Interpretation of the evolution parameter of the Feynman parametrization of the Dirac equation

The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The Stueckelberg interpretation of antiparticles naturally arises from the formalism.Comment: 6 pages, RevTex, no figures, submitted to Phys. Lett.

The detection of globular clusters in galaxies as a data mining problem

We present an application of self-adaptive supervised learning classifiers derived from the Machine Learning paradigm, to the identification of candidate Globular Clusters in deep, wide-field, single band HST images. Several methods provided by the DAME (Data Mining & Exploration) web application, were tested and compared on the NGC1399 HST data described in Paolillo 2011. The best results were obtained using a Multi Layer Perceptron with Quasi Newton learning rule which achieved a classification accuracy of 98.3%, with a completeness of 97.8% and 1.6% of contamination. An extensive set of experiments revealed that the use of accurate structural parameters (effective radius, central surface brightness) does improve the final result, but only by 5%. It is also shown that the method is capable to retrieve also extreme sources (for instance, very extended objects) which are missed by more traditional approaches.Comment: Accepted 2011 December 12; Received 2011 November 28; in original form 2011 October 1

Real World Interpretations of Quantum Theory

I propose a new class of interpretations, {\it real world interpretations}, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one factor. They give a mathematical characterisation of the different possible worlds arising in an evolving closed quantum system, in which each possible world corresponds to a (generally mixed) evolving quantum state. In a realistic model, the states corresponding to different worlds should be expected to tend towards orthogonality as different possible quasiclassical structures emerge or as measurement-like interactions produce different classical outcomes. However, as the worlds have a precise mathematical definition, real world interpretations need no definition of quasiclassicality, measurement, or other concepts whose imprecision is problematic in other interpretational approaches. It is natural to postulate that precisely one world is chosen randomly, using the natural probability distribution, as the world realised in Nature, and that this world's mathematical characterisation is a complete description of reality.Comment: Minor revisions. To appear in Foundations of Physic

Metric tensor as the dynamical variable for variable cell-shape molecular dynamics

We propose a new variable cell-shape molecular dynamics algorithm where the dynamical variables associated with the cell are the six independent dot products between the vectors defining the cell instead of the nine cartesian components of those vectors. Our choice of the metric tensor as the dynamical variable automatically eliminates the cell orientation from the dynamics. Furthermore, choosing for the cell kinetic energy a simple scalar that is quadratic in the time derivatives of the metric tensor, makes the dynamics invariant with respect to the choice of the simulation cell edges. Choosing the densitary character of that scalar allows us to have a dynamics that obeys the virial theorem. We derive the equations of motion for the two conditions of constant external pressure and constant thermodynamic tension. We also show that using the metric as variable is convenient for structural optimization under those two conditions. We use simulations for Ar with Lennard-Jones parameters and for Si with forces and stresses calculated from first-principles of density functional theory to illustrate the applications of the method.Comment: 10 pages + 6 figures, Latex, to be published in Physical Review

Second order gradient ascent pulse engineering

We report some improvements to the gradient ascent pulse engineering (GRAPE) algorithm for optimal control of quantum systems. These include more accurate gradients, convergence acceleration using the BFGS quasi-Newton algorithm as well as faster control derivative calculation algorithms. In all test systems, the wall clock time and the convergence rates show a considerable improvement over the approximate gradient ascent.Comment: Submitted for publicatio