Localization in splitting of matter waves

In this paper we present an analysis of how matter waves, guided as propagating modes in potential structures, are split under adiabatic conditions. The description is formulated in terms of localized states obtained through a unitary transformation acting on the mode functions. The mathematical framework results in coupled propagation equations that are decoupled in the asymptotic regions as well before as after the split. The resulting states have the advantage of describing propagation in situations, for instance matter-wave interferometers, where local perturbations make the transverse modes of the guiding potential unsuitable as a basis. The different regimes of validity of adiabatic propagation schemes based on localized versus delocalized basis states are also outlined. Nontrivial dynamics for superposition states propagating through split potential structures is investigated through numerical simulations. For superposition states the influence of longitudinal wave-packet extension on the localization is investigated and shown to be accurately described in quantitative terms using the adiabatic formulations presented here.

From the road network database to a graph for localization purposes

The problems of finding best facility locations require complete and accurate road network with the corresponding population data in a specific area. However the data obtained in road network databases usually do not fit in this usage. In this paper we propose our procedure of converting the road network database to a road graph which could be used in localization problems. The road network data come from the National road data base in Sweden. The graph derived is cleaned, and reduced to a suitable level for localization problems. The population points are also processed in ordered to match with that graph. The reduction of the graph is done maintaining most of the accuracy for distance measures in the network.

Gravitational self-localization for spherical masses

In this work, I consider the center-of-mass wave function for a homogenous sphere under the influence of the self-interaction due to Newtonian gravity. I solve for the ground state numerically and calculate the average radius as a measure of its size. For small masses, M≲10−17 kg, the radial size is independent of density, and the ground state extends beyond the extent of the sphere. For masses larger than this, the ground state is contained within the sphere and to a good approximation given by the solution for an effective radial harmonic-oscillator potential. This work thus determines the limits of applicability of the point-mass Newton Schrödinger equations for spherical masses. In addition, I calculate the fringe visibility for matter-wave interferometry and find that in the low-mass case, interferometry can in principle be performed, whereas for the latter case, it becomes impossible. Based on this, I discuss this transition as a possible boundary for the quantum-classical crossover, independent of the usually evoked environmental decoherence. The two regimes meet at sphere sizes R≈10−7 m, and the density of the material causes only minor variations in this value.

The meta-object facility typed

The Object Managment Group’s Meta-Object Facility (MOF) is a semiformal approach to writing models and metamodels (models of models). The MOF was developed to enable systematic model/metamodel interchange and integration. The approach is problematic, unless metamodels are correctly specified: an error in a metamodel specification will propagate throughout instantiating models and final model implementations. An important open question is how to develop provably correct metamodels. This paper outlines a solution to the question, in which the MOF metamodelling approach is formalized within constructive type theory.