Fractal index, central charge and fractons

We introduce the notion of fractal index associated with the universal class $h$ of particles or quasiparticles, termed fractons, which obey specific fractal statistics. A connection between fractons and conformal field theory(CFT)-quasiparticles is established taking into account the central charge $c[\nu]$ and the particle-hole duality $\nu\longleftrightarrow\frac{1}{\nu}$, for integer-value $\nu$ of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as $v\sim\frac{c[\nu]}{\nu+1}$. The Hausdorff dimension $h$ which labelled the universal classes of particles and the conformal anomaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.Comment: latex, 12 pages, To appear in Mod. Phys. Lett. A (2000

Complex evolution of the electronic structure from polycrystalline to monocrystalline graphene: generation of a new Dirac point

First principles calculations, employed to address the properties of polycrystalline graphene, indicate that the electronic structure of tilt grain boundaries in this system displays a rather complex evolution towards graphene bulk, as the tilt angle decreases, with the generation of a new Dirac point at the Fermi level, and an anisotropic Dirac cone of low energy excitations. Moreover, the usual Dirac point at the {\bf K} point falls below the Fermi level, and rises towards it as the tilt angle decreases. Further, our calculations indicate that the grain-boundary formation energy behaves non-monotonically with the tilt angle, due to a change in the the spatial distribution and relative contributions of the bond-stretching and bond-bending deformations associated with the formation of the defect.Comment: 4 pages (+ a few references on 5th page). Contains text (.tex) file + 4 figures + pdf fil

A novel and precise time domain description of MOSFET low frequency noise due to random telegraph signals

Nowadays, random telegraph signals play an important role in integrated circuit performance variability, leading for instance to failures in memory circuits. This problem is related to the successive captures and emissions of electrons at the many traps stochastically distributed at the silicon-oxide (Si-SiO2) interface of MOS transistors. In this paper we propose a novel analytical and numerical approach to statistically describe the fluctuations of current due to random telegraph signal in time domain. Our results include two distinct situations: when the density of interface trap density is uniform in energy, and when it is an u-shape curve as prescribed in literature, here described as simple quadratic function. We establish formulas for relative error as function of the parameters related to capture and emission probabilities. For a complete analysis experimental u-shape curves are used and compared with the theoretical aproach

Hamiltonian formulation of general relativity in the teleparallel geometry

We establish the Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing the Legendre transform. The time gauge condition, previously considered, restricts the teleparallel geometry to the three-dimensional spacelike hypersurface. Geometrically, the teleparallel geometry is now extended to the four-dimensional space-time. The resulting Hamiltonian formulation is different from the standard ADM formulation in many aspects, the main one being that the dynamics is now governed by the Hamiltonian constraint H_0 and a set of primary constraints. The vector constraint H_i is derived from the Hamiltonian constraint. The vanishing of the latter implies the vanishing of the vector constraint.Comment: 22 pages, Latex file, no figures. The title has been changed. The complete constraint algebra is presented. The derivation of the vector constraint from the Hamiltonian constraint is presented with further details. Version to appear in the PR