1,275 research outputs found
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
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