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Records |
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Author |
Marquez-Martin, I.; Arnault, P.; Di Molfetta, G.; Perez, A. |
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Title |
Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks |
Type |
Journal Article |
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Year |
2018 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
98 |
Issue |
3 |
Pages |
032333 - 8pp |
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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. |
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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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Publisher |
Amer Physical Soc |
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English |
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ISSN |
2469-9926 |
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Conference |
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Notes |
WOS:000446163200006 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3750 |
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Permanent link to this record |
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Author |
Arrighi, P.; Di Molfetta, G.; Marquez-Martin, I.; Perez, A. |
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Title |
Dirac equation as a quantum walk over the honeycomb and triangular lattices |
Type |
Journal Article |
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Year |
2018 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
97 |
Issue |
6 |
Pages |
062111 - 5pp |
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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. |
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Address |
[Arrighi, Pablo; Di Molfetta, Giuseppe; Marquez-Martin, Ivan] Aix Marseille Univ, Univ Toulon, LIS, CNRS, Marseille, France, Email: pablo.arrighi@univ-amu.fr; |
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Publisher |
Amer Physical Soc |
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Language |
English |
Summary Language |
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Original Title |
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Abbreviated Series Title |
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Series Volume |
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ISSN |
2469-9926 |
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Expedition |
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Conference |
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Notes |
WOS:000435076800001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3624 |
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Permanent link to this record |
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Author |
Di Molfetta, G.; Soares-Pinto, D.O.; Duarte Queiros, S.M. |
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Title |
Elephant quantum walk |
Type |
Journal Article |
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Year |
2018 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
97 |
Issue |
6 |
Pages |
062112 - 6pp |
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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. |
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Address |
[Di Molfetta, Giuseppe] Univ Toulon & Var, Aix Marseille Univ, Nat Computat Res Grp, CNRS,LIS, Marseille, France, Email: giuseppe.dimolfetta@lis-lab.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 |
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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 |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3625 |
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Permanent link to this record |
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Author |
Marquez-Martin, I.; Di Molfetta, G.; Perez, A. |
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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 |
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 |
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Author |
Arnault, P.; Di Molfetta, G.; Brachet, M.; Debbasch, F. |
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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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Keywords |
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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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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: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 |