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Oscar Arratia

Publications and source records attributed to Oscar Arratia.

6 recordsLinked to original sources

Long-term impact risk for (101955) 1999 RQ36

The potentially hazardous asteroid (101955) 1999 RQ36 has the possibility of collision with the Earth in the latter half of the 22nd century, well beyond the traditional 100-year time horizon for routine impact monitoring. The probabilities accumulate to a total impact probability of approximately 10E-3, with a pair of closely related routes to impact in 2182 comprising more than half of the total. The analysis of impact possibilities so far in the future is strongly dependent on the action of the Yarkovsky effect, which raises new challenges in the careful assessment of longer term impact hazards. Even for asteroids with very precisely determined orbits, a future close approach to Earth can scatter the possible trajectories to the point that the problem becomes like that of a newly discovered asteroid with a weakly determined orbit. If the scattering takes place late enough so that the target plane uncertainty is dominated by Yarkovsky accelerations then the thermal properties of the asteroid,which are typically unknown, play a major role in the impact assessment. In contrast, if the strong planetary interaction takes place sooner, while the Yarkovsky dispersion is still relatively small compared to that derived from the measurements, then precise modeling of the nongravitational acceleration may be unnecessary.

astro-ph.EP

Dynamical Systems and Quantum Bicrossproduct Algebras

We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, like Poincare, Galilei and Euclidean in N dimensions. The action associated to the bicrossproduct structure allows to obtain a nonlinear action over a new group linked to the translations. This new nonlinear action associates a dynamical system to each generator which is the object of study in this paper.

math-ph

Induced Representations of Quantum Kinematical Algebras and Quantum Mechanics

Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper (olmo01), to induce representations of quantum bicrossproduct algebras we construct the representations of the family of standard quantum inhomogeneous algebras $U_λ(iso_ω(2))$. This family contains the quantum Euclidean, Galilei and Poincaré algebras, all of them in (1+1) dimensions. As byproducts we obtain the actions of these quantum algebras on regular co-spaces that are an algebraic generalization of the homogeneous spaces and $q$--Casimir equations which play the role of $q$--Schrödinger equations.

math.QA

Deformation in Phase Space

We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the commutative algebra of smooth functions on M in a new non-commutative algebra. These ideas lead in a natural way to Quantum Groups as deformation (or quantization, in a broad sense) of Poisson-Lie groups, which is also analysed here.

math-ph