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Arganda, E., Marcano, X., Martin Lozano, V., Medina, A. D., Perez, A. D., Szewc, M., et al. (2022). A method for approximating optimal statistical significances with machine-learned likelihoods. Eur. Phys. J. C, 82(11), 993–14pp.
Abstract: Machine-learning techniques have become fundamental in high-energy physics and, for new physics searches, it is crucial to know their performance in terms of experimental sensitivity, understood as the statistical significance of the signal-plus-background hypothesis over the background-only one. We present here a simple method that combines the power of current machine-learning techniques to face high-dimensional data with the likelihood-based inference tests used in traditional analyses, which allows us to estimate the sensitivity for both discovery and exclusion limits through a single parameter of interest, the signal strength. Based on supervised learning techniques, it can perform well also with high-dimensional data, when traditional techniques cannot. We apply the method to a toy model first, so we can explore its potential, and then to a LHC study of new physics particles in dijet final states. Considering as the optimal statistical significance the one we would obtain if the true generative functions were known, we show that our method provides a better approximation than the usual naive counting experimental results.
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Angles-Castillo, A., & Perez, A. (2022). A quantum walk simulation of extra dimensions with warped geometry. Sci Rep, 12(1), 1926–12pp.
Abstract: We investigate the properties of a quantum walk which can simulate the behavior of a spin 1/2 particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry between two branes. Such a setup constitutes a 1+ 1 dimensional version of the Randall-Sundrum model, which plays an important role in high energy physics. In the continuum spacetime limit, the quantum walk reproduces the Dirac equation corresponding to the model, which allows to anticipate some of the properties that can be reproduced by the quantum walk. In particular, we observe that the probability distribution becomes, at large time steps, concentrated near the “low energy” brane, and can be approximated as the lowest eigenstate of the continuum Hamiltonian that is compatible with the symmetries of the model. In this way, we obtain a localization effect whose strength is controlled by a warp coefficient. In other words, here localization arises from the geometry of the model, at variance with the usual effect that is originated from random irregularities, as in Anderson localization. In summary, we establish an interesting correspondence between a high energy physics model and localization in quantum walks.
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Hinarejos, M., Bañuls, M. C., & Perez, A. (2013). A Study of Wigner Functions for Discrete-Time Quantum Walks. J. Comput. Theor. Nanosci., 10(7), 1626–1633.
Abstract: We perform a systematic study of the discrete time Quantum Walk on one dimension using Wigner functions, which are generalized to include the chirality (or coin) degree of freedom. In particular, we analyze the evolution of the negative volume in phase space, as a function of time, for different initial states. This negativity can be used to quantify the degree of departure of the system from a classical state. We also relate this quantity to the entanglement between the coin and walker subspaces.
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Bernal, A., & Perez, A. (2012). Analytic behavior of the QED polarizability function at finite temperature. AIP Adv., 2(1), 012152–9pp.
Abstract: We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is non analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.
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Perez, A. (2016). Asymptotic properties of the Dirac quantum cellular automaton. Phys. Rev. A, 93(1), 012328–10pp.
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.
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Angles-Castillo, A., Perez, A., & Roldan, E. (2024). Bright and dark solitons in a photonic nonlinear quantum walk: lessons from the continuum. New J. Phys., 26(2), 023004–16pp.
Abstract: We propose a nonlinear quantum walk model inspired in a photonic implementation in which the polarization state of the light field plays the role of the coin-qubit. In particular, we take profit of the nonlinear polarization rotation occurring in optical media with Kerr nonlinearity, which allows to implement a nonlinear coin operator, one that depends on the state of the coin-qubit. We consider the space-time continuum limit of the evolution equation, which takes the form of a nonlinear Dirac equation. The analysis of this continuum limit allows us to gain some insight into the existence of different solitonic structures, such as bright and dark solitons. We illustrate several properties of these solitons with numerical calculations, including the effect on them of an additional phase simulating an external electric field.
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Hinarejos, M., Di Franco, C., Romanelli, A., & Perez, A. (2014). Chirality asymptotic behavior and non-Markovianity in quantum walks on a line. Phys. Rev. A, 89(5), 052330–7pp.
Abstract: We investigate the time evolution of the chirality reduced density matrix for a discrete-time quantum walk on a one-dimensional lattice. The matrix is obtained by tracing out the spatial degree of freedom. We analyze the standard case, without decoherence, and the situation in which decoherence appears in the form of broken links in the lattice. By examining the trace distance for possible pairs of initial states as a function of time, we conclude that the evolution of the reduced density matrix is non-Markovian, in the sense defined by Breuer, Laine, and Piilo [Phys. Rev. Lett. 103, 210401 (2009)]. As the level of noise increases, the dynamics approaches a Markovian process. The highest non-Markovianity corresponds to the case without decoherence. The reduced density matrix tends always to a well-defined limit that we calculate, but only in the decoherence-free case is this limit nontrivial.
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Lopez-Fogliani, D. E., Perez, A. D., & Ruiz de Austri, R. (2021). Dark matter candidates in the NMSSM with RH neutrino superfields. J. Cosmol. Astropart. Phys., 04(4), 067–35pp.
Abstract: R-parity conserving supersymmetric models with right-handed (RH) neutrinos are very appealing since they could naturally explain neutrino physics and also provide a good dark matter (DM) candidate such as the lightest supersymmetric particle (LSP). In this work we consider the next-to-minimal supersymmetric standard model (NMSSM) plus RH neutrino superfields, with effective Majorana masses dynamically generated at the electroweak scale (EW). We perform a scan of the relevant parameter space and study both possible DM candidates: RH sneutrino and neutralino. Especially for the case of RH sneutrino DM we analyse the intimate relation between both candidates to obtain the correct amount of relic density. Besides the well-known resonances, annihilations through scalar quartic couplings and coannihilation mechanisms with all kind of neutralinos, are crucial. Finally, we present the impact of current and future direct and indirect detection experiments on both DM candidates.
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Gomis, P., & Perez, A. (2016). Decoherence effects in the Stern-Gerlach experiment using matrix Wigner functions. Phys. Rev. A, 94(1), 012103–11pp.
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.
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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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