Relativistic Wigner Function for Quantum Walks

,; Debbasch, Fabrice

doi:10.21926/rpm.2001002

Cited by 1 publication

(4 citation statements)

References 57 publications

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“…(51) to Eqs. (52). The case of a non-vanishing mass, m = 0, and no noise, Γ = 0, simply corresponds to standard, Dirac propagation [63,64], and is recalled in Appendix C.…”

Section: System Of Equations In Position Space and Remarksmentioning

confidence: 99%

“…(61) alone: because of the vanishing mass, it contains no quantum feature. If one can write down a dynamical equation for the density and current density, and needs no quantum amplitude of probability 11 , this means that the essence of the quantumness of the system, that is, coherence and entanglement, is, if any, limited to the internal off-diagonal space, described byr 1 andr 2 , coupled to each other through the system of equations (52), which is autonomous (i.e., independent of (51)) because m vanishes. That Eq.…”

Section: System Of Equations In Position Space and Remarksmentioning

confidence: 99%

“…It was first revisited by Cattaneo [9], who suggested to model relativistic diffusion through the telegraph equation, and whose work, coupled with the Grad expansion technique [10] (see also Ref. [52] in Ref. [11]), laid the basis of the * pablo.arnault@ific.uv.es so-called Extended Thermodynamics theories [12].…”

Section: Introductionmentioning

confidence: 99%

“…The connections between DTQWs and lattice gauge theories have also been explored [46][47][48][49], and Wigner functions for DTQWs have been proposed in Refs. [50][51][52]. A crucial feature of DTQWs is that they are intrinsically causal, i.e., information propagates, at most, at a finite velocity c = 1, which is why DTQWs are a priori especially suited to model quantum relativistic diffusions.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantum simulation of quantum relativistic diffusion via quantum walks

Arnault¹,

Macquet²,

Anglés-Castillo³

et al. 2020

J. Phys. A: Math. Theor.

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Two models are first presented, of 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 byconstruction (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.

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“…(51) to Eqs. (52). The case of a non-vanishing mass, m = 0, and no noise, Γ = 0, simply corresponds to standard, Dirac propagation [63,64], and is recalled in Appendix C.…”

Section: System Of Equations In Position Space and Remarksmentioning

confidence: 99%

Section: System Of Equations In Position Space and Remarksmentioning

confidence: 99%