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Author |
Arnault, P.; Di Molfetta, G.; Brachet, M.; Debbasch, F. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
Quantum walks and non-Abelian discrete gauge theory |
Type |
Journal Article |
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Year |
2016 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
94 |
Issue |
1 |
Pages |
012335 - 6pp |
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Abstract ![sorted by Abstract field, ascending order (up)](img/sort_asc.gif) |
A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1) Maxwell fields and SU(N) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs. |
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Address |
[Arnault, Pablo; Debbasch, Fabrice] Univ Paris 06, Univ Paris 04, PSL Res Univ, LERMA,Observ Paris,CNRS,UMR 8112, F-75014 Paris, France, Email: pablo.arnault@upmc.fr; |
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Amer Physical Soc |
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English |
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ISSN |
2469-9926 |
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Notes |
WOS:000380095000005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
2761 |
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Author |
Jay, G.; Arnault, P.; Debbasch, F. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
Dirac quantum walks with conserved angular momentum |
Type |
Journal Article |
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Year |
2021 |
Publication |
Quantum Studies-Mathematics and Foundations |
Abbreviated Journal |
Quantum Stud. Math. Found. |
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Volume |
8 |
Issue |
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Pages |
419-430 |
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Keywords |
Quantum walks; Quantum simulation; Lattice field theory |
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Abstract ![sorted by Abstract field, ascending order (up)](img/sort_asc.gif) |
A quantum walk (QW) simulating the flat (1+2)D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group SO(3), but rather of its double cover SU(2), the QW can only be defined globally on an extended spacetime where the polar angle extends from 0 to 4 pi. The coupling of the QW with arbitrary electromagnetic fields is also presented. Finally, the cylindrical relativistic Landau levels of the Dirac equation are computed explicitly and simulated by the QW. |
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Address |
[Jay, Gareth] Univ Western Australia, Phys Dept, Perth, WA 6009, Australia, Email: gareth.jay@uwa.edu.au; |
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Springer |
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English |
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ISSN |
2196-5609 |
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Notes |
WOS:000697709700001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4975 |
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Author |
Arnault, P.; Pepper, B.; Perez, A. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
Quantum walks in weak electric fields and Bloch oscillations |
Type |
Journal Article |
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Year |
2020 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
101 |
Issue |
6 |
Pages |
062324 - 12pp |
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Abstract ![sorted by Abstract field, ascending order (up)](img/sort_asc.gif) |
Bloch oscillations appear when an electric field is superimposed on a quantum particle that evolves on a lattice with a tight-binding Hamiltonian (TBH), i.e., evolves via what we call an electric TBH; this phenomenon will be referred to as TBH Bloch oscillations. A similar phenomenon is known to show up in so-called electric discrete-time quantum walks (DQWs) [C. Cedzich et al., Phys. Rev. Lett. 111, 160601 (2013);] this phenomenon will be referred to as DQW Bloch oscillations. This similarity is particularly salient when the electric field of the DQW is weak. For a wide, i.e., spatially extended, initial condition, one numerically observes semiclassical oscillations, i.e., oscillations of a localized particle, for both the electric TBH and the electric DQW. More precisely, the numerical simulations strongly suggest that the semiclassical DQW Bloch oscillations correspond to two counterpropagating semiclassical TBH Bloch oscillations. In this work it is shown that, under certain assumptions, the solution of the electric DQW for a weak electric field and a wide initial condition is well approximated by the superposition of two continuous-time expressions, which are counterpropagating solutions of an electric TBH whose hopping amplitude is the cosine of the arbitrary coin-operator mixing angle. In contrast, if one wishes the continuous-time approximation to hold for spatially localized initial conditions, one needs at least the DQW to be lazy, as suggested by numerical simulations and by the fact that this has been proven in the case of a vanishing electric field [F. W. Strauch, Phys. Rev. A 74, 030301(R) (2006)]. |
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Address |
[Arnault, Pablo; Pepper, Benjamin; Perez, A.] Univ Valencia, CSIC, Dept Fis Teor, Cerrer Dr Moliner 50, Burjassot 46100, Spain, Email: pablo.arnault@ific.uv.es; |
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Publisher |
Amer Physical Soc |
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English |
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ISSN |
1050-2947 |
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Notes |
WOS:000541400900002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4431 |
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Permanent link to this record |
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Author |
Marquez-Martin, I.; Arnault, P.; Di Molfetta, G.; Perez, A. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks |
Type |
Journal Article |
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Year |
2018 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
98 |
Issue |
3 |
Pages |
032333 - 8pp |
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Abstract ![sorted by Abstract field, ascending order (up)](img/sort_asc.gif) |
Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two steps of the evolution, we define a density current which is gauge invariant and conserved. In the continuum limit, the dynamics of the particle, under a suitable choice of the parameters, becomes the Dirac equation and the conserved current satisfies the corresponding conservation equation. |
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Address |
[Marquez-Martin, Ivan; Arnault, Pablo; Di Molfetta, Giuseppe; Perez, Armando] Univ Valencia, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: ivan.marquez@uv.es; |
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Publisher |
Amer Physical Soc |
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Language |
English |
Summary Language |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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ISSN |
2469-9926 |
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Notes |
WOS:000446163200006 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3750 |
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Permanent link to this record |
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Author |
Arnault, P.; Perez, A.; Arrighi, P.; Farrelly, T. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
Discrete-time quantum walks as fermions of lattice gauge theory |
Type |
Journal Article |
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Year |
2019 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
99 |
Issue |
3 |
Pages |
032110 - 16pp |
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Keywords |
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Abstract ![sorted by Abstract field, ascending order (up)](img/sort_asc.gif) |
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also ultralocal, i.e., the particle's speed is upper bounded, as in standard relativistic quantum field theories. The lattice chiral symmetry of staggered fermions, which corresponds to a translational invariance, is lost after the requirement of ultralocality of the evolution; this fact is an instance of Meyer's 1996 no-go results stating that no nontrivial scalar quantum cellular automaton can be translationally invariant [D. A. Meyer, J. Stat. Phys. 85, 551 (1996); Phys. Lett. A 223, 337 (1996)]. All results are presented in a single-particle framework and for a (1+1)-dimensional space-time. |
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Address |
[Arnault, Pablo; Perez, Armando] Univ Valencia, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: pablo.arnault@ific.uv.es |
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Corporate Author |
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Thesis |
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Publisher |
Amer Physical Soc |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2469-9926 |
ISBN |
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Medium |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000461896700002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3950 |
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Permanent link to this record |