| Records |
| Author |
Arnault, P.; Di Molfetta, G.; Brachet, M.; Debbasch, F. |
| Title |
Quantum walks and non-Abelian discrete gauge theory |
Type |
Journal Article |
| Year |
2016 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
| Volume |
94 |
Issue |
1 |
Pages |
012335 - 6pp |
| Keywords |
|
Abstract  |
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. |
| 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; |
| 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 |
|
Series Issue |
|
Edition |
|
| ISSN |
2469-9926 |
ISBN |
|
Medium |
|
| Area |
|
Expedition |
|
Conference |
|
| Notes |
WOS:000380095000005 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
2761 |
| Permanent link to this record |
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| Author |
Arrighi, P.; Di Molfetta, G.; Marquez-Martin, I.; Perez, A. |
| Title |
Dirac equation as a quantum walk over the honeycomb and triangular lattices |
Type |
Journal Article |
| Year |
2018 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
| Volume |
97 |
Issue |
6 |
Pages |
062111 - 5pp |
| Keywords |
|
| Abstract |
A discrete-time quantum walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in (2 + 1) dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice, both of interest in the study of quantum propagation on the nonrectangular grids, as in graphene-like materials. The latter, in particular, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces. |
| Address |
[Arrighi, Pablo; Di Molfetta, Giuseppe; Marquez-Martin, Ivan] Aix Marseille Univ, Univ Toulon, LIS, CNRS, Marseille, France, Email: pablo.arrighi@univ-amu.fr; |
| Corporate Author |
|
Thesis |
|
| Publisher |
Amer Physical Soc |
Place of Publication |
|
Editor |
|
| Language |
English |
Summary Language |
|
Original Title |
|
| Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
| Series Volume |
|
Series Issue |
|
Edition |
|
| ISSN |
2469-9926 |
ISBN |
|
Medium |
|
| Area |
|
Expedition |
|
Conference |
|
| Notes |
WOS:000435076800001 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
3624 |
| Permanent link to this record |
