arXiv subjects

A. Pérez

Publications and source records attributed to A. Pérez.

17 recordsLinked to original sources

arXiv2024

Controllability for a non-local formulation of surface gravity waves

In this paper, we study the approximate controllability of a system governed by an evolution problem known as the sloshing problem. This problem involves a spatial, nonlocal differential operator inherent in the dynamics of a two-dimensional, incompressible, non-viscous fluid within a confined domain. Our work establishes unique continuation results that enable the application of source control localized in an interior domain, allowing the aforementioned controllability.

math.AP↗

arXiv2023

Timing performances of NectarCAM, a Medium Sized Telescope Camera for the Cherenkov Telescope Array

NectarCAM is a Cherenkov camera that will be installed on Medium-Sized Telescopes of the northern array of the Cherenkov Telescope Array Observatory (CTAO). It is composed of 265 modules, each of which includes 7 photo-multiplier tubes, a Front-End Board and a camera trigger system for data collection. The first NectarCAM unit is currently being integrated at CEA Paris-Saclay in France. Once installed at the CTAO's northern site, the NectarCAM's timing abilities will be crucial for reducing noise in images, improving image cleaning, and distinguishing between gamma-ray photons and cosmic-ray background. Additionally, it will enable coincidence identification with neighboring telescopes for stereoscopic observations. The timing system of NectarCAM has been tested in a dark room with various light sources. The results of the tests, including timing precision and accuracy of the trigger arrival relative to a laser source, and the timing of individual and multiple pixel signals, will be presented.

astro-ph.IM↗

arXiv2023

The NectarCAM Timing System

NectarCAM is a Cherenkov camera which is going to equip the Medium-Sized Telescopes (MST) of the northern site of the Cherenkov Telescope Array Observatory (CTAO). NectarCAM is equipped with 265 modules, each consisting of 7 photo-multiplier tubes (PMTs), a Front-End Board and a local camera trigger system used for data acquisition. This paper addresses the timing performance of NectarCAM which are crucial to reduce the noise in shower images and improve image cleaning as well as to discriminate between gamma-ray photons and cosmic-ray background and finally to allow coincidence identification with neighbouring telescopes for stereoscopic operations. Verification tests of the system have been performed in a dark room using various light sources to illuminate the first NectarCAM unit. The resulting timing precision and accuracy of the trigger arrival relative to a laser source, of individual and multiple pixel signals have been studied and are shown to comply to CTAO requirements.

astro-ph.IM↗

arXiv2022

On a class of robust nonconvex quadratic optimization problems

Let us consider the following robust nonconvex quadratic optimization problem: \begin{equation*} \begin{split} \min &~ \dfrac{1}{2} x^\top Ax+a^\top x \\ \text{s.t.}~ & α\leq\dfrac{1}{2}x^\top (B_1+μB_2)x+(b_1+δb_2)^\top x \leqβ,~ \forall~ μ\in [μ_1,μ_2],\forall~δ\in[δ_1,δ_2], \end{split} \end{equation*} where $A$, $B_1$, $B_2$ are real symmetric matrices, $μ_1,μ_2,δ_1,δ_2,α$, $β\in\mathbb{R}$ satisfying $μ_1\leq μ_2$, $δ_1\leqδ_2$ and $α<β$. We establish the robust alternative result; the robust S-lemma and the robust optimality for the above nonconvex problem.

math.OC↗

arXiv2020

Pre-deployment Verification and Predicted Mapping Speed of MUSCAT

The Mexico-UK Submillimetre Camera for AsTronomy (MUSCAT) is a 1.1 mm receiver consisting of 1,500 lumped-element kinetic inductance detectors (LEKIDs) for the Large Millimeter Telescope (LMT; Volcán Sierra Negra in Puebla, México). MUSCAT utilises the maximum field of view of the LMT's upgraded 50-metre primary mirror and is the first México-UK collaboration to deploy a millimetre/sub-mm receiver on the Large Millimeter Telescope. Using a simplistic simulator, we estimate a predicted mapping speed for MUSCAT by combining the measured performance of MUSCAT with the observed sky conditions at the LMT. We compare this to a previously calculated bolometric-model mapping speed and find that our mapping speed is in good agreement when this is scaled by a previously reported empirical factor. Through this simulation we show that signal contamination due to sky fluctuations can be effectively removed through the use of principle component analysis. We also give an overview of the instrument design and explain how this design allows for MUSCAT to be upgraded and act as an on-sky demonstration testbed for novel technologies after the facility-class TolTEC receiver comes online.

astro-ph.IM↗

arXiv2020

MUSCAT focal plane verification

The Mexico-UK Submillimetre Camera for Astronomy (MUSCAT) is the second-generation large-format continuum camera operating in the 1.1 mm band to be installed on the 50-m diameter Large Millimeter Telescope (LMT) in Mexico. The focal plane of the instrument is made up of 1458 horn coupled lumped-element kinetic inductance detectors (LEKID) divided equally into six channels deposited on three silicon wafers. Here we present the preliminary results of the complete characterisation in the laboratory of the MUSCAT focal plane. Through the instrument's readout system, we perform frequency sweeps of the array to identify the resonance frequencies, and continuous timestream acquisitions to measure and characterise the intrinsic noise and 1/f knee of the detectors. Subsequently, with a re-imaging lens and a black body point source, the beams of every detector are mapped, obtaining a mean FWHM size of $\sim$3.27 mm, close to the expected 3.1 mm. Then, by varying the intensity of a beam filling black body source, we measure the responsivity and noise power spectral density (PSD) for each detector under an optical load of 300 K, obtaining the noise equivalent power (NEP), with which we verify that the majority of the detectors are photon noise limited. Finally, using a Fourier Transform Spectrometer (FTS), we measure the spectral response of the instrument, which indicate a bandwidth of 1.0--1.2 mm centred on 1.1 mm, as expected.

astro-ph.IM↗

arXiv2020

Empirical best prediction of small area bivariate parameters

This paper introduces empirical best predictors of small area bivariate parameters, like ratios of sums or sums of ratios, by assuming that the target unit-level vector follows a bivariate nested error regression model. The corresponding means squared errors are estimated by parametric bootstrap. Several simulation experiments empirically study the behavior of the introduced statistical methodology. An application to real data from the Spanish household budget survey gives estimators of ratios of food household expenditures by provinces.

stat.ME↗

arXiv2020

Quantum walks in weak electric fields and Bloch oscillations

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 will 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); 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 semi-classical oscillations, i.e., oscillations of a localized particle, both for the electric TBH and the electric DQW. More precisely: The numerical simulations strongly suggest that the semi-classical DQW Bloch oscillations correspond to two counter-propagating semi-classical 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 counter-propagating 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.

quant-ph↗

arXiv2016

A Bourgain-like property of Banach spaces with no copies of $c_0$

We give a characterization of the existence of copies of $c_{0}$ in Banach spaces in terms of indexes. As an application, we deduce new proofs of James Distortion theorem and Bessaga-Pełczynski theorem about weakly unconditionally Cauchy series.

math.FA↗

arXiv2016

Baire theorem for ideals of sets

We study ideals $\mathcal{I}$ on $\mathbb{N}$ satisfying the following Baire-type property: if $X$ is a complete metric space and $\{X_{A} \colon A \in \mathcal{I} \}$ is a family of nowhere dense subsets of $X$ with $X_{A} \subset X_{B}$ whenever $A \subset B$, then $\bigcup_{A \in \mathcal{I}}{X_{A}} \neq X$. We give several characterizations and determine the ideals having this property among certain classes like analytic ideals and P-ideals. We also discuss similar covering properties when considering families of compact and meager subsets of $X$.

math.FA↗

arXiv2016

Asymptotic properties of the Dirac quantum cellular automaton

We show that the Dirac quantum cellular automaton [Ann. Phys. 354 (2015) 244] 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, which 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 are similar to the ones achieved by highly localized states of the Dirac equation.

quant-ph↗

arXiv2015

A study of decoherence effects in the Stern-Gerlach experiment using matrix Wigner functions

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 apparatus. 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 presence of decoherence, that show 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 non-diagonal 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.

quant-ph↗

arXiv2015

Obtaining a contradiction between local realism and quantum mechanics using only one correlation function

An ensemble consisting on systems of two entangled spin 1/2 particles, all of them in the same global quantum state, are considered. The two spins are measured, each of them, on a fixed direction, at two randomly selected measurement times. Realism, plus locality and freedom of choice referred to these chosen times, are assumed. Then, from the sole correlation function related to the two measurements, without considering any Bell inequalities, a contradiction between these assumptions and quantum mechanics is found.

quant-ph↗

arXiv2015

Wigner formalism for a particle on an infinite lattice: dynamics and spin

The recently proposed Wigner function for a particle in an infinite lattice [NJP 14, 103009 (2012)] is extended here to include an internal degree of freedom, as spin. 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. Discrete processes are also discussed. Finally we discuss the possibility of introducing a negativity concept for the Wigner function in the case in which the spin degree of freedom is included.

quant-ph↗

arXiv2012

Wigner function for a particle in an infinite lattice

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.

quant-ph↗

arXiv2010

Effects of dissipation in an adiabatic quantum search algorithm

We consider the effect of two different environments on the performance of the quantum adiabatic search algorithm, a thermal bath at finite temperature, and a structured environment similar to the one encountered in systems coupled to the electromagnetic field that exists within a photonic crystal. While for all the parameter regimes explored here, the algorithm performance is worsened by the contact with a thermal environment, the picture appears to be different when considering 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 particularly, we find that the imaginary part of the rates can not be neglected with the usual argument that it simply amounts to an energy shift, and in fact influences crucially the system dynamics.

quant-ph↗

arXiv2004

Equilibrium properties of self-interacting neutrinos in the quasi-particle approach

In this work a neutrino gas in equilibrium is studied both at T=0 and at finite temperature. Neutrinos are treated as massive Dirac quasi-particles with two generations. We include self-interactions among the neutrinos via neutral currents, as well as the interaction with a background of matter. To obtain the equilibrium properties we use Wigner function techniques. To account for corrections beyond the Hartree approximation, we also introduce correlation functions. We prove that, under the quasi-particle approximation, these correlation functions can be expressed as products of Wigner functions. We analyze the main properties of the neutrino eigenmodes in the medium, such as effective masses and mixing angle. We show that the formulae describing these quantities will differ with respect to the case with no self-interactions.

astro-ph↗