74,736 research outputs found
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
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