Records |
Author |
Perez, A. |
Title |
Asymptotic properties of the Dirac quantum cellular automaton |
Type |
Journal Article |
Year |
2016 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
Volume |
93 |
Issue |
1 |
Pages |
012328 - 10pp |
Keywords |
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Abstract |
We show that the Dirac quantum cellular automaton [A. Bisio, G. M. D'Ariano, and A. Tosini, Ann. Phys. (N. Y.) 354, 244 (2015)] shares many properties in common with the discrete-time quantum walk. These similarities can be exploited to study the automaton as a unitary process that takes place at regular time steps on a one-dimensional lattice, in the spirit of general quantum cellular automata. In this way, it becomes an alternative to the quantum walk, with a dispersion relation that can be controlled by a parameter that plays a similar role to the coin angle in the quantum walk. The Dirac Hamiltonian is recovered under a suitable limit. We provide two independent analytical approximations to the long-term probability distribution. It is shown that, starting from localized conditions, the asymptotic value of the entropy of entanglement between internal and motional degrees of freedom overcomes the known limit that is approached by the quantum walk for the same initial conditions and is similar to the ones achieved by highly localized states of the Dirac equation. |
Address |
[Perez, A.] Univ Valencia, CSIC, IFIC, Dept Fis Teor, E-46100 Valencia, Spain |
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Thesis |
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Publisher |
Amer Physical Soc |
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English |
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Edition |
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ISSN |
1050-2947 |
ISBN |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000368291600005 |
Approved |
no |
Is ISI |
yes |
International Collaboration |
no |
Call Number |
IFIC @ pastor @ |
Serial |
2520 |
Permanent link to this record |
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Author |
Gomis, P.; Perez, A. |
Title |
Decoherence effects in the Stern-Gerlach experiment using matrix Wigner functions |
Type |
Journal Article |
Year |
2016 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
Volume |
94 |
Issue |
1 |
Pages |
012103 - 11pp |
Keywords |
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Abstract |
We analyze the Stern-Gerlach experiment in phase space with the help of the matrix Wigner function, which includes the spin degree of freedom. Such analysis allows for an intuitive visualization of the quantum dynamics of the device. We include the interaction with the environment, as described by the Caldeira-Leggett model. The diagonal terms of the matrix provide us with information about the two components of the state that arise from interaction with the magnetic field gradient. In particular, from the marginals of these components, we obtain an analytical formula for the position and momentum probability distributions in the presence of decoherence that shows a diffusive behavior for large values of the decoherence parameter. These features limit the dynamics of the present model. We also observe the decay of the nondiagonal terms with time and use this fact to quantify the amount of decoherence from the norm of those terms in phase space. From here, we can define a decoherence time scale, which differs from previous results that make use of the same model. We analyze a typical experiment and show that, for that setup, the decoherence time is much smaller than the characteristic time scale for the separation of the two beams, implying that they can be described as an incoherent mixture of atoms traveling in the up and down directions with opposite values of the spin projection. Therefore, entanglement is quickly destroyed in the setup we analyzed. |
Address |
[Gomis, P.] Univ Valencia, CSIC, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: Pablo.Gomis@uv.es; |
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Thesis |
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Publisher |
Amer Physical Soc |
Place of Publication |
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English |
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Original Title |
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Series Editor |
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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:000378909000003 |
Approved |
no |
Is ISI |
yes |
International Collaboration |
no |
Call Number |
IFIC @ pastor @ |
Serial |
2739 |
Permanent link to this record |
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Author |
Arnault, P.; Di Molfetta, G.; Brachet, M.; Debbasch, F. |
Title |
Quantum walks and non-Abelian discrete gauge theory |
Type |
Journal Article |
Year |
2016 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
Volume |
94 |
Issue |
1 |
Pages |
012335 - 6pp |
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. |
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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Thesis |
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Publisher |
Amer Physical Soc |
Place of Publication |
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Editor |
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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 |
Is ISI |
yes |
International Collaboration |
yes |
Call Number |
IFIC @ pastor @ |
Serial |
2761 |
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. |
Title |
Quantum walk on a cylinder |
Type |
Journal Article |
Year |
2016 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
Volume |
94 |
Issue |
3 |
Pages |
032328 - 7pp |
Keywords |
|
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. |
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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Amer Physical Soc |
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English |
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Series Editor |
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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 |
Is ISI |
yes |
International Collaboration |
yes |
Call Number |
IFIC @ pastor @ |
Serial |
2823 |
Permanent link to this record |
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Author |
Marquez-Martin, I.; Di Molfetta, G.; Perez, A. |
Title |
Fermion confinement via quantum walks in (2+1)-dimensional and (3+1)-dimensional space-time |
Type |
Journal Article |
Year |
2017 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
Volume |
95 |
Issue |
4 |
Pages |
042112 - 5pp |
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. |
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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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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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 |
Is ISI |
yes |
International Collaboration |
yes |
Call Number |
IFIC @ pastor @ |
Serial |
3102 |
Permanent link to this record |
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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 |
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Publisher |
Amer Physical Soc |
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Editor |
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English |
Summary Language |
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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 |
Permanent link to this record |
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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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Publisher |
Amer Physical Soc |
Place of Publication |
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Editor |
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English |
Summary Language |
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Series Editor |
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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 |
Permanent link to this record |
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Author |
Martone, G.I.; Larre, P.E.; Fabbri, A.; Pavloff, N. |
Title |
Momentum distribution and coherence of a weakly interacting Bose gas after a quench |
Type |
Journal Article |
Year |
2018 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
Volume |
98 |
Issue |
6 |
Pages |
063617 - 21pp |
Keywords |
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Abstract |
We consider a weakly interacting uniform atomic Bose gas with a time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov treatment we investigate the time evolution of several observables, including the momentum distribution, the degree of coherence in the system, and their dependence on dimensionality and temperature. We rigorously prove that the low-momentum Bogoliubov modes remain frozen during the whole evolution, while the high-momentum ones adiabatically follow the change in time of the interaction strength. At intermediate momenta we point out the occurrence of oscillations, which are analogous to Sakharov oscillations. We identify two wide classes of time-dependent behaviors of the coupling for which an exact solution of the problem can be found, allowing for an analytic computation of all the relevant observables. A special emphasis is put on the study of the coherence property of the system in one spatial dimension. We show that the system exhibits a smooth “light-cone effect,” with typically no prethermalization. |
Address |
[Martone, Giovanni I.; Pavloff, Nicolas] Univ Paris Saclay, Univ Paris Sud, CNRS, LPTMS,UMR 8626, F-91405 Orsay, France |
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Amer Physical Soc |
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English |
Summary Language |
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Series Editor |
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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:000452949900009 |
Approved |
no |
Is ISI |
yes |
International Collaboration |
yes |
Call Number |
IFIC @ pastor @ |
Serial |
3841 |
Permanent link to this record |
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Author |
Arnault, P.; Perez, A.; Arrighi, P.; Farrelly, T. |
Title |
Discrete-time quantum walks as fermions of lattice gauge theory |
Type |
Journal Article |
Year |
2019 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
Volume |
99 |
Issue |
3 |
Pages |
032110 - 16pp |
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. |
Address |
[Arnault, Pablo; Perez, Armando] Univ Valencia, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: pablo.arnault@ific.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 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:000461896700002 |
Approved |
no |
Is ISI |
yes |
International Collaboration |
yes |
Call Number |
IFIC @ pastor @ |
Serial |
3950 |
Permanent link to this record |