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Author  |
Arnault, P.; Pepper, B.; Perez, A. |
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Title |
Quantum walks in weak electric fields and Bloch oscillations |
Type |
Journal Article |
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Year |
2020 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
101 |
Issue |
6 |
Pages |
062324 - 12pp |
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Keywords |
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Abstract |
Bloch oscillations appear when an electric field is superimposed on a quantum particle that evolves on a lattice with a tight-binding Hamiltonian (TBH), i.e., evolves via what we call an electric TBH; this phenomenon will be referred to as TBH Bloch oscillations. A similar phenomenon is known to show up in so-called electric discrete-time quantum walks (DQWs) [C. Cedzich et al., Phys. Rev. Lett. 111, 160601 (2013);] this phenomenon will be referred to as DQW Bloch oscillations. This similarity is particularly salient when the electric field of the DQW is weak. For a wide, i.e., spatially extended, initial condition, one numerically observes semiclassical oscillations, i.e., oscillations of a localized particle, for both the electric TBH and the electric DQW. More precisely, the numerical simulations strongly suggest that the semiclassical DQW Bloch oscillations correspond to two counterpropagating semiclassical TBH Bloch oscillations. In this work it is shown that, under certain assumptions, the solution of the electric DQW for a weak electric field and a wide initial condition is well approximated by the superposition of two continuous-time expressions, which are counterpropagating solutions of an electric TBH whose hopping amplitude is the cosine of the arbitrary coin-operator mixing angle. In contrast, if one wishes the continuous-time approximation to hold for spatially localized initial conditions, one needs at least the DQW to be lazy, as suggested by numerical simulations and by the fact that this has been proven in the case of a vanishing electric field [F. W. Strauch, Phys. Rev. A 74, 030301(R) (2006)]. |
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Address |
[Arnault, Pablo; Pepper, Benjamin; Perez, A.] Univ Valencia, CSIC, Dept Fis Teor, Cerrer Dr Moliner 50, Burjassot 46100, Spain, Email: pablo.arnault@ific.uv.es; |
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Publisher |
Amer Physical Soc |
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Language |
English |
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ISSN |
1050-2947 |
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Conference |
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Notes |
WOS:000541400900002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4431 |
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Author |
Arnault, P.; Perez, A.; Arrighi, P.; Farrelly, T. |
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Title |
Discrete-time quantum walks as fermions of lattice gauge theory |
Type |
Journal Article |
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Year |
2019 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
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Volume |
99 |
Issue |
3 |
Pages |
032110 - 16pp |
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Keywords |
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Abstract |
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also ultralocal, i.e., the particle's speed is upper bounded, as in standard relativistic quantum field theories. The lattice chiral symmetry of staggered fermions, which corresponds to a translational invariance, is lost after the requirement of ultralocality of the evolution; this fact is an instance of Meyer's 1996 no-go results stating that no nontrivial scalar quantum cellular automaton can be translationally invariant [D. A. Meyer, J. Stat. Phys. 85, 551 (1996); Phys. Lett. A 223, 337 (1996)]. All results are presented in a single-particle framework and for a (1+1)-dimensional space-time. |
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Address |
[Arnault, Pablo; Perez, Armando] Univ Valencia, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: pablo.arnault@ific.uv.es |
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Corporate Author |
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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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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:000461896700002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3950 |
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Author |
Arrechea, J.; Delhom, A.; Jimenez-Cano, A. |
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Title |
Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity |
Type |
Journal Article |
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Year |
2021 |
Publication |
Chinese Physics C |
Abbreviated Journal |
Chin. Phys. C |
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Volume |
45 |
Issue |
1 |
Pages |
013107 - 8pp |
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Keywords |
alternative theories of gravity; singularities; Einstein-Gauss-Bonnet |
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Abstract |
We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined terms in the four dimensional field equations. Potential ways to circumvent this issue are discussed, alongside remarks regarding specific solutions of the theory. We prove that, although linear perturbations are well behaved around maximally symmetric backgrounds, the equations for second-order perturbations are ill-defined even around a Minkowskian background. Additionally, we perform a detailed analysis of the spherically symmetric solutions and find that the central curvature singularity can be reached within a finite proper time. |
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Address |
[Arrechea, Julio] CSIC, Inst Astrofis Andalucia, Granada, Spain, Email: arrechea@iaa.es; |
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Publisher |
Iop Publishing Ltd |
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English |
Summary Language |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1674-1137 |
ISBN |
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Conference |
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Notes |
WOS:000606026400001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
4676 |
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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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Corporate Author |
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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 |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3624 |
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Author |
Arrighi, P.; Di Molfetta, G.; Marquez-Martin, I.; Perez, A. |
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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 |
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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Corporate Author |
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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 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 |
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 |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4081 |
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