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Convegno Nazionale "Metodi e Problemi Matematici in Meccanica Quantistica" Modena, 5-7 ottobre 2006
Presentare lo stato dell'arte dal punto di vista della trattazione matematica in alcuni problemi aperti della meccanica quantistica e delle sue applicazioni. Una sessione speciale sarà dedicata a un incontro con esperti di applicazioni nell'ambito delle nanoscienze
BLOW UP SOLUTIONS FOR THE SCHR\"ODINGER EQUATION WITH A CONCENTRATED NONLINEARITY IN DIMENSION THREE
A one-dimensional model for ionization induced by scattering with a heavy particle
The ionization probability for a one-dimensional model atom perturbed by a moving repulsive scatterer is considered. The moving scattering centre is meant to mimic a second quantum particle crossing the region where a much lighter particle is initially bound in the atom. We compute the first three terms (of order t3/2, t2, t5/2 respectively) in the expansion for small times of the ionization probability and we deduce that the first term showing explicit dependence on the velocity of the scatterer is of order t5/2. A possible application of the model for the description of a quantum particle in a cloud chamber is also outlined
Going Beyond Counting First Authors in Author Co-citation Analysis
The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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