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

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

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

Luxación anterior de cadera: presentación de un caso y revisión de la literatura.

La luxación anterior de cadera es una lesión poco frecuente y que se produce por traumatismos de alta energía. Este tipo de luxación requiere maniobras especiales para su reducción. El tratamiento ortopédico puede dar buenos resultados, aunque en ocasiones es necesaria la reducción abierta y el tratamiento quirúrgico de lesiones asociadas. Presentamos el caso de un varón de 27 años que presentaba una luxación anterior de cadera derecha debido a accidente automovilístico. Además tenía lesiones asociadas en pie derecho. Se realizó reducción cerrada y tratamiento conservador con buenos resultados. El pronóstico de una luxación de cadera depende de la gravedad de la lesión así como del tiempo que se tarda en realizar la reducción, que está relacionando con el riesgo de desarrollo de necrosis avascular. La luxación anterior de cadera tiene mejor pronóstico que la luxación posterior cuando se realiza un tratamiento temprano adecuado.The anterior hip dislocation is a little frequent injury and is produced by high energy traumatisms. This type of dislocation requires special maneuvers for its reduction. The orthopaedic treatment can give good results, although sometimes it is necessary the open reduction and the surgical treatment of associate injuries. We present a case of a 27 year-old man who presented an anterior hip dislocation due to automobile accident. He had associated injuries on right food. He was treated by closed reduction and orthopaedic treatment and he had good results. The prognosis of a hip dislocation depends on the gravity of the injury as well as the time that takes in realizing the reduction, that it is relating to the risk of development of avascular necrosis. The anterior hip dislocation has better prognosis than the posterior dislocation when a suitable treatment is early realized

Entropy and canonical ensemble of hybrid quantum classical systems

We generalize von Neumann entropy function to hybrid quantum-classical systems by considering the principle of exclusivity of hybrid events. For non-interacting quantum and classical subsystems, this entropy function separates into the sum of the usual classical (Gibbs) and quantum (von Neumann) entropies, whereas if the two parts do interact, it can be properly separated into the classical entropy for the marginal classical probability, and the conditional quantum entropy. We also deduce the hybrid canonical ensemble (HCE) as the one that maximizes this entropy function, for a fixed ensemble energy average. We prove that the HCE is additive for non-interacting systems for all thermodynamic magnitudes, and reproduces the appropriate classical- and quantum-limit ensembles. Furthermore, we discuss how and why Ehrenfest dynamics does not preserve the HCE and does not yield the correct ensemble averages when time-averages of simulations are considered -- even if it can still be used to obtain correct averages by modifying the averaging procedure.Comment: 6 pages + 4 pages Supp. Ma