Majorana Fermions and Orthogonal Complex Structures

Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain "doubling" of the Hilbert space. In this work we show that this redundancy in the Hilbert space can be completely lifted if the relevant orthogonal structure is taken into account. Such an approach allows for a treatment of Majorana fermions which is both physically and mathematically transparent. Furthermore, an explicit connection between orthogonal complex structures and the topological $\mathbb Z_2$-invariant is given.Comment: 15 pages, 6 figures, typos correcte

Thermal properties of composite materials with a complex fractal structure

In this work, we report the thermal characterization of platelike composite samples made of polyester resin and magnetite inclusions. By means of photoacoustic spectroscopy and thermal relaxation, the thermal diffusivity, conductivity and volumetric heat capacity of the samples were experimentally measured. The volume fraction of inclusions was systematically varied in order to study the changes in the effective thermal conductivity of the composites. In some samples, a static magnetic field was applied during the polymerization process resulting in anisotropic inclusion distributions. Our results show a decrease in the thermal conductivity of some of the anisotropic samples compared to the isotropic randomly distributed ones. Our analysis indicates that the development of elongated inclusion structures leads to the formation of magnetite and resin domains causing this effect. We correlate the complexity of the inclusion structure with the observed thermal response by a multifractal and lacunarity analysis. All the experimental data are contrasted with the well known Maxwell-Garnett's effective media approximation for composite materials.Comment: 20 pages, 9 figures. arXiv admin note: text overlap with arXiv:cond-mat/0209328 by other author

Quantization of the Myers-Pospelov model: the photon sector interacting with standard fermions as a perturbation of QED

We study the quantization of the electromagnetic sector of the Myers-Pospelov model coupled to standard fermions. Our main objective, based upon experimental and observational evidence, is to construct an effective theory which is a genuine perturbation of QED, such that setting zero the Lorentz invariance violation parameters will reproduce it. To this end we provide a physically motivated prescription, based on the effective character of the model, regarding the way in which the model should be constructed and how the QED limit should be approached. This amounts to the introduction of an additional coarse-graining physical energy scale $M$, under which we can trust the effective field theory formulation. The prescription is successfully tested in the calculation of the Lorentz invariance violating contributions arising from the electron self-energy. Such radiative corrections turn out to be properly scaled by very small factors for any reasonable values of the parameters and no fine-tuning problems are found. Microcausality violations are highly suppressed and occur only in a space-like region extremely close to the light-cone. The stability of the model is guaranteed by restricting to concordant frames satisfying $1-|\mathbf{v}_{max}|> 6.5\times10^{-11}$.Comment: 24 pages, revtex, no figure

Helical magnetic fields via baryon asymmetry

There is strong observational evidence for the presence of large-scale magnetic fields MF in galaxies and clusters, with strength $\sim \mu$G and coherence lenght on the order of Kpc. However its origin remains as an outstanding problem. One of the possible explanations is that they have been generated in the early universe. Recently, it has been proposed that helical primordial magnetic fields PMFs, could be generated during the EW or QCD phase transitions, parity-violating processes and predicted by GUT or string theory. Here we concentrate on the study of two mechanisms to generate PMFs, the first one is the $\nu$MSM which triggers instability in the Maxwell's equations and leads to the generation of helical PMFs. The second one is the usual electroweak baryogenesis scenario. Finally, we calculate the exact power spectra of these helical PMFs and we show its role in the production of gravitational waves finding a scale-invariant on large scales and an oscillatory motion (damping) for $k\eta \gg 1$Comment: 7 pages, to appear in the proceedings of the First Astrostatistics School: Bayesian Methods in Cosmology, June 9-13, 2014, Bogot\'a, Colombi

Principal Component Analysis of computed emission lines from proto-stellar jets

A very important issue concerning protostellar jets is the mechanism behind their formation. Obtaining information on the region at the base of a jet can shed light into the subject and some years ago this has been done through a search for a rotational signature at the jet line spectrum. The existence of such signatures, however, remains controversial. In order to contribute to the clarification of this issue, in this paper we show that the Principal Component Analysis (PCA) can potentially help to distinguish between rotation and precession effects in protostellar jet images. We apply the PCA to synthetic spectro-imaging datacubes generated as an output of numerical simulations of protostellar jets. In this way we generate a benchmark to which a PCA diagnostics of real observations can be confronted. Using the computed emission line profiles for [O I]6300A and [S II]6716A, we recover and analyze the effects of rotation and precession in tomograms generated by PCA. We show that different combinations of the eigenvectors can be used to enhance and to identify the rotation features present in the data. Our results indicate that the PCA can be useful for disentangling rotation from precession in jets with an inclination of the jet with respect to the plane of the sky as high as 45 degrees. We have been able to recover the initially imposed rotation jet profile for models at moderate inclination angle (< 15 degrees) and without precession (abridged).Comment: 19 pages, 19 figures, Accepted for publication in A

Maximum principles, extension problem and inversion for nonlocal one-sided equations

We study one-sided nonlocal equations of the form $$\int_{x_0}^\infty\frac{u(x)-u(x_0)}{(x-x_0)^{1+\alpha}} dx=f(x_0),$$ on the real line. Notice that to compute this nonlocal operator of order $0<\alpha<1$ at a point $x_0$ we need to know the values of $u(x)$ to the right of $x_0$, that is, for $x\geq x_0$. We show that the operator above corresponds to a fractional power of a one-sided first order derivative. Maximum principles and a characterization with an extension problem in the spirit of Caffarelli--Silvestre and Stinga--Torrea are proved. It is also shown that these fractional equations can be solved in the general setting of weighted one-sided spaces. In this regard we present suitable inversion results. Along the way we are able to unify and clarify several notions of fractional derivatives found in the literature.Comment: 20 pages. To appear in Journal of Differential Equation

Centered honeycomb NiSe2 nanoribbons, structure and electronic properties

Quasi one-dimensional nanoribbons are excellent candidates for nanoelectronics, therefore here we investigate by means of density functional theory the structure and electronic properties of a new kind of 1D ribbons, namely: centered honeycomb NiSe2 nanoribbons. Depending on the crystallography and atomic composition of the edges, these ribbons can belong to one of six (two) zigzag (armchair) families. In the zigzag families, after edge reconstruction, all the bare ribbons are metallic. The influence of edge hydrogen passivation produces band gaps in two of the six families. For the armchair nanoribbons, the geometrical reconstruction leads to semiconductors with small band gap and the hydrogen passivation of the edges increases the band gap up to ~0.6 eV.Comment: 8 pages, 5 figure

On Non-Abelian Holonomies

We provide a method and the results for the calculation of the holonomy of a Yang-Mills connection in an arbitrary triangular path, in an expansion (developed here to fifth order) in powers of the corresponding segments. The results might have applications in generalizing to Yang-Mills fields previous calculations of the corrections to particle dynamics induced by loop quantum gravity, as well as in the field of random lattices.Comment: latex, 17 pages, 2 figures, shorter versio

Critical properties of weakly interacting Bose gases as modified by a harmonic confinement

The critical properties of the phase transition from a normal gas to a BEC (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas-Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the {\it global} thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.Comment: 24 pages, 8 figure

The Trace of the CNO Cycle in the Ring Nebula NGC6888

We present new results on the chemical composition of the Galactic ring nebula NGC6888 surrounding the WN6(h) star WR136. The data are based on deep spectroscopical observations taken with the High Dispersion Spectrograph at the 8.2m Subaru Telescope. The spectra cover the optical range from 3700 to 7400 A. The effect of the CNO cycle is well identified in the abundances of He, N, and O, while elements not involved in the synthesis such as Ar, S, and Fe present values consistent with the solar vicinity and the ambient gas. The major achievement of this work is the first detection of the faint CII 4267 recombination line in a Wolf-Rayet nebula. This allows to estimate the C abundance in NGC6888 and therefore investigate for the first time the trace of the CNO cycle in a ring nebula around a Wolf-Rayet star. Although the detection of the CII line has a low signal-to-noise ratio, the C abundance seems to be higher than the predictions of recent stellar evolution models of massive stars. The Ne abundance also show a puzzling pattern with an abundance of about 0.5 dex lower than the solar vicinity, which may be related to the action of the NeNa cycle. Attending to the constraints imposed by the dynamical timescale and the He/H and N/O ratios of the nebula, the comparison with stellar evolution models indicates that the initial mass of the stellar progenitor of NGC6888 is between 25 Msun and 40 Msun.Comment: 14 pages, 5 figures. Accepted for publication in The Astrophysical Journa