| Records |
| 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 |
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| 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 |
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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:000435076800001 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
3624 |
| Permanent link to this record |
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| 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; |
| 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 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 |
Di Molfetta, G.; Perez, A. |
| Title |
Quantum walks as simulators of neutrino oscillations in a vacuum and matter |
Type |
Journal Article |
| Year |
2016 |
Publication |
New Journal of Physics |
Abbreviated Journal |
New J. Phys. |
| Volume |
18 |
Issue |
|
Pages |
103038 - 8pp |
| Keywords |
quantum walks; neutrino oscillations; quantum simulation |
| Abstract |
We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in a vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing one to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, the simulation of neutrino oscillations with the help of quantum walks might be useful to illustrate these effects in extreme conditions, such as the solar interior or supernovae. |
| Address |
[Di Molfetta, G.] Univ Valencia, CSIC, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: giuseppe.dimolfetta@lif.univ-mrs.fr |
| 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 |
1367-2630 |
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:000386816100004 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
2846 |
| Permanent link to this record |
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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 |
