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Arnault, P., Pepper, B., & Perez, A. (2020). Quantum walks in weak electric fields and Bloch oscillations. Phys. Rev. A, 101(6), 062324–12pp.
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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Arnault, P., Perez, A., Arrighi, P., & Farrelly, T. (2019). Discrete-time quantum walks as fermions of lattice gauge theory. Phys. Rev. A, 99(3), 032110–16pp.
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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Arrechea, J., Delhom, A., & Jimenez-Cano, A. (2021). Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity. Chin. Phys. C, 45(1), 013107–8pp.
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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Arrighi, P., Di Molfetta, G., Marquez-Martin, I., & Perez, A. (2019). From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks. Sci Rep, 9, 10904–10pp.
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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Asai, M., Cortes-Giraldo, M. A., Gimenez-Alventosa, V., Gimenez, V., & Salvat, F. (2021). The PENELOPE Physics Models and Transport Mechanics. Implementation into Geant4. Front. Physics, 9, 738735–20pp.
Abstract: A translation of the penelope physics subroutines to C++, designed as an extension of the Geant4 toolkit, is presented. The Fortran code system penelope performs Monte Carlo simulation of coupled electron-photon transport in arbitrary materials for a wide energy range, nominally from 50 eV up to 1 GeV. Penelope implements the most reliable interaction models that are currently available, limited only by the required generality of the code. In addition, the transport of electrons and positrons is simulated by means of an elaborate class II scheme in which hard interactions (involving deflection angles or energy transfers larger than pre-defined cutoffs) are simulated from the associated restricted differential cross sections. After a brief description of the interaction models adopted for photons and electrons/positrons, we describe the details of the class-II algorithm used for tracking electrons and positrons. The C++ classes are adapted to the specific code structure of Geant4. They provide a complete description of the interactions and transport mechanics of electrons/positrons and photons in arbitrary materials, which can be activated from the G4ProcessManager to produce simulation results equivalent to those from the original penelope programs. The combined code, named PenG4, benefits from the multi-threading capabilities and advanced geometry and statistical tools of Geant4.
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