi, A. (2025) · Physics of Fluids · doi:10.1063/5.0260872
A quantum lattice algorithm with fourth-order accuracy for the one-dimensional Dirac equation
Dellar, P. J. (2025) · Journal of Computational Physics · doi:10.1016/j.jcp.2025.113991
Quantum walks : background geometry and gauge invariance
Márquez-Martín, I. (2019) · theses.fr (ABES) · doi:10.70675/8d7024f3z592fz4cb1z9f10z46474a4e0721
Marches quantiques sous champ magnétique et cages d’Aharonov-Bohm
Perrin, H. (2021) · theses.fr (ABES) · doi:10.70675/a7c32d2bz9caaz4ec0z8380z92fc4da9d335
Fragile single-cone Dirac quantum walks in two dimensions
Beenakker, C. W. J., Fernán, J. S., & Tworzydło, J. (2026) · Physical Review A · doi:10.1103/cdkh-h1jx
Metadata
- Authors
- Succi, S., & Benzi, R.
- Affiliations
- University of Rome Tor Vergata (IT)
- ORCID
- Benzi, R.
- Venue
- Physica D: Nonlinear Phenomena
- Publisher
- Elsevier BV
- Published
- 1993-12
- Volume
- 69
- Issue
- 3-4
- Pages
- 327-332
- ISSN
- 0167-2789 (ISSN-L)
- OpenAlex
- W1999574688
- Cited by
- 217
- References
- 7
- Citations by year
- 2026: 3 · 2025: 9 · 2024: 6 · 2023: 3 · 2022: 8 · 2021: 7 · 2020: 6 · 2019: 17 · 2018: 13 · 2017: 9 · 2016: 13 · 2015: 22 · 2014: 13 · 2013: 8 · 2012: 6
- FWCI
- 2.36
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physica D Nonlinear Phenomena (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Lattice Boltzmann Simulation Studies
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
- Keywords
- lattice Boltzmann equation, quantum mechanics, non-relativistic quantum mechanics, hydrodynamics, quantum hydrodynamics, kinetic theory
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