Local structure of directed networks

Previous work on undirected small-world networks established the paradigm that locally structured networks tend to have high density of short loops. On the other hand, many realistic networks are directed. Here we investigate the local organization of directed networks and find, surprisingly, that real networks often have very few short loops as compared to random models. We develop a theory and derive conditions for determining if a given network has more or less loops than its randomized counterpart. These findings carry broad implications for structural and dynamical processes sustained by directed networks

A Superconductor Made by a Metal Heterostructure at the Atomic Limit Tuned at the "Shape Resonance": MgB2

We have studied the variation of Tc with charge density and lattice parameters in Mg1-xAlxB2 superconducting samples at low Al doping x<8%. We show that high Tc occurs where the chemical potential is tuned at a "superconducting shape resonance" near the energy Ec of the quantum critical point (QCP) for the dimensional transition from 2D to 3D electronic structure in a particular subband of the natural superlattice of metallic atomic boron layers. At the "shape resonance" the electrons pairs see a 2D Fermi surface at EF-w0 and a 3D Fermi surface at EF+wo, where wo is the energy cut off of the pairing interaction. The resonant amplification occurs in a narrow energy range where EF-Ec is in the range of 2wo.Comment: 16 page

From Majorana theory of atomic autoionization to Feshbach resonances in high temperature superconductors

The Ettore Majorana paper - Theory of incomplete P triplets- published in 1931, focuses on the role of selection rules for the non-radiative decay of two electron excitations in atomic spectra, involving the configuration interaction between discrete and continuum channels. This work is a key step for understanding the 1935 work of Ugo Fano on the asymmetric lineshape of two electron excitations and the 1958 Herman Feshbach paper on the shape resonances in nuclear scattering arising from configuration interaction between many different scattering channels. The Feshbach resonances are today of high scientific interest in many different fields and in particular for ultracold gases and high Tc superconductivity.Comment: 13 pages, 7 figures. Journal of Superconductivity and Novel Magnetism to be publishe

Study of temperature dependent atomic correlations in MgB2_{2}

We have studied the evolution with temperature of the local as well as the average crystal structure of MgB$_2$ using the real-space atomic pair distribution function (PDF) measured by high resolution neutron powder diffraction. We have investigated the correlations of the B-B and B-Mg nearest neighbor pair motion by comparing, in the wide temperature range from T=10 K up to T=600 K, the mean-square displacements (MSD) of single atoms with the mean-square relative displacements (MSRD) obtained from the PDF peak linewidths. The results show that the single atom B and Mg vibrations are mostly decoupled from each other, with a small predominance of positive (in phase) correlation factor for both the B-B and B-Mg pairs. The small positive correlation is almost temperature independent, in contrast with our theoretical calculations; this can be a direct consequence of the strong decay processes of the $E_{2g}$ anharmonic phonons

Ising spin glass models versus Ising models: an effective mapping at high temperature II. Applications to graphs and networks

By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.Comment: 11 pages, 1 Postscript figur

An algorithm for counting circuits: application to real-world and random graphs

We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world networks, it allows to estimate exponentially large numbers of circuits in polynomial time. We illustrate the method by studying a graph of the Internet structure.Comment: 7 pages, 3 figures, minor corrections, accepted versio