Quantum speed limit for a relativistic electron in a uniform magnetic field
Open accessAbstract
We analyze the influence of relativistic effects on the minimum evolution time between two orthogonal states of a quantum system. Defining the initial state as a homogeneous superposition between two Hamiltonian eigenstates of an electron in a uniform magnetic field, we obtain a relation between the minimum evolution time and the displacement of the mean radial position of the electron wave packet. The quantum speed limit time is calculated for an electron dynamics described by Dirac and Schr\"odinger-Pauli equations considering different parameters, such as the strength of magnetic field and the linear momentum of the electron in the axial direction. We highlight that when the electron undergoes a region with extremely strong magnetic field the relativistic and nonrelativistic dynamics differ substantially, so that the description given by the Schr\"odinger-Pauli equation enables the electron to travel faster than $c$, which is prohibited by Einstein's theory of relativity. This approach allows a connection between the abstract Hilbert space and the space-time coordinates, besides the identification of the most appropriate quantum dynamics used to describe the electron motion.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For relativistic Dirac dynamics, Villamizar and Duzzioni derived the quantum speed limit time in equation (130), which becomes equivalent to the Schrödinger quantum speed limit time in the non-relativistic limit.
“For the relativistic Dirac dynamics (126) we obtain [227] τ D QSL = π (mc 2 ) 2 + 4 c 2 e B -(mc 2 ) 2 + 2 c 2 e B π 2cβ √ 2 -1 (130 ) where the second equality holds for strong magnetic fields, c 2 e B (mc 2 ) 2 , and where β = eB/2 .Note that in the non-relativistic limit τ S QSL and τ D QSL become equivalent.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [227]
Villamizar and Duzzioni resolved the Einstein-Bohr debate by bringing the energy-time uncertainty principle into agreement with special relativity.
“Finally, it is interesting to note that in passing Villamizar and Duzzioni [227] resolved the longstanding debate of Einstein and Bohr (see section 1) by bringing the energy-time uncertainty principle in full agreement with special relativity.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [227]
For strong magnetic fields, the average speed computed from Schrödinger dynamics can exceed the speed of light, whereas the Dirac average speed remains below c even for arbitrarily strong fields.
“We immediately see that for strong magnetic fields, B 1, the average speed computed from the Schrödinger dynamics can surpass the speed of light, c.As expected, this is not the case for the Dirac equation, and even for arbitrarily strong fields B we always have v D < c.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [227]
Villamizar and Duzzioni concluded that the quantum speed limit can be used to check the physical consistency of a physical model.
“Thus, Villamizar and Duzzioni [227] conclude that the quantum speed limit can be used to check the physical consistency of a physical model.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [227]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
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
Ultimate physical limits to computation
Lloyd, S. (2000) · Nature · doi:10.1038/35023282 · Cited by 1,120 · see citing works
The maximum speed of dynamical evolution
Margolus, N., & Levitin, L. B. (1998) · Physica D: Nonlinear Phenomena · doi:10.1016/s0167-2789(98)00054-2 · Cited by 887 · see citing works
Physics of strongly magnetized neutron stars
Harding, A. K., & Lai, D. (2006) · Reports on Progress in Physics · doi:10.1088/0034-4885/69/9/r03 · Cited by 823 · see citing works
Computational Capacity of the Universe
Lloyd, S. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.237901 · Cited by 571 · see citing works
Optimal Control at the Quantum Speed Limit
Caneva, T., Murphy, M., Calarco, T., Fazio, R., Montangero, S., Giovannetti, V., & Santoro, G. E. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.240501 · Cited by 509 · see citing works
Quantum Speed Limits in Open System Dynamics
del Campo, A., Egusquiza, I. L., Plenio, M. B., & Huelga, S. F. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.050403 · Cited by 493 · see citing works
More bang for your buck: super-adiabatic quantum engines
Campo, A. D., Goold, J., & Paternostro, M. (2014) · Scientific Reports · doi:10.1038/srep06208 · Cited by 306 · see citing works
Fundamental Limit on the Rate of Quantum Dynamics: The Unified Bound Is Tight
Levitin, L. B., & Toffoli, T. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.160502 · Cited by 302 · see citing works
A unitarity bound on the evolution of nonstationary states
Fleming, G. N. (1973) · Il Nuovo Cimento A · doi:10.1007/bf02819419 · Cited by 218 · see citing works
Energy–time uncertainty relation for driven quantum systems
Deffner, S., & Lutz, E. (2013) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/46/33/335302 · Cited by 199 · see citing works
Quantum speed limit for arbitrary initial states
Zhang, Y.-J., Han, W., Xia, Y.-J., Cao, J.-P., & Fan, H. (2014) · Scientific Reports · doi:10.1038/srep04890 · Cited by 176 · see citing works
Environment-Assisted Speed-up of the Field Evolution in Cavity Quantum Electrodynamics
Cimmarusti, A. D., Yan, Z., Patterson, B. D., Corcos, L. P., Orozco, L. A., & Deffner, S. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.233602 · Cited by 124 · see citing works
Classical-driving-assisted quantum speed-up
Zhang, Y.-J., Han, W., Xia, Y.-J., Cao, J.-P., & Fan, H. (2015) · Physical Review A · doi:10.1103/physreva.91.032112 · Cited by 95 · see citing works
Quantum-speed-limit time for multiqubit open systems
Liu, C., Xu, Z.-Y., & Zhu, S. (2015) · Physical Review A · doi:10.1103/physreva.91.022102 · Cited by 83 · see citing works
Flagged first, then by citations
Research works printed but not linked: 4
- [21]Paul Strange, Relativistic Quantum Mechanics: with applications in condensed matter and atomic physics , ISBN : 9780521565837, Cambridge University Press (1998).
- [22]For a review on relativistic quantum mechanics at lowenergies see Pekka Pyykk¨ o, Ann. Rev. Phys. Chem. 63 , 45 (2012).
- [23]Claude Cohen-Tannoudji, Bernard Diu, Franck Lalo; Quantum mechanics vol.1 Section D VI , ISBN : 978-0471-16433-3, Wiley (1991).
- [24]Daijiro Yoshioka, The Quantum Hall Effect , Chapter 2, ISBN : 978-3-642-07720-3, Springer (2002).
Cited by
Sorted by citations
Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control
Deffner, S., & Campbell, S. (2017) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/aa86c6 · Cited by 585 · see citing works
- Authors
- Villamizar, D. V., & Duzzioni, E. I.
- Affiliations
- Universidade Federal de Santa Catarina (BR)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2015-10-09
- Volume
- 92
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2259713265
- Cited by
- 29
- References
- 15
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 4 · 2022: 4 · 2021: 7 · 2020: 1 · 2018: 2 · 2017: 5 · 2016: 1 · 2015: 2
- FWCI
- 1.69
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- quantum speed limit, relativistic electrons, uniform magnetic field, Dirac equation, Schrödinger-Pauli equation, electron wave packets, superluminal motion, high magnetic fields
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
