Localization properties of a tight-binding electronic model on the Apollonian network

An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex network, and as a substrate, on the top of which physical models can defined. The Schrodinger equation of the model, which includes only nearest neighbor interactions, is written in a matrix formulation. In the uniform case, the resulting Hamiltonian is proportional to the adjacency matrix of the Apollonian network. The characterization of the electronic eigenstates is based on the properties of the spectrum, which is characterized by a very large degeneracy. The $2\pi /3$ rotation symmetry of the network and large number of equivalent sites are reflected in all eigenstates, which are classified according to their parity. Extended and localized states are identified by evaluating the participation rate. Results for other two non-uniform models on the Apollonian network are also presented. In one case, interaction is considered to be dependent of the node degree, while in the other one, random on-site energies are considered.Comment: 7pages, 7 figure

Fluctuation of the Initial Conditions and Its Consequences on Some Observables

We show effects of the event-by-event fluctuation of the initial conditions (IC) in hydrodynamic description of high-energy nuclear collisions on some observables. Such IC produce not only fluctuations in observables but, due to their bumpy structure, several non-trivial effects appear. They enhance production of isotropically distributed high-pT particles, making v2 smaller there. Also, they reduce v2 in the forward and backward regions where the global matter density is smaller, so where such effects become more efficacious. They may also produce the so-called ridge effect in the two large-pT particle correlation.Comment: 6 pages, 6 figures, presented at the IV Workshop on Particle Correlations and Femtoscopy (WPCF2008), Krakow, Poland, 11-14 Sep 200

Non-nequilibrium model on Apollonian networks

We investigate the Majority-Vote Model with two states ($-1,+1$) and a noise $q$ on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter $q$. We also studies de effect of redirecting a fraction $p$ of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio $\gamma/\nu$, $\beta/\nu$, and $1/\nu$ for several values of rewiring probability $p$. The critical noise was determined $q_{c}$ and $U^{*}$ also was calculated. The effective dimensionality of the system was observed to be independent on $p$, and the value $D_{eff} \approx1.0$ is observed for these networks. Previous results on the Ising model in Apollonian Networks have reported no presence of a phase transition. Therefore, the results present here demonstrate that the Majority-Vote Model belongs to a different universality class as the equilibrium Ising Model on Apollonian Network.Comment: 5 pages, 5 figure