Tensorial dynamics on the space of quantum states

A geometric description of the space of states of a finite-dimensional quantum system and of the Markovian evolution associated with the Kossakowski-Lindblad operator is presented. This geometric setting is based on two composition laws on the space of observables defined by a pair of contravariant tensor fields. The first one is a Poisson tensor field that encodes the commutator product and allows us to develop a Hamiltonian mechanics. The other tensor field is symmetric, encodes the Jordan product and provides the variances and covariances of measures associated with the observables. This tensorial formulation of quantum systems is able to describe, in a natural way, the Markovian dynamical evolution as a vector field on the space of states. Therefore, it is possible to consider dynamical effects on non-linear physical quantities, such as entropies, purity and concurrence. In particular, in this work the tensorial formulation is used to consider the dynamical evolution of the symmetric and skew-symmetric tensors and to read off the corresponding limits as giving rise to a contraction of the initial Jordan and Lie products.Comment: 31 pages, 2 figures. Minor correction

Tangent bundle geometry from dynamics: application to the Kepler problem

In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which are diffeomorphic with affine spaces. In particular, we consider the problem in connection with conformal vector fields of second order and apply the procedure to vector fields conformally related with the harmonic oscillator (f-oscillators) . We select one which covers the vector field describing the Kepler problem.Comment: 17 pages, 2 figure

Comment on "Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction" [J. Chem. Phys. 137, 22A530 (2012)]

In spite of the relevance of the proposal introduced in the recent work A. Abedi, N. T. Maitra and E. K. U. Gross, J. Chem. Phys. 137, 22A530, 2012, there is an important ingredient which is missing. Namely, the proof that the norms of the electronic and nuclear wavefunctions which are the solutions to the nonlinear equations of motion are preserved by the evolution. To prove the conservation of these norms is precisely the objective of this Comment.Comment: 2 pages, published versio

SPORTS-RELATED ORO-FACIAL INJURIES: WHICH KIND OF MOUTHGUARD WILL BE THE MOST SUITABLE TO PLAY SAFE?

The risk of sports-related injuries is constantly present in various sporting activities, like box, rugby, tae-kwon-do, etc. Athletes should be informed of the best characteristics of a custom-made mouthguard in order to prevent oro-facial trauma. Materials used in the manufacture of mouthguards should satisfy a number of physical, mechanical and biological requirements. It is essential to differentiate the intra-oral devices available for the athletes to play safe. There are three main goals that should be taken into account, and that are provided by the authors’ modified occlusion outhguard (MOM): (i) the occlusal stability, by the contacts of the mouthguard with the antagonist teeth, (ii) the equilibrium of the masticatory muscles and (iii) the temporomandibular joint protection from excessive unbalanced forces

Nonextensive thermodynamic functions in the Schr\"odinger-Gibbs ensemble

Schr\"odinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schr\"odinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions, and we prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schr\"odinger's idea can not be used to construct an appropriate quantum equilibrium thermodynamics.Comment: 32 pages, revtex 4.1 preprint style, 5 figures. Published version with several changes with respect to v2 in text and reference

US state health expenditure convergence: A revisited analysis

This paper studies the evolution of US state health expenditure for a sample that covers 1966–2014. Our results provide evidence against the existence of a single pattern of behavior of personal health care expenditure across the US states. Rather, we can observe the existence of two statistically different convergence clubs. We cannot find evidence of convergence when we disaggregate health expenditure into its three main payers: Medicare, Medicaid and private health insurance expenditure, whilst we again find evidence of convergence clubs. However, the estimated clubs for Medicaid and private health insurance expenditure are statistically different that estimated for total health expenditure. Consequently, our results offer strong evidence of heterogeneity in the evolution of US health expenditure. The analysis of the forces that drive club creation shows that economic situation and some supply-side factors are important. We can also appreciate that some healthcare outcome variables are only related to private insurance health expenditure. The other health expenditures, thus, show a certain lack of efficiency which may be due to practices that have little benefit for patient health

Statistics and Nos\'e formalism for Ehrenfest dynamics

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial text overlap with arXiv:1010.149

Teacher participation & qualifications regarding extra-curricula sport activities

En la presente investigación se aborda el estudio y análisis de la intervención docente del profesorado de las actividades físico-deportivas extraescolares en los centros educativos de Educación Secundaria de la Comunidad de Madrid en función de su formación inicial. La investigación sigue una metodología cuantitativa de corte descriptivo, a través de la encuesta. El tamaño de la muestra es de 350 personas y para su cálculo se consideraron varios aspectos: la población era finita; se recurre en la varianza poblacional al supuesto más desfavorable donde “P” y “Q” son iguales con el 50% cada uno; el intervalo de confianza es del 95,5%, con un margen de error del ± 4,75%. Los resultados revelan que existe un alto porcentaje de profesores que no realizan una programación de sus actividades ni tampoco evalúan a sus alumnos. Asimismo, los resultados sugieren que la intervención docente de las personas no tituladas es menos adecuada.In this research is done the study and analysis of teacher intervention in the extra-curricular sport activities of educational centres for secondary education in Comunidad de Madrid. The research follows a quantitative methodology with a descriptive profile which, across survey, in which a cross-sectional survey have been carried out.The size of the sample is 350 people and for its calculation, several aspects have been considered: The population was finite; the least favourable hypothesis is considered in the population variation, where “P” and “Q” are equal, with 50% each; the confidence interval is 95%, with an error margin of ± 4.75%. The results reveal that exits a high percentage of teachers who don’t programme their activities and don’t evaluate their students. Furthermore, the results suggest that the teacher intervention is less adequate to the teachers who don’t have any qualification

Marine Biodiversity and Ecosystem Health of Ilhas Selvagens, Portugal

In September 2015, National Geographic's Pristine Seas project, in conjunction with the Instituto Universitário-Portugal, The Waitt Institute, the University of Western Australia, and partners conducted a comprehensive assessment of the rarely surveyed Ilhas Selvagens to explore the marine environment, especially the poorly understood deep sea and open ocean areas, and quantify the biodiversity of the nearshore marine environment