Correlated electrons systems on the Apollonian network

Strongly correlated electrons on an Apollonian network are studied using the Hubbard model. Ground-state and thermodynamic properties, including specific heat, magnetic susceptibility, spin-spin correlation function, double occupancy and one-electron transfer, are evaluated applying direct diagonalization and quantum Monte Carlo. The results support several types of magnetic behavior. In the strong-coupling limit, the quantum anisotropic spin 1/2 Heisenberg model is used and the phase diagram is discussed using the renormalization group method. For ferromagnetic coupling, we always observe the existence of long-range order. For antiferromagnetic coupling, we find a paramagnetic phase for all finite temperatures.Comment: 7 pages, 8 figure

Discrete and finite Genral Relativity

We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a finite, singularity-free, point-like field that we associate to a ``classical graviton". The standard Einstein's continuous formalism is retrieved by means of an averaging process, and its continuous solutions are determined by the chosen imposed symetry. The Schwarzschild metric is obtained by the imposition of spherical symmetry on the averaged field.Comment: Modified conform the version to appear in Classical and Quantum Gravit

Ionic and Electronic Conductivity of Nanostructured, Samaria-Doped Ceria

The ionic and electronic conductivities of samaria doped ceria electrolytes, Ce_(0.85)Sm_(0.15)O_(1.925−δ), with nanometric grain size have been evaluated. Nanostructured bulk specimens were obtained using a combination of high specific-surface-area starting materials and suitable sintering profiles under conventional, pressureless conditions. Bulk specimens with relatively high density (≥92% of theoretical density) and low medium grain size (as small as 33 nm) were achieved. Electrical A.C. impedance spectra were recorded over wide temperature (150 to 650°C) and oxygen partial pressure ranges (0.21 to 10^(−31) atm). Under all measurement conditions the total conductivity decreased monotonically with decreasing grain size. In both the electrolytic and mixed conducting regimes this behavior is attributed to the high number density of high resistance grain boundaries. The results suggest a possible variation in effective grain boundary width with grain size, as well as a possible variation in specific grain boundary resistance with decreasing oxygen partial pressure. No evidence appears for either enhanced reducibility or enhanced electronic conductivity upon nanostructuring

Noether symmetry for non-minimally coupled fermion fields

A cosmological model where a fermion field is non-minimally coupled with the gravitational field is studied. By applying Noether symmetry the possible functions for the potential density of the fermion field and for the coupling are determined. Cosmological solutions are found showing that the non-minimally coupled fermion field behaves as an inflaton describing an accelerated inflationary scenario, whereas the minimally coupled fermion field describes a decelerated period being identified as dark matter.Comment: Revised version accepted for publication in Classical and Quantum Gravit