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Arrighi, P., Di Molfetta, G., Marquez-Martin, I., & Perez, A. (2018). Dirac equation as a quantum walk over the honeycomb and triangular lattices. Phys. Rev. A, 97(6), 062111–5pp.
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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Di Molfetta, G., Soares-Pinto, D. O., & Duarte Queiros, S. M. (2018). Elephant quantum walk. Phys. Rev. A, 97(6), 062112–6pp.
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.
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Marquez-Martin, I., Arnault, P., Di Molfetta, G., & Perez, A. (2018). Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks. Phys. Rev. A, 98(3), 032333–8pp.
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.
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Senes, E., Argyropoulos, T., Tecker, F., & Wuensch, W. (2018). Beam-loading effect on breakdown rate in high-gradient accelerating cavities: An experiment at the Compact Linear Collider Test Facility at CERN. Phys. Rev. Accel. Beams, 21(10), 102001–8pp.
Abstract: Radio frequency breakdown rate is a crucial performance parameter that ensures that the design luminosity is achieved in the CLIC linear collider. The required low breakdown rate for CLIC, of the order of 10(-7) breakdown pulse(-1) m(-1), has been demonstrated in a number of 12 GHz CLIC prototype structures at gradients in excess of the design 100 MV/m accelerating gradient, however without the presence of the accelerated beam and associated beam loading. The beam loading induced by the approximately 1 A CLIC main beam significantly modifies the field distribution inside the structures, and the effect on breakdown rate is potentially significant so needs to be determined. A dedicated experiment has been carried out in the CLIC Test Facility CTF3 to measure this effect, and the results are presented.
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Martone, G. I., Larre, P. E., Fabbri, A., & Pavloff, N. (2018). Momentum distribution and coherence of a weakly interacting Bose gas after a quench. Phys. Rev. A, 98(6), 063617–21pp.
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.
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