Exact and approximate results of non-extensive quantum statistics

We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson system which we compare with other approximate scheme (i.e. factorization approach), and with the recently obtained exact result. To do this, we investigate the predictions on Bose-Einstein condensation and the blackbody radiation. We find that both approximation techniques give results similar to (up to ${\cal O}(q-1)$) the exact ones, making them a useful tool for computations. Because of the simplicity of the factorization approach formulae, it appears that this is the easiest way to handle with physical systems which might exhibit slight deviations from extensivity.Comment: 15 pages, prl revtex style, 4 ps figures. New -shortened- version accepted for publication in Eur. Phys. J.

Systematic and quantitative approach for the identification of high energy gamma-ray source populations

A large fraction of the detections to be made by the Gamma-ray Large Area Space Telescope (GLAST) will initially be unidentified. We argue that traditional methodological approaches to identify individuals and/or populations of $\gamma$-ray sources will encounter procedural limitations. These limitations will hamper our ability to classify source populations lying in the anticipated dataset with the required degree of confidence, particularly those for which no member has yet been convincingly detected in the predecessor experiment EGRET. Here we suggest a new paradigm for achieving the classification of $\gamma$-ray source populations based on the implementation of an a priori protocol to search for theoretically-motivated candidate sources. In order to protect the discovery potential of the sample, it is essential that such paradigm will be defined before the data is unblinded. Key to the new procedure is a statistical assessment by which the discovery of a new population can be claimed. Although we explicitly refer here to the case of GLAST, the scheme we present may be adapted to other experiments confronted with a similar problematic.Comment: In press in The Astrophysical Journal Letters. Accepted on July 12, 200