A Secular Relativistic Model For Solar System's Numerical Simulations

Using Gauss' averaged equations, we compute the secular relativistic effects generated by the Sun on the argument of the perihelion and the mean anomaly of an orbit. Then we test different alternative simpler models that have been proposed to reproduce the secular relativistic effects in the orbital elements. Generally, models introduce artificial perturbations that are velocity-independent but that depend on the heliocentric distance. If these perturbations are set as an impulse in a constant timestep integrator, when the particle approaches perihelion the generated impulse could be very strong and badly sampled, originating a spurious orbital evolution. In order to overcome this setback, we propose two new models based on a constant, distance-independent, perturbation. With these models we obtain the correct secular drift in the argument of perihelion and the expected secular orbital evolution is reproduced. We also discuss with some detail the secular effect generated on the mean anomaly by different models.Comment: This work is an expanded version of Venturini and Gallardo (2010

The space of density states in geometrical quantum mechanics

We present a geometrical description of the space of density states of a quantum system of finite dimension. After presenting a brief summary of the geometrical formulation of Quantum Mechanics, we proceed to describe the space of density states \D(\Hil) from a geometrical perspective identifying the stratification associated to the natural GL(\Hil)--action on \D(\Hil) and some of its properties. We apply this construction to the cases of quantum systems of two and three levels.Comment: Amslatex, 18 pages, 4 figure

Inverse Neutrino-less Double Beta Decay Revisited: Neutrinos, Higgs Triplets and a Muon Collider

We revisit the process of inverse neutrino-less double beta decay (e e -> W W) at future linear colliders. The cases of Majorana neutrino and Higgs triplet exchange are considered. We also discuss the processes e mu -> W W and mu mu -> W W, which are motivated by the possibility of muon colliders. For heavy neutrino exchange and center-of-mass energies larger than 1 TeV, we show that masses up to 10^6 (10^5) GeV could be probed for e-e and e-mu machines, respectively. The stringent limits for mixing of heavy neutrinos with muons render mu mu -> W W less promising, even though this process is not constrained by limits from neutrino-less double beta decay. If Higgs triplets are responsible for inverse neutrino-less double beta decay, observable signals are only possible if a very narrow resonance is met. We also consider unitarity aspects of the process in case both Higgs triplets and neutrinos are exchanged. An exact see-saw relation connecting low energy data with heavy neutrino and triplet parameters is found.Comment: 19 pages, 6 figure

Tensorial description of quantum mechanics

Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group.Comment: 8 page

Basics of Quantum Mechanics, Geometrization and some Applications to Quantum Information

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally, after reviewing the basics of the geometric formulation of quantum mechanics, we apply the methods presented to the most interesting cases of finite dimensional Hilbert spaces: those of two, three and four level systems (one qubit, one qutrit and two qubit systems). As a more practical application, we discuss the advantages that the geometric formulation of quantum mechanics can provide us with in the study of situations as the functional independence of entanglement witnesses.Comment: AmsLaTeX, 37 pages, 8 figures. This paper is an expanded version of some lectures delivered by one of us (G. M.) at the ``Advanced Winter School on the Mathematical Foundation of Quantum Control and Quantum Information'' which took place at Castro Urdiales (Spain), February 11-15, 200

High Energy Colliders

We consider the high energy advantages, disadvantages and luminosity requirements of hadrons, leptons and photon-photon colliders. Technical problems in obtaining increased energy in each type of machine are presented. The machines relative size are also discussed.Comment: LaTeX, 27 pages, 8 figures (eps, ps). Submitted to the Proceedings of the Princeton's 250th Anniversary Conference on Critical Problems in Physic

High Luminosity Muon Collider Design

Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadrons and electron machines. They should be regarded as complementary. Parameters are given of a 4 TeV high luminosity muon-muon collider, and of a 0.5 TeV demonstration machine. We discuss the various systems in such muon collider.Comment: LaTeX 5 pages 4 figure

Future Colliders

The high energy physics advantages, disadvantages and luminosity requirements of hadrons, of leptons and photon-photon colliders are considered. Technical arguments for increased energy in each type of machine are presented. Their relative size, and the implications of size on cost are discussed.Comment: LaTeX, 10 pages, 10figure

Reactions induced by 9^9Be in a four-body continuum-discretized coupled-channels framework

We investigate the elastic scattering of $^9$Be on $^{208}$Pb at beam energies above (50 MeV) and below (40 MeV) the Coulomb barrier. The reaction is described within a four-body framework using the Continuum-Discretized Coupled-Channels (CDCC) method. The $^9$Be projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Our calculations confirm the importance of continuum effects at low energies.Comment: 2 pages, 1 figure. Proceedings of the International Scientific Meeting on Nuclear Physics, RABIDA15, La R\'abida (Spain), June 1-5, 201