Complex behavior of the density in composite quantum systems

In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the pattern of this distribution. We discuss the main features of the latter and explain analytically those that we understand. In particular, we prove that it is a nonperturbative property and we find out a large/small coupling constant duality. We also find and study features that may connect our problem with certain aspects of nonlinear classical dynamics, such as the existence of resonances and sensitive dependence on the state of the system. We show that the latter has, indeed, a similar origin than in classical mechanics: the appearance of small denominators in the perturbative series. Inspired by the proof of the Kolmogorov-Arnold-Moser theorem, we are able to deal with this problem by introducing a cutoff in energies that eliminates these small denominators. We also formulate some conjectures that we are not able to prove at present but can be supported by numerical experiments

Sublogarithmic behaviour of the entanglement entropy in fermionic chains

In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the R\'enyi entanglement entropy for the ground state of long-range Kitaev chains with slow decaying couplings. We obtain that, under some circumstances, the entropy grows sublogarithmically with the length of the subsystem. Our result is based on the asymptotic behaviour of a new class of Toeplitz determinants whose symbol does not lie within the application domain of the Strong Szeg\H{o} Theorem or the Fisher-Hartwig conjecture.Comment: 30 pages, 4 figures, 1 table. Final version to appear in JSTAT. One new figure. Some comments and references adde

Sublogarithmic behaviour of the entanglement entropy in fermionic chains

In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the Rényi entanglement entropy for the ground state of long-range Kitaev chains with slow decaying couplings. We obtain that, under some circumstances, the entropy grows sublogarithmically with the length of the subsystem. Our result is based on the asymptotic behaviour of a new class of Toeplitz determinants whose symbol does not lie within the application domain of the Strong Szegő theorem or the Fisher–Hartwig conjecture

On the number of kk-cycles in the assignment problem for random matrices

We continue the study of the assignment problem for a random cost matrix. We analyse the number of $k$-cycles for the solution and their dependence on the symmetry of the random matrix. We observe that for a symmetric matrix one and two-cycles are dominant in the optimal solution. In the antisymmetric case the situation is the opposite and the one and two-cycles are suppressed. We solve the model for a pure random matrix (without correlations between its entries) and give analytic arguments to explain the numerical results in the symmetric and antisymmetric case. We show that the results can be explained to great accuracy by a simple ansatz that connects the expected number of $k$-cycles to that of one and two cycles.Comment: To appear in Journal of Statistical Mechanic

Generalized Central Limit Theorem and Renormalization Group

We introduce a simple instance of the renormalization group transformation in the Banach space of probability densities. By changing the scaling of the renormalized variables we obtain, as fixed points of the transformation, the L\'evy strictly stable laws. We also investigate the behavior of the transformation around these fixed points and the domain of attraction for different values of the scaling parameter. The physical interest of a renormalization group approach to the generalized central limit theorem is discussed.Comment: 16 pages, to appear in J. Stat. Phy

Burden of respiratory disease attributable to secondhand smoke exposure at home in children in Spain (2015)

This study aimed to estimate the number of incident cases and hospital admissions attributable to secondhand smoke (SHS) exposure at home for asthma, otitis media (OM), and lower respiratory infections (LRI) in children in Spain. The burden of respiratory disease caused by SHS exposure was estimated in terms of incident cases and hospitalized cases for asthma, OM, and LRI. Estimates were calculated using the population attributable fraction. The age-specific (0-1 year, 0-4 years, 5-11 years, and 0-11 years) prevalence of SHS exposure in children was estimated through a telephone survey performed in a representative sample of Spanish households with children in 2016. The risk estimates for all diseases were selected from international meta-analyses. The number of hospitalized cases was obtained for each disease from the Hospital Minimum Data Set provided by the Ministry of Health of Spain. Incident cases were obtained from the Global Health Data Exchange. In 2015, SHS exposure caused an estimated total of 136,403 incident cases of the following respiratory diseases: 9058 (8.5%) cases of asthma, 120,248 (8.5%) of OM, and 7097 (13.5%) of LRI in children aged 0–14 years old in Spain. Likewise, SHS exposure caused a total of 3028 hospitalized cases, with 379 (8.5%) for asthma and 167 (8.5%) for OM in children 0–11 years old, and 2482 (11.6%) for LRI in children <2 years old. The high burden of respiratory disease attributed to SHS exposure supports the need to improve protection of children against SHS exposure by extending smoke-free regulations to homes and cars.This work was supported by the Instituto de Salud Carlos III (PN I+D+I 2013–2016) and co-funded by the European Regional Development Fund (FEDER) (grant number PI13/02734). The Evaluation and Intervention Methods Service of the Public Health Agency of Barcelona and the Tobacco Control Unit of the Catalan Institute of Oncology were also partially supported by the Ministry of Universities and Research of Catalonia (AGAUR) (grant numbers 2014SGR1373 and 2014SGR319). This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 681040S

Changes in prevalence and socioeconomic inequalities in secondhand smoke exposure in Spanish children 2016-2019

Introduction: Children are vulnerable to secondhand smoke (SHS) exposure, especially those with lower socioeconomic status. This study assesses the changes in prevalence and socioeconomic inequalities in SHS exposure in children younger than 12 years old in Spain between 2016 and 2019. Methods: We conducted two cross-sectional studies among representative samples of households with children aged 0.05), while decreased in smoke-free rules in cars (p=0.039). Conclusions: Reported SHS exposure among children in Spain remained high between 2016 and 2019. Inequalities persisted at home, highlighting the need for measures to reduce such exposure with an equity perspective

Study of the correlation between columnar aerosol burden, suspended matter at ground and chemical components in a background European environment

Although routinely monitored by ground based air quality networks, the particulate matter distribution could be eventually better described with remote sensing techniques. However, valid relationships between ground level and columnar ground based quantities should be known beforehand. In this study we have performed a comparison between particulate matter measurements at ground level at different cut sizes (10, 2.5 and 1.0 mm), and the aerosol optical depth obtained by means of a ground based sunphotometer during a multiinstrumental field campaign held in El Arenosillo (Huelva, Spain) from 28 June to 4 July 2006. All the PM fractions were very well correlated with AOD with correlation coefficients that ranged from 0.71 to 0.81 for PM10, PM2.5 and PM1. Furthermore, the influence of the mixing layer height in the correlations was explored. The improvement in the correlation when the vertical distribution is taken into account was significant for days with a homogeneous mixing layer. Moreover, the chemical analysis of the individual size fractions allowed us to study the origin of the particulate matter. Secondary components were the most abundant and also well correlated in the three size fractions; but for PM10 fraction, chemical species related to marine origin were best correlated. Finally, we obtained a relationship between MODIS L3 AOD from collection 5.1 and the three PM cut sizes. In spite of being a relatively clean environment, all the techniques were able to capture similar day to day variations during this field campaign.Peer ReviewedPostprint (published version

Burden of respiratory disease attributable to secondhand smoke exposure at home in children in Spain (2015)

This study aimed to estimate the number of incident cases and hospital admissions attributable to secondhand smoke (SHS) exposure at home for asthma, otitis media (OM), and lower respiratory infections (LRI) in children in Spain. The burden of respiratory disease caused by SHS exposure was estimated in terms of incident cases and hospitalized cases for asthma, OM, and LRI. Estimates were calculated using the population attributable fraction. The age-specific (0-1 year, 0-4 years, 5-11 years, and 0-11 years) prevalence of SHS exposure in children was estimated through a telephone survey performed in a representative sample of Spanish households with children in 2016. The risk estimates for all diseases were selected from international meta-analyses. The number of hospitalized cases was obtained for each disease from the Hospital Minimum Data Set provided by the Ministry of Health of Spain. Incident cases were obtained from the Global Health Data Exchange. In 2015, SHS exposure caused an estimated total of 136,403 incident cases of the following respiratory diseases: 9058 (8.5%) cases of asthma, 120,248 (8.5%) of OM, and 7097 (13.5%) of LRI in children aged 0-14 years old in Spain. Likewise, SHS exposure caused a total of 3028 hospitalized cases, with 379 (8.5%) for asthma and 167 (8.5%) for OM in children 0-11 years old, and 2482 (11.6%) for LRI in children <2 years old. The high burden of respiratory disease attributed to SHS exposure supports the need to improve protection of children against SHS exposure by extending smoke-free regulations to homes and cars