| Records |
| Author |
Di Molfetta, G.; Soares-Pinto, D.O.; Duarte Queiros, S.M. |
| Title |
Elephant quantum walk |
Type |
Journal Article |
| Year |
2018 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
| Volume |
97 |
Issue |
6 |
Pages |
062112 - 6pp |
| Keywords |
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| Abstract |
We introduce an analytically treatable discrete time quantum walk in a one-dimensional lattice which combines non-Markovianity and hyperballistic diffusion associated with a Gaussian whose variance sigma(2)(t) grows cubicly with time sigma alpha t(3). These properties have have been numerically found in several systems, namely, tight-binding lattice models. For its rules, our model can be understood as the quantum version of the classical non-Markovian “elephant random walk” process for which the quantum coin operator only changes the value of the diffusion constant although, contrarily, to the classical coin. |
| Address |
[Di Molfetta, Giuseppe] Univ Toulon & Var, Aix Marseille Univ, Nat Computat Res Grp, CNRS,LIS, Marseille, France, Email: giuseppe.dimolfetta@lis-lab.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 |
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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:000435076800002 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
3625 |
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| Author |
Marquez-Martin, I.; Arnault, P.; Di Molfetta, G.; Perez, A. |
| Title |
Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks |
Type |
Journal Article |
| Year |
2018 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
| Volume |
98 |
Issue |
3 |
Pages |
032333 - 8pp |
| Keywords |
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| Abstract |
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. |
| 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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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:000446163200006 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
3750 |
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| Author |
Hatifi, M.; Di Molfetta, G.; Debbasch, F.; Brachet, M. |
| Title |
Quantum walk hydrodynamics |
Type |
Journal Article |
| Year |
2019 |
Publication |
Scientific Reports |
Abbreviated Journal |
Sci Rep |
| Volume |
9 |
Issue |
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Pages |
2989 - 7pp |
| Keywords |
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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). |
| 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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Thesis |
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| Publisher |
Nature Publishing Group |
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 Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
2045-2322 |
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:000459799800138 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
3923 |
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| Author |
Arrighi, P.; Di Molfetta, G.; Marquez-Martin, I.; Perez, A. |
| Title |
From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks |
Type |
Journal Article |
| Year |
2019 |
Publication |
Scientific Reports |
Abbreviated Journal |
Sci Rep |
| Volume |
9 |
Issue |
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Pages |
10904 - 10pp |
| 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. |
| 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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Thesis |
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| Publisher |
Nature Publishing Group |
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 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 |
2045-2322 |
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:000477701800007 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
4081 |
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| Author |
Arnault, P.; Macquet, A.; Angles-Castillo, A.; Marquez-Martin, I.; Pina-Canelles, V.; Perez, A.; Di Molfetta, G.; Arrighi, P.; Debbasch, F. |
| Title |
Quantum simulation of quantum relativistic diffusion via quantum walks |
Type |
Journal Article |
| Year |
2020 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
| Volume |
53 |
Issue |
20 |
Pages |
205303 - 39pp |
| Keywords |
noisy quantum walks; noisy quantum systems; decoherence; Lindblad equation; quantum simulation; relativistic diffusions; telegraph equation |
| Abstract |
Two models are first presented, of a one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: the diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position. |
| Address |
[Arnault, Pablo; Angles-Castillo, Andreu; Marquez-Martin, Ivan; Pina-Canelles, Vicente; Perez, Armando; Di Molfetta, Giuseppe] Univ Valencia, Dept Fis Teor, Dr Moliner 50, Burjassot 46100, Spain, Email: pablo.arnault@ic.uv.es |
| Corporate Author |
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Thesis |
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| Publisher |
Iop Publishing Ltd |
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 |
1751-8113 |
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:000531359000001 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
4390 |
| Permanent link to this record |
