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de Vega, I., Bañuls, M. C., & Perez, A. (2010). Effects of dissipation on an adiabatic quantum search algorithm. New J. Phys., 12, 123010–19pp.
Abstract: According to recent studies (Amin et al 2008 Phys. Rev. Lett. 100 060503), the effect of a thermal bath may improve the performance of a quantum adiabatic search algorithm. In this paper, we compare the effects of such a thermal environment on the algorithm performance with those of a structured environment similar to the one encountered in systems coupled to an electromagnetic field that exists within a photonic crystal. Whereas for all the parameter regimes explored here, the algorithm performance is worsened by contact with a thermal environment, the picture appears to be different when one considers a structured environment. In this case we show that by tuning the environment parameters to certain regimes, the algorithm performance can actually be improved with respect to the closed system case. Additionally, the relevance of considering the dissipation rates as complex quantities is discussed in both cases. More specifically, we find that the imaginary part of the rates cannot be neglected with the usual argument that it simply amounts to an energy shift and in fact influences crucially the system dynamics.
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Hinarejos, M., Perez, A., & Bañuls, M. C. (2012). Wigner function for a particle in an infinite lattice. New J. Phys., 14, 103009–19pp.
Abstract: We study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a one-dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definition of the Wigner function in this case and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system, which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states and to their superpositions.
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Hinarejos, M., Perez, A., Roldan, E., Romanelli, A., & de Valcarcel, G. J. (2013). Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more. New J. Phys., 15, 073041–31pp.
Abstract: The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrodinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-dimensional Grover walks are presented.
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Hinarejos, M., Bañuls, M. C., & Perez, A. (2015). Wigner formalism for a particle on an infinite lattice: dynamics and spin. New J. Phys., 17, 013037–16pp.
Abstract: The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Banuls MC and Perez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included.
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Di Molfetta, G., & Perez, A. (2016). Quantum walks as simulators of neutrino oscillations in a vacuum and matter. New J. Phys., 18, 103038–8pp.
Abstract: We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in a vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing one to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, the simulation of neutrino oscillations with the help of quantum walks might be useful to illustrate these effects in extreme conditions, such as the solar interior or supernovae.
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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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Kim, J. S., Lopez-Fogliani, D. E., Perez, A. D., & Ruiz de Austri, R. (2022). The new (g-2)(mu) and right-handed sneutrino dark matter. Nucl. Phys. B, 974, 115637–23pp.
Abstract: In this paper we investigate the (g – 2)(mu) discrepancy in the context of the R-parity conserving next-to minimal supersymmetric Standard Model plus right-handed neutrinos superfields. The model has the ability to reproduce neutrino physics data and includes the interesting possibility to have the right-handed sneutrino as the lightest supersymmetric particle and a viable dark matter candidate. Since right-handed sneutrinos are singlets, no new contributions for delta a(mu) with respect to the MSSM and NMSSM are present. However, the possibility to have the right-handed sneutrino as the lightest supersymmetric particle opens new ways to escape Large Hadron Collider and direct detection constraints. In particular, we find that dark matter masses within 10 less than or similar to m((upsilon) over tildeR) less than or similar to 600 GeV are fully compatible with current experimental constraints. Remarkably, not only spectra with light sleptons are needed, but we obtain solutions with m((mu) over tilde) greater than or similar to 600 GeV in the entire dark matter mass range that could be probed by new (g – 2)(mu) data in the near future. In addition, dark matter direct detection experiments will be able to explore a sizable portion of the allowed parameter space with mvR < 300 GeV, while indirect detection experiments will be able to probe a much smaller fraction within 200 less than or similar to m((nu)over tilde>R) less than or similar to 350 GeV.
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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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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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