Isotropy of three-dimensional quantum lattice Boltzmann schemes
Abstract
Numerical simulations with previous formulations of the quantum lattice Boltzmann (QLB) scheme in three spatial dimensions showed significant lack of isotropy. In two or more spatial dimensions the QLB approach relies upon operator splitting to decompose the time evolution into a sequence of applications of the one-dimensional QLB scheme along coordinate axes. Each application must be accompanied by a rotation of the wave function into a basis of chiral eigenstates aligned along the relevant axis. The previously observed lack of isotropy was due to an inconsistency in the application of these rotations. Once this inconsistency is removed, the QLB scheme is shown to exhibit isotropic behavior to within a numerical error that scales approximately linearly with the lattice spacing. This establishes the viability of the QLB approach in two and three spatial dimensions.
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Consistency of the (1+1)-dimensional Dirac QW has been observed numerically in [9] and in (3+1)-dimensions in [10-12].
“It has been observed numerically in + (1 1) -dimensions in [9] and in + (3 1)-dimensions in [10-12].”
From The Dirac equation as a quantum walk: higher dimensions, observational convergence (2014) · cites this paper as [12]
Cites
Two-dimensional gas of massless Dirac fermions in graphene
Novoselov, K. S., Geim, A. K., Morozov, S. V., Jiang, D., Katsnelson, M. I., Grigorieva, I. V., Dubonos, S. V., & Firsov, A. A. (2005) · Nature · doi:10.1038/nature04233 · Cited by 21,611 · see citing works
Lattice Boltzmann equation for quantum mechanics
Succi, S., & Benzi, R. (1993) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(93)90096-j · Cited by 217 · see citing works
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The Dirac equation as a quantum walk: higher dimensions, observational convergence
Arrighi, P., Nesme, V., & Forets, M. (2014) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/47/46/465302 · Cited by 72 · see citing works
- Authors
- Dellar, P. J., Lapitski, D., Palpacelli, S., & Succi, S.
- Affiliations
- University of Oxford (GB)
- ORCID
- Dellar, P. J.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2011-04-07
- Volume
- 83
- Issue
- 4
- Pages
- 046706-046706
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2036519712
- Cited by
- 30
- References
- 2
- Citations by year
- 2025: 1 · 2022: 1 · 2021: 1 · 2019: 5 · 2018: 4 · 2015: 8 · 2014: 2 · 2013: 2 · 2012: 4
- FWCI
- 3.22
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Lattice Boltzmann Simulation Studies
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- isotropy, operator splitting, quantum many-body dynamics
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