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Author |
Hatifi, M.; Di Molfetta, G.; Debbasch, F.; Brachet, M. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
Quantum walk hydrodynamics |
Type |
Journal Article |
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Year |
2019 |
Publication ![sorted by Publication field, descending order (down)](img/sort_desc.gif) |
Scientific Reports |
Abbreviated Journal |
Sci Rep |
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Volume |
9 |
Issue |
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Pages |
2989 - 7pp |
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Abstract |
A simple Discrete-Time Quantum Walk (DTQW) on the line is revisited and given an hydrodynamic interpretation through a novel relativistic generalization of the Madelung transform. Numerical results show that suitable initial conditions indeed produce hydrodynamical shocks and that the coherence achieved in current experiments is robust enough to simulate quantum hydrodynamical phenomena through DTQWs. An analytical computation of the asymptotic quantum shock structure is presented. The non-relativistic limit is explored in the Supplementary Material (SM). |
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Address |
[Hatifi, Mohamed] Aix Marseille Univ, CNRS, Ecole Cent Marseille, Inst Fresnel,UMR 7249, F-13013 Marseille, France, Email: giuseppe.dimolfetta@lis-lab.fr |
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Nature Publishing Group |
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English |
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ISSN |
2045-2322 |
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Notes |
WOS:000459799800138 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3923 |
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Permanent link to this record |
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Author |
Arrighi, P.; Di Molfetta, G.; Marquez-Martin, I.; Perez, A. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks |
Type |
Journal Article |
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Year |
2019 |
Publication ![sorted by Publication field, descending order (down)](img/sort_desc.gif) |
Scientific Reports |
Abbreviated Journal |
Sci Rep |
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Volume |
9 |
Issue |
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Pages |
10904 - 10pp |
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Keywords |
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Abstract |
A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. In a previous paper, we showed that QWs over the honeycomb and triangular lattices can be used to simulate the Dirac equation. We apply a spacetime coordinate transformation upon the lattice of this QW, and show that it is equivalent to introducing spacetime-dependent local unitaries-whilst keeping the lattice fixed. By exploiting this duality between changes in geometry, and changes in local unitaries, we show that the spacetime-dependent QW simulates the Dirac equation in (2 + 1)-dimensional curved spacetime. Interestingly, the duality crucially relies on the non linear-independence of the three preferred directions of the honeycomb and triangular lattices: The same construction would fail for the square lattice. At the practical level, this result opens the possibility to simulate field theories on curved manifolds, via the quantum walk on different kinds of lattices. |
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Address |
[Arrighi, Pablo; Di Molfetta, Giuseppe; Marquez-Martin, Ivan] Univ Toulon & Var, Aix Marseille Univ, CNRS, LIS, Marseille, France, Email: pablo.arrighi@univ-amu.fr; |
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Publisher |
Nature Publishing Group |
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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Abbreviated Series Title |
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ISSN |
2045-2322 |
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Conference |
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Notes |
WOS:000477701800007 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4081 |
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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 ![sorted by Publication field, descending order (down)](img/sort_desc.gif) |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
94 |
Issue |
1 |
Pages |
012335 - 6pp |
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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. |
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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 |
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English |
Summary Language |
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Abbreviated Series Title |
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Series Volume |
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Edition |
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ISSN |
2469-9926 |
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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 |
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Author |
Bru, L.A.; de Valcarcel, G.J.; Di Molfetta, G.; Perez, A.; Roldan, E.; Silva, F. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
Quantum walk on a cylinder |
Type |
Journal Article |
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Year |
2016 |
Publication ![sorted by Publication field, descending order (down)](img/sort_desc.gif) |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
94 |
Issue |
3 |
Pages |
032328 - 7pp |
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Abstract |
We consider the two-dimensional alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or “hidden” extra dimension. If one starts from localized initial conditions on the lattice, the dynamics of the quantum walk that is obtained after tracing out the small dimension shows the contribution of several components which can be understood from the study of the dispersion relations for this problem. In fact, these components originate from the contribution of the possible values of the quasimomentum in the closed dimension. In the continuous space-time limit, the different components manifest as a set of Dirac equations, with each quasimomentum providing the value of the corresponding mass. We briefly discuss the possible link of these ideas to the simulation of high-energy physical theories that include extra dimensions. Finally, entanglement between the coin and spatial degrees of freedom is studied, showing that the entanglement entropy clearly overcomes the value reached with only one spatial dimension. |
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Address |
[Bru, Luis A.] Univ Politecn Valencia, ITEAM Res Inst, Opt & Quantum Commun Grp, Camino Vera S-N, E-46022 Valencia, Spain |
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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 |
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:000384060700005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
2823 |
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Permanent link to this record |
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Author |
Marquez-Martin, I.; Di Molfetta, G.; Perez, A. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
Fermion confinement via quantum walks in (2+1)-dimensional and (3+1)-dimensional space-time |
Type |
Journal Article |
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Year |
2017 |
Publication ![sorted by Publication field, descending order (down)](img/sort_desc.gif) |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
95 |
Issue |
4 |
Pages |
042112 - 5pp |
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Keywords |
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Abstract |
We analyze the properties of a two-and three-dimensional quantum walk that are inspired by the idea of a brane-world model put forward by Rubakov and Shaposhnikov [Phys. Lett. B 125, 136 (1983)]. In that model, particles are dynamically confined on the brane due to the interaction with a scalar field. We translated this model into an alternate quantum walk with a coin that depends on the external field, with a dependence which mimics a domain wall solution. As in the original model, fermions (in our case, the walker) become localized in one of the dimensions, not from the action of a random noise on the lattice (as in the case of Anderson localization) but from a regular dependence in space. On the other hand, the resulting quantum walk can move freely along the “ordinary” dimensions. |
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Address |
[Marquez-Martin, I.; Di Molfetta, G.; Perez, A.] Univ Valencia, CSIC, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: giuseppe.dimolfetta@lif.univ-mrs.fr |
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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:000399931500006 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3102 |
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Permanent link to this record |