Records |
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 |
|
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 |
|
Series Issue |
|
Edition |
|
ISSN |
2469-9926 |
ISBN |
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Medium |
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Area |
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Expedition |
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Conference |
|
Notes |
WOS:000461896700002 |
Approved |
no |
Is ISI |
yes |
International Collaboration |
yes |
Call Number |
IFIC @ pastor @ |
Serial |
3950 |
Permanent link to this record |
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Author |
Arnault, P.; Pepper, B.; Perez, A. |
Title |
Quantum walks in weak electric fields and Bloch oscillations |
Type |
Journal Article |
Year |
2020 |
Publication |
Physical Review A |
Abbreviated Journal |
Phys. Rev. A |
Volume |
101 |
Issue |
6 |
Pages |
062324 - 12pp |
Keywords |
|
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)]. |
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; |
Corporate Author |
|
Thesis |
|
Publisher |
Amer Physical Soc |
Place of Publication |
|
Editor |
|
Language |
English |
Summary Language |
|
Original Title |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
1050-2947 |
ISBN |
|
Medium |
|
Area |
|
Expedition |
|
Conference |
|
Notes |
WOS:000541400900002 |
Approved |
no |
Is ISI |
yes |
International Collaboration |
yes |
Call Number |
IFIC @ pastor @ |
Serial |
4431 |
Permanent link to this record |