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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, descending order (down)](img/sort_desc.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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Publisher |
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.; 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, descending order (down)](img/sort_desc.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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Publisher |
Amer Physical Soc |
Place of Publication |
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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 |
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Expedition |
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Conference |
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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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Permanent link to this record |