Remarks on the use of projected densities in the density dependent part of Skyrme or Gogny functionals

I discuss the inadequacy of the "projected density" prescription to be used in density dependent forces/functionals when calculations beyond mean field are pursued. The case of calculations aimed at the symmetry restoration of mean fields obtained with effective realistic forces of the Skyrme or Gogny type is considered in detail. It is shown that at least for the restoration of spatial symmetries like rotations, translations or parity the above prescription yields catastrophic results for the energy that drive the intrinsic wave function to configurations with infinite deformation, preventing thereby its use both in projection after and before variation.Comment: To be published as a contribution to J. Phys G, Special Issue, Focus Section: Open Problems in Nuclear Structur

Critical fluctuations, intermittent dynamics and Tsallis statistics

It is pointed out that the dynamics of the order parameter at a thermal critical point obeys the precepts of the nonextensive Tsallis statistics. We arrive at this conclusion by putting together two well-defined statistical-mechanical developments. The first is that critical fluctuations are correctly described by the dynamics of an intermittent nonlinear map. The second is that intermittency in the neighborhood of a tangent bifurcation in such map rigorously obeys nonextensive statistics. We comment on the implications of this result. Key words: critical fluctuations, intermittency, nonextensive statistics, anomalous stationary statesComment: Contribution to the proceedings of International Workshop on Trends and Perspectives on Extensive and Non-Extensive Statistical Mechanics (q-60), Angra dos Reis, Brazil, 17-21/11/2003. Submitted to Physica