Ergodic statistical models: Entropic dynamics and chaos

We present an extension of the ergodic, mixing and Bernoulli levels of the ergodic hierarchy in dynamical systems, the information geometric ergodic hierarchy, making use of statistical models on curved manifolds in the context of information geometry. We discuss the 2×2 Gaussian Orthogonal Ensembles (GOE) within a 2D correlated model. For values of the correlation coefficient vanishingly small, we find that GOE belong to the information geometric (IG) mixing level having a maximum negative value of scalar curvature. Moreover, we propose a measure of distinguishability for the family of distributions of the 2D correlated model that results to be an upper bound of the IG correlation.Instituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica

Aspectos asintóticos y geométricos del caos cuántico

En esta Tesis Doctoral se desarrollan herramientas geométricas desde el marco teórico de la geometría diferencial y de la teoría de la información para estudiar el caos cuántico y de esta forma dar una visión más completa del mismo. Para ello, en primer lugar estudiamos los fenómenos característicos del caos cuántico y de sus correspondientes escalas temporales en términos de valores medios cuánticos. Esto permitió obtener a una caracterización asintótica de fenómenos del caos cuántico expresada por: 1) la jerarquía ergódica cuántica (abreviadamente QEH, del inglés Quantum Ergodic Hierarchy), 2) una versión cuántica del Teorema de Descomposición Espectral de Sistemas Dinámicos (abreviadamente QSDT, del inglés Quantum Spectrum Decomposition Theorem), 3) la granulosidad fundamental, 4) una condición de caos en el límite clásico basada en el teorema de Pesin y 5) una derivación de los ensambles gaussianos desde el nivel mixing de la QEH.Facultad de Ciencias Exacta

About the concept of quantum chaos

The research on quantum chaos finds its roots in the study of the spectrum of complex nuclei in the 1950s and the pioneering experiments in microwave billiards in the 1970s. Since then, a large number of new results was produced. Nevertheless, the work on the subject is, even at present, a superposition of several approaches expressed in different mathematical formalisms and weakly linked to each other. The purpose of this paper is to supply a unified framework for describing quantum chaos using the quantum ergodic hierarchy. Using the factorization property of this framework, we characterize the dynamical aspects of quantum chaos by obtaining the Ehrenfest time. We also outline a generalization of the quantum mixing level of the kicked rotator in the context of the impulsive differential equations.Instituto de Física La Plat

Distinguishability notion based on Wootters statistical distance : Application to discrete maps

We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d for an arbitrary discrete map. Moreover, from d, we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the metric d, which allows us to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and analytically, and we obtain d and the wandering set for some characteristic values of their parameters. Finally, an extension of the metric space associated for arbitrary probability distributions (not necessarily invariant densities) is given along with some consequences. The statistical properties of distributions given by histograms are characterized in terms of the cardinal of the associated metric space. For two conjugate variables, the uncertainty principle is expressed in terms of the diameters of the associated metric space with those variables.Instituto de Física La Plat

Gaussian ensembles distributions from mixing quantum systems

In the context of dynamical systems we present a derivation of the Gaussian ensembles distributions from quantum systems having a classical analogue that is mixing. We find that factorization property is satisfied for the mixing quantum systems expressed as a factorization of quantum mean values. For the case of the kicked rotator and in its fully chaotic regime, the factorization property links decoherence by dephasing with Gaussian ensembles in terms of the weak limit, interpreted as a decohered state. Moreover, a discussion about the connection between random matrix theory and quantum chaotic systems, based on some attempts made in previous works and from the viewpoint of the mixing quantum systems, is presented.Instituto de Física La Plat

About the concept of quantum chaos

The research on quantum chaos finds its roots in the study of the spectrum of complex nuclei in the 1950s and the pioneering experiments in microwave billiards in the 1970s. Since then, a large number of new results was produced. Nevertheless, the work on the subject is, even at present, a superposition of several approaches expressed in different mathematical formalisms and weakly linked to each other. The purpose of this paper is to supply a unified framework for describing quantum chaos using the quantum ergodic hierarchy. Using the factorization property of this framework, we characterize the dynamical aspects of quantum chaos by obtaining the Ehrenfest time. We also outline a generalization of the quantum mixing level of the kicked rotator in the context of the impulsive differential equations.Instituto de Física La Plat

Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping

In this work we explore a generalization of the Dirac and Klein-Gordon (KG) oscillators, provided with a deformed linear momentum inspired in nonextensive statistics, that gives place to the Morse potential in relativistic contexts by first principles. In the (1+1)-dimensional case the relativistic oscillators are mapped into the quantum Morse potential. Using the Pekeris approximation, in the (3+1)-dimensional case we study the thermodynamics of the S-waves states (l=0) of the H2, LiH, HCl and CO molecules (in the non-relativistic limit) and of a relativistic electron, where Schottky anomalies (due to the finiteness of the Morse spectrum) and spin contributions to the heat capacity are reported. By revisiting a generalized Pekeris approximation, we provide a mapping from (3+1)-dimensional Dirac and KG equations with a spherical potential to an associated one-dimensional Schrödinger-like equation, and we obtain the family of potentials for which this mapping corresponds to a Schr\"odinger equation with non-minimal coupling.Instituto de Física La Plat

Enigmatic traces in infaunal bivalves from the late Quaternary of Argentina, Southwestern Atlantic. Bioerosion, bioclaustration or nothing?

Ichnological investigations were carried out on late Quaternary shells of the intertidal deep infaunal bivalve Tagelus plebeius (Lightfoot, 1786) found along the southwestern Atlantic, between Uruguay and the southernmost Buenos Aires Province in Argentina. Analyses reveal distinctive marks that are spread on the outer shell surface only. The marks are regular-unbranched-elongate, perpendicular to the outer shell growth lines, with deflections on the margins, never interconnected, without bifurcations, conforming bottom-up constructions. They occur in hundreds of specimens from many samples taken from sediments ranging in age from the late Pleistocene to the Recent. These marks have never been reported or described for this species and their origin and formation remain elusive. We describe these traces thoroughly and we propose an explanation for their preservation on about half the shells examined. Potential destructive boring structures (excavated from outside-in) or bioerosion activities by other macro- or micro-organisms are dismissed. These antimarginal asymmetric traces point instead to a process of constructive bioclaustrations (grown from the bottom-up) produced in situ during the life of the bivalve by unknown symbiont organisms. Additionally, the regular pattern observed for the marks exclude host growth as a consequence of abiotic/extrinsic causes. From a palaeoecological perspective, these structures suggest a biotic interaction that was hitherto undescribed neither for bivalves nor for the late Quaternary of the southwestern Atlantic.Facultad de Ciencias Naturales y MuseoCentro de Investigaciones Geológica

Enigmatic traces in infaunal bivalves from the late Quaternary of Argentina, Southwestern Atlantic. Bioerosion, bioclaustration or nothing?

Ichnological investigations were carried out on late Quaternary shells of the intertidal deep infaunal bivalve Tagelus plebeius (Lightfoot, 1786) found along the southwestern Atlantic, between Uruguay and the southernmost Buenos Aires Province in Argentina. Analyses reveal distinctive marks that are spread on the outer shell surface only. The marks are regular-unbranched-elongate, perpendicular to the outer shell growth lines, with deflections on the margins, never interconnected, without bifurcations, conforming bottom-up constructions. They occur in hundreds of specimens from many samples taken from sediments ranging in age from the late Pleistocene to the Recent. These marks have never been reported or described for this species and their origin and formation remain elusive. We describe these traces thoroughly and we propose an explanation for their preservation on about half the shells examined. Potential destructive boring structures (excavated from outside-in) or bioerosion activities by other macro- or micro-organisms are dismissed. These antimarginal asymmetric traces point instead to a process of constructive bioclaustrations (grown from the bottom-up) produced in situ during the life of the bivalve by unknown symbiont organisms. Additionally, the regular pattern observed for the marks exclude host growth as a consequence of abiotic/extrinsic causes. From a palaeoecological perspective, these structures suggest a biotic interaction that was hitherto undescribed neither for bivalves nor for the late Quaternary of the southwestern Atlantic.Fil: Richiano, Sebastián Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico; ArgentinaFil: Aguirre, Marina Laura. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Farinati, Ester Amanda. Universidad Nacional del Sur. Departamento de Geología; ArgentinaFil: Davies, Karen Elizabeth. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo; ArgentinaFil: Castellanos, Ignacio. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo; ArgentinaFil: Gómez-Peral, Lucia. E.. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Geológicas. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. Centro de Investigaciones Geológicas; Argentin

Abdominal adiposity increases lordosis and doubles the risk of low back pain

Vertebral disorders have significant health and economic impacts, and due to aging and current lifestyle habits, there is a trend toward their increase. Obesity and the alignment of vertebral curvatures can be associated with back pain. Objective: This study aims to analyze whether general and abdominal obesity are associated with cervical, dorsal, and lumbar vertebral pain as well as increased or decreased values of cervical, dorsal, and lumbar vertebral curvatures. Methodology: Body composition, degree of vertebral curvature, and the perception of cervical, dorsal, and lumbar pain were evaluated in a study population of 301 people (>18 years old). Linear and logistic regression analyses were performed to evaluate the influence of several variables of body composition on vertebral angles and cervical, dorsal, and lumbar pain. Results: Lumbar pain was the most prevalent (66.1%), mainly affecting women (70.9%). They were also shown to have greater lumbar angles (p < 0.001). The degrees of lumbar curvature increased, as did the BMI, waist circumference, and waist-to-height ratio. Cervical and dorsal curvatures were increased by all the variables of adiposity and abdominal adiposity. It was found that people with abdominal obesity carried twice the risk of lower back pain than those without abdominal obesity (OR = 2.172, p < 0.05). In addition, an increased lumbar angle was related to an increased risk of low back pain (OR = 1.031, p < 0.05). Cervical pain, on the other hand, was associated with the waist-height index (OR = 0.948, p <0.01). Conclusions: This study shows that increased lumbar curvature and abdominal obesity may be risk factors for lower back pain. In addition, it shows an association between the amount of body and abdominal fat in relation to the degree of curvature of the spine in the sagittal plane. Investigating the effect of obesity on vertebral morphology and musculoskeletal disorders makes it possible to prescribe interventions and therapeutic strategie