Growing Cayley trees described by Fermi distribution

We introduce a model for growing Cayley trees with thermal noise. The evolution of these hierarchical networks reduces to the Eden model and the Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively. We show that the distribution of the bond strengths (energies) is described by the Fermi statistics. We discuss the relation of the present results with the scale-free networks described by Bose statistics

Quantum statistics in complex networks

In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random parameter that we call energy, and includes rewiring of the links. The system described by the mixed statistics is an inhomogemeous system formed by two class of nodes. In fact there is a threshold energy $\epsilon_s$ such that nodes with lower energy $(\epsilon<\epsilon_s)$ increase their connectivity while nodes with higher energy $(\epsilon>\epsilon_s)$ decrease their connectivity in time.Comment: 5 pages, 2 figure

Multiband superconductors close to a 3D-2D electronic topological transition

Within the two-band model of superconductivity, we study the dependence of the critical temperature Tc and of the isotope exponent alpha in the proximity to an electronic topological transition (ETT). The ETT is associated with a 3D-2D crossover of the Fermi surface of one of the two bands: the sigma subband of the diborides. Our results agree with the observed dependence of Tc on Mg content in A_{1-x}Mg_xB_2 (A=Al or Sc), where an enhancement of Tc can be interpreted as due to the proximity to a "shape resonance". Moreover we have calculated a possible variation of the isotope effect on the superconducting critical temperature by tuning the chemical potential.Comment: J. Supercond., to appea

Infrared signature of active massive black holes in nearby dwarf galaxies

We investigate the possible presence of active galactic nuclei (AGN) in dwarf galaxies and other nearby galaxies to identify candidates for follow-up confirmation and dynamical mass measurements. We use the Wide-field Infrared Survey Explorer (WISE) All-Sky Release Source Catalog and examine the infrared colours of a sample of dwarf galaxies and other nearby galaxies in order to identify both unobscured and obscured candidate AGN by applying the infrared colour diagnostic. Stellar masses of galaxies are obtained using a combination of three independent methods. Black hole masses are estimated using the bolometric luminosity of the AGN candidates and computed for three cases of the bolometric-to-Eddington luminosity ratio. We identify 303 candidate AGN, of which 276 were subsequently found to have been independently identified as AGN via other methods. The remaining 9% require follow-up observations for confirmation. The activity is detected in galaxies with stellar masses from ~ 10^6 to 10^9 solar masses; assuming the candidates are AGN, the black hole masses are estimated to be ~ 10^3 - 10^6 solar masses, adopting L_bol = 0.1 L_Edd. The black hole masses probed are several orders of magnitude smaller than previously reported for centrally located massive black holes. We examine the stellar mass versus black hole mass relationship in this low galaxy mass regime. We find that it is consistent with the existing relation extending linearly (in log-log space) into the lower mass regime. These findings suggest that CMBH are present in low-mass galaxies and in the Local Universe, and provide new impetus for follow-up dynamical studies of quiescent black holes in local dwarf galaxies.Comment: 14 pages, 9 figures, 4 tables, accepted for publication in Astronomy & Astrophysics. The first version of this paper appeared on astro-ph in 2014 (arXiv:1411.3844). The new version includes 3 new tables, 1 new figure and updated discussio

Calculation of fragmentation functions in two-hadron semi-inclusive processes

We investigate the properties of interference fragmentation functions arising from the emission of two leading hadrons inside the same jet for inclusive lepton-nucleon deep-inelastic scattering. Using an extended spectator model for the mechanism of the hadronization, we give a complete calculation and numerical estimates for the examples of a proton-pion pair produced with invariant mass on the Roper resonance, and of two pions produced with invariant mass close to the $\rho$ mass. We discuss azimuthal angular dependence of the leading order cross section to point up favourable conditions for extracting transversity from experimental data.Comment: 5 pages, 3 figures in .eps format, AIP and epsfig styles included, to appear in proceedings of "Second Workshop on Physics with an Electron Polarized Light Ion Collider", MIT, Sept. 14-16, 200

On the flexibility of complex systems

Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the system must satisfy a set of random dense linear constraints. By statistical mechanics techniques, we describe the transition between a non-flexible system in which the constraints are not fully satisfied, to a flexible system, in which the constraints can be satisfied in many ways. This phase transition is described in terms of the appearance of zeros modes in the statistical mechanics problem

Two-bands superconductivity with intra- and interband pairing for synthetic superlattices

We consider a model for superconductivity in a two-band superconductor, having an anisotropic electronic structure made of two partially overlapping bands with a first hole-like and a second electron-like fermi surface. In this pairing scenario, driven by the interplay between interband $V_{i,j}$ and intraband $V_{i,i}$ pairing terms, we have solved the two gap equations at the critical temperature $T = T_c$ and calculate $T_c$ and the chemical potential $\mu$ as a function of the number of carriers $n$ for various values of pairing interactions, $V_{1,1}$, $V_{2,2}$, and $V_{1,2}$. The results show the complexity of the physics of condensates with multiple order parameters with the chemical potential near band edges.Comment: 6 pages, 2 figure

The Feshbach resonance and nanoscale phase separation in a polaron liquid near the quantum critical point for a polaron Wigner crystal

The additional long range order parameter that competes with the high Tc superconductivity long range order is identified as an electronic crystal of pseudo Jahn-Teller polarons beyond the critical value of the electron lattice interaction. We show that the region of quantum critical fluctuations in the two variables phase diagram of cuprates: the doping (delta) and the chemical pressure (i.e., the tolerance factor, or the average ionic radius of A-site cations) can be measured via the microstrain (eta) of the Cu-O length in the CuO2 lattice. The fluctuating order in the proximity of the microstrain quantum critical point that competes with the superconducting long range order is the polaron electronic crystalline phase called a Wigner polaron crystal and the variation of the spin gap energy as a function of microstrain provides a strong experimental support for this proposal.Comment: 13 pages, 3 figure

An extended formalism for preferential attachment in heterogeneous complex networks

In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an arbitrary metric space, and introduce an affinity function that biases the attachment probabilities of links. We perform an analytical study of the stationary degree distributions in heterogeneous PA networks. We show that their degree densities exhibit a richer scaling behavior than their homogeneous counterparts, and that the power law scaling in the degree distribution is robust in presence of heterogeneity