Information entropy of classical versus explosive percolation

We study the Shannon entropy of the cluster size distribution in classical as well as explosive percolation, in order to estimate the uncertainty in the sizes of randomly chosen clusters. At the critical point the cluster size distribution is a power-law, i.e. there are clusters of all sizes, so one expects the information entropy to attain a maximum. As expected, our results show that the entropy attains a maximum at this point for classical percolation. Surprisingly, for explosive percolation the maximum entropy does not match the critical point. Moreover, we show that it is possible determine the critical point without using the conventional order parameter, just analysing the entropy's derivatives.Comment: 6 pages, 6 figure

The class of n-entire operators

We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1,1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized sense due to M. G. Krein. We show that these classes of operators have several distinctive properties, some of them related to the spectra of their canonical selfadjoint extensions. In particular, we provide necessary and sufficient conditions on the spectra of two canonical selfadjoint extensions of an operator for it to belong to one of our classes. Our discussion is based on some recent results in the theory of de Branges spaces.Comment: 33 pages. Typos corrected. Changes in the wording of Section 2. References added. Examples added. arXiv admin note: text overlap with arXiv:1104.476

One-magnon Raman scattering in La(2)CuO(4): the origin of the field-induced mode

We investigate the one-magnon Raman scattering in the layered antiferromagnetic La(2)CuO(4) compound. We find that the Raman signal is composed by two one-magnon peaks: one in the B1g channel, corresponding to the Dzyaloshinskii-Moryia (DM) mode, and another in the B3g channel, corresponding to the XY mode. Furthermore, we show that a peak corresponding to the XY mode can be induced in the planar (RR) geometry when a magnetic field is applied along the easy axis for the sublattice magnetization. The appearance of such field-induced mode (FIM) signals the existence of a new magnetic state above the Neel temperature T_N, where the direction of the weak-ferromagnetic moment (WFM) lies within the CuO(2) planes.Comment: 4 pages, 3 figure

A Physical Model for Co-evolution of QSOs and of their Spheroidal Hosts

At variance with most semi-analytic models, in the Anti-hierarchical Baryon Collapse scenario (Granato et al. 2001, 2004) the main driver of the galaxy formation and evolution is not the merging sequence but are baryon processes. This approach emphasizes, still in the framework of the hierarchical clustering paradigm for dark matter halos, feedback processes from supernova explosions and from active nuclei, that tie together star formation in spheroidal galaxies and the growth of black holes at their centers. We review some recent results showing the remarkably successful predictive power of this scenario, which allows us to account for the evolution with cosmic time of a broad variety of properties of galaxies and active nuclei, which proved to be very challenging for competing models.Comment: Invited talk at the Specola Vaticana Workshop on "AGN and Galaxy Evolution", Castel Gandolfo, 3-6 October 2005, 10 pages, 2 figure