Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields

We present an exact algebraic solution of a single graphene plane in transverse electric and perpendicular magnetic fields. The method presented gives both the eigen-values and the eigen-functions of the graphene plane. It is shown that the eigen-states of the problem can be casted in terms of coherent states, which appears in a natural way from the formalism.Comment: 11 pages, 5 figures, accepted for publication in Journal of Physics Condensed Matte

Cluster detection in networks using percolation

We consider the task of detecting a salient cluster in a sensor network, that is, an undirected graph with a random variable attached to each node. Motivated by recent research in environmental statistics and the drive to compete with the reigning scan statistic, we explore alternatives based on the percolative properties of the network. The first method is based on the size of the largest connected component after removing the nodes in the network with a value below a given threshold. The second method is the upper level set scan test introduced by Patil and Taillie [Statist. Sci. 18 (2003) 457-465]. We establish the performance of these methods in an asymptotic decision- theoretic framework in which the network size increases. These tests have two advantages over the more conventional scan statistic: they do not require previous information about cluster shape, and they are computationally more feasible. We make abundant use of percolation theory to derive our theoretical results, and complement our theory with some numerical experiments.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ412 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The Blackbody Radiation in D-Dimensional Universes

The blackbody radiation is analyzed in universes with $D$ spatial dimensions. With the classical electrodynamics suited to the universe in focus and recurring to the hyperspherical coordinates, it is shown that the spectral energy density as well as the total energy density are sensible to the dimensionality of the universe. Wien's displacement law and the Stefan-Boltzmann law are properly generalized

Scaling cosmology with variable dark-energy equation of state

Interactions between dark matter and dark energy which result in a power-law behavior (with respect to the cosmic scale factor) of the ratio between the energy densities of the dark components (thus generalizing the LCDM model) have been considered as an attempt to alleviate the cosmic coincidence problem phenomenologically. We generalize this approach by allowing for a variable equation of state for the dark energy within the CPL-parametrization. Based on analytic solutions for the Hubble rate and using the Constitution and Union2 SNIa sets, we present a statistical analysis and classify different interacting and non-interacting models according to the Akaike (AIC) and the Bayesian (BIC) information criteria. We do not find noticeable evidence for an alleviation of the coincidence problem with the mentioned type of interaction.Comment: 21 pages, 11 figures, 11 tables, discussion improve

Absence of Klein's paradox for massive bosons coupled by nonminimal vector interactions

A few properties of the nonminimal vector interactions in the Duffin-Kemmer-Petiau theory are revised. In particular, it is shown that the space component of the nonminimal vector interaction plays a peremptory role for confining bosons whereas its time component contributes to the leakage. Scattering in a square step potential with proper boundary conditions is used to show that Klein's paradox does not manifest in the case of a nonminimal vector coupling

Solid flow drives surface nanopatterning by ion-beam irradiation

Ion Beam Sputtering (IBS) is known to produce surface nanopatterns over macroscopic areas on a wide range of materials. However, in spite of the technological potential of this route to nanostructuring, the physical process by which these surfaces self-organize remains poorly under- stood. We have performed detailed experiments of IBS on Si substrates that validate dynamical and morphological predictions from a hydrodynamic description of the phenomenon. Our results elucidate flow of a nanoscopically thin and highly viscous surface layer, driven by the stress created by the ion-beam, as a description of the system. This type of slow relaxation is akin to flow of macroscopic solids like glaciers or lead pipes, that is driven by defect dynamics.Comment: 12 pages, 4 figure

A Laplace transform approach to the quantum harmonic oscillator

The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity

Excitonic effects in the optical conductivity of gated graphene

We study the effect of electron-electron interactions in the optical conductivity of graphene under applied bias and derive a generalization of Elliot's formula, commonly used for semiconductors, for the optical intensity. We show that {\it excitonic resonances} are responsible for several features of the experimentally measured mid-infrared response of graphene such as the increase of the conductivity beyond the "universal" value above the Fermi blocked regime, the broadening of the absorption at the threshold, and the decrease of the optical conductivity at higher frequencies. Our results are also in agreement with {\it ab initio} calculations in the neutral regime.Comment: New version with discussion improve