Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

Preparation and electrical properties of graphene nanosheet/Al2O3 composites

Fully dense graphene nanosheet(GNS)/Al2O3 composites with homogeneously distributed GNSs of thicknesses ranging from 2.5 to 20 nm have been fabricated from ball milled expanded graphite and Al2O3 by spark plasma sintering. The percolation threshold of electrical conductivity of the as-prepared GNS/Al2O3 composites is around 3 vol.%, and this new composite outperforms most of carbon nanotube/Al2O3 composites in electrical conductivity. The temperature dependence of electrical conductivity indicated that the as-prepared composites behaved as a semimetal in a temperature range from 2 to 300 K.

Sparsity and "something else": an approach to encrypted image folding

A property of sparse representations in relation to their capacity for information storage is discussed. It is shown that this feature can be used for an application that we term Encrypted Image Folding. The proposed procedure is realizable through any suitable transformation. In particular, in this paper we illustrate the approach by recourse to the Discrete Cosine Transform and a combination of redundant Cosine and Dirac dictionaries. The main advantage of the proposed technique is that both storage and encryption can be achieved simultaneously using simple processing steps.

Transport properties of hot-pressed bulk carbon nanotubes compacted by spark plasma sintering

Electrical and thermal transport properties of the carbon nanotube bulk material compacted by spark plasma sintering have been investigated. The electrical conductivity of the as-prepared sample shows a lnT dependence from 4 to 50 K, after which the conductivity begins to increase approximately linearly with temperature. A magnetic field applied perpendicularly to the sample increases the electrical conductivity in the range of 0-8T at all testing temperatures, indicating that the sample possesses the two-dimensional weak localization at lower temperatures (?50 K), while behaviors like a semimetal at higher temperatures (?50 K). This material acts like a uniform compact consisting of randomly distributed two dimensional graphene layers. For the same material, the thermal conductivity is found to decrease almost linearly with decreasing temperature, similar to that of a single multi-walled carbon nanotube. Magnetic fields applied perpendicularly to the sample cause the thermal conductivity to decrease significantly, but the influence of the magnetic fields becomes weak when temperature increases.

High-frequency conductivity of optically excited charge carriers in hydrogenated nanocrystalline silicon investigated by spectroscopic femtosecond pump-probe reflectivity measurements

We report an investigation into the high-frequency conductivity of optically excited charge carriers far from equilibrium with the lattice. The investigated samples consist of hydrogenated nanocrystalline silicon films grown on a thin film of silicon oxide on top of a silicon substrate. For the investigation, we used an optical femtosecond pump-probe setup to measure the reflectance change of a probe beam. The pump beam ranged between 580 and 820nm, whereas the probe wavelength spanned 770 to 810nm. The pump fluence was fixed at 0.6mJ/cm2. We show that at a fixed delay time of 300fs, the conductivity of the excited electron-hole plasma is described well by a classical conductivity model of a hot charge carrier gas found at Maxwell-Boltzmann distribution, while Fermi-Dirac statics is not suitable. This is corroborated by values retrieved from pump-probe reflectance measurements of the conductivity and its dependence on the excitation wavelength and carrier temperature. The conductivity decreases monotonically as a function of the excitation wavelength, as expected for a nondegenerate charge carrier gas.

Notes on sufficient conditions for a graph to be Hamiltonian

The first part of this paper deals with an extension of Dirac's Theorem to directed graphs. It is related to a result often referred to as the Ghouila-Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila-Houri Theorem is redundant. The Second part of the paper shows that a condition on the number of edges for a graph to be hamiltonian implies Ore's condition on the degrees of the vertices.

Simulação computacional de materiais bidimensionais: funcionalização de defeitos extensos no grafeno e retenção de contaminantes por argilominerais

In this work are considered two bidimensional systems, with distints chacacteristcs and applicabilitys. Is studied the adsorption of transition metals (MT) Fe, Co, Mn and Ru in extended defects, formed by graphene grain boundaries. First in pristine graphene The hollow site of carbon hexagon, in pristine graphene, are the most stable for MT adsorption. The Dirac cone in eletronic structure of graphene was manteined with the presence of MT. For the considered grain boundaries the MT has a greater stability for absorption in the grain boundaries sites in comparison with pristine graphene. Through the energy barrier values, are observed diffusion chanels for MT localized on the grain boundaries. This diffusion chanels indicate a possible formation of nanolines of MT in graphene. For the first stage of the nanolines, ate observed a better stability for the system with greater MT concentration, due to MT-MT interactions. Also, due to the magnetic moment of the MT, the nanolines show a magnetization. For the most stable configurations the system are metallics, particularly for Fe the band structure indicates an anisotropic spin current. In a second study, are considereted the retention capacity for metallic contaminants Cd and Hg in clayminerals, kaolinite (KAO) and montmorillonite (MMT). Through the adsorption energies of contaminantes in the clayminerals, was observed a increase in stability with the increase of contaminants concentration, due to the interaction Cd-Cd and Hg-Hg. Also, was observed that KAO has a strong interaction beteween monolayers than MMT. In this sence, for the adsoption process of contaminantes in the natural form of KAO and MMT, the latter has a better retention capacity, due to the small net work for contaminant intercalation. However, when the modification of clayminerals, with molecules that increase the spacing between monolayers, exist a optimal condition, which the contaminant absorption are more stable in KAO system than in MMT. In the Langmuir adsorption model for the clayminerals in the optimal monolayer spacing, the retention capacity for Cd and Hg in KAO system are 21% greater than in MMT system. Also, for the X-ray Absorption Near Edge Spectroscopy (XANES) for the K edge of Cd and Hg, are found a positive shift of absorption edge with the decreasing of monolayer spacing. This result indicates a possible way to determine the concentration of adsorbed contaminats in relation to unabsorbed ones, from the decomposition of experimental XANES in the obteined spectras.

G2-Monopoles with Singularities (Examples)

© 2016 Springer Science+Business Media DordrechtG2-Monopoles are solutions to gauge theoretical equations on G2-manifolds. If the G2-manifolds under consideration are compact, then any irreducible G2-monopole must have singularities. It is then important to understand which kind of singularities G2-monopoles can have. We give examples (in the noncompact case) of non-Abelian monopoles with Dirac type singularities, and examples of monopoles whose singularities are not of that type. We also give an existence result for Abelian monopoles with Dirac type singularities on compact manifolds. This should be one of the building blocks in a gluing construction aimed at constructing non-Abelian ones.

Benchmarking a modified version of the civ3 nonrelativistic atomic-structure code within Na-like-tungsten R -matrix calculations

In this work we explore the validity of employing a modified version of the nonrelativistic structure code civ3 for heavy, highly charged systems, using Na-like tungsten as a simple benchmark. Consequently, we present radiative and subsequent collisional atomic data compared with corresponding results from a fully relativistic structure and collisional model. Our motivation for this line of study is to benchmark civ3 against the relativistic grasp0 structure code. This is an important study as civ3 wave functions in nonrelativistic R-matrix calculations are computationally less expensive than their Dirac counterparts. There are very few existing data for the W LXIV ion in the literature with which we can compare except for an incomplete set of energy levels available from the NIST database. The overall accuracy of the present results is thus determined by the comparison between the civ3 and grasp0 structure codes alongside collisional atomic data computed by the R-matrix Breit-Pauli and Dirac codes. It is found that the electron-impact collision strengths and effective collision strengths computed by these differing methods are in good general agreement for the majority of the transitions considered, across a broad range of electron temperatures.

A boron nitride - graphene - C60 heterostructure

We have fabricated a new van-der-Waals heterostructure composed by BN/graphene/C60. We performed transport measurements on the preliminary BN/graphene device finding a sharp Dirac point at the neutrality point. After the deposition of a C60 thin film by thermal evaporation, we have observed a significant n-doping of the heterostructure. This suggests an unusual electron transfer from C60 into the BN/graphene structure. This BN/graphene/C60 heterostructure can be of interest in photovoltaic applications. It can be used to build devices like p-n junctions, where C60 can be easily deposited in defined regions of a graphene junction by the use of a shadow mask. Our results are contrasted with theoretical calculations.

Clifford-Hermite polynomials in fractional Clifford analysis

In this paper we generalize radial and standard Clifford-Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann-Liouville derivative in a symbolic way. As main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven.

Superlattice structures in twisted bilayers of folded graphene

The electronic properties of bilayer graphene strongly depend on relative orientation of the two atomic lattices. Whereas Bernal-stacked graphene is most commonly studied, a rotational mismatch between layers opens up a whole new field of rich physics, especially at small interlayer twist. Here we report on magnetotransport measurements on twisted graphene bilayers, prepared by folding of single layers. These reveal a strong dependence on the twist angle, which can be estimated by means of sample geometry. At small rotation, superlattices with a wavelength in the order of 10 nm arise and are observed by friction atomic force microscopy. Magnetotransport measurements in this small-angle regime show the formation of satellite Landau fans. These are attributed to additional Dirac singularities in the band structure and discussed with respect to the wide range of interlayer coupling models.

Quantizzazione in gauge di cono-luce di particelle e stringhe

In questa tesi si discute la formulazione di una teoria quantistica della dinamica libera di particelle e stringhe relativistiche. La dinamica relativistica viene costruita in entrambi i casi a partire dalla formulazione classica con invarianza di gauge della parametrizzazione di, rispettivamente, linee e fogli di mondo. Si scelgono poi condizioni di gauge-fixing dette di cono-luce. La teoria quantistica viene poi formulata usando le prescrizioni di quantizzazione canonica di Dirac.

On the trace anomaly of a Weyl fermion

La seguente tesi si sviluppa in tre parti: un'introduzione alle simmetrie conformi e di scala, una parte centrale dedicata alle anomalie quantistiche ed una terza parte dedicata all'anomalia di traccia per fermioni. Nella seconda parte in particolare si introduce il metodo di calcolo alla Fujikawa e si discute la scelta di regolatori adeguati ed un metodo per ottenerli, si applicano poi questi metodi ai campi, scalare e vettoriale, per l'anomalia di traccia in spazio curvo. Nell'ultimo capitolo si calcolano le anomalie di traccia per un fermione di Dirac e per uno di Weyl; la motivazione per calcolare queste anomalie nasce dal fatto che recenti articoli hanno suggerito che possa emergere un termine immaginario proporzionale alle densità di Pontryagin nell'anomalia di Weyl. Noi non abbiamo trovato questo termine e il risultato è che l'anomalia di traccia risulta essere metà di quella per il caso di Dirac.