Solving simple quaternionic differential equations

The renewed interest in investigating quaternionic quantum mechanics, in particular tunneling effects, and the recent results on quaternionic differential operators motivate the study of resolution methods for quaternionic differential equations. In this paper, by using the real matrix representation of left/right acting quaternionic operators, we prove existence and uniqueness for quaternionic initial value problems, discuss the reduction of order for quaternionic homogeneous differential equations and extend to the non-commutative case the method of variation of parameters. We also show that the standard Wronskian cannot uniquely be extended to the quaternionic case. Nevertheless, the absolute value of the complex Wronskian admits a non-commutative extension for quaternionic functions of one real variable. Linear dependence and independence of solutions of homogeneous (right) H-linear differential equations is then related to this new functional. Our discussion is, for simplicity, presented for quaternionic second order differential equations. This involves no loss of generality. Definitions and results can be readily extended to the n-order case.Comment: 9 pages, AMS-Te

Graphene tests of Klein phenomena

Graphene is characterized by chiral electronic excitations. As such it provides a perfect testing ground for the production of Klein pairs (electron/holes). If confirmed, the standard results for barrier phenomena must be reconsidered with, as a byproduct, the accumulation within the barrier of holes.Comment: 8 page

Quaternionic eigenvalue problem

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te

Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te

Universal Elasticity and Fluctuations of Nematic Gels

We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infared fixed point. Namely, at long scales, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local hetergeneities down to d_lc < 3.Comment: 4 RevTeX pgs, submitted to PR

Dirac Equation Studies in the Tunnelling Energy Zone

We investigate the tunnelling zone V0 < E < V0+m for a one-dimensional potential within the Dirac equation. We find the appearance of superluminal transit times akin to the Hartman effect.Comment: 12 pages, 4 figure

The EGNoG Survey: Gas Excitation in Normal Galaxies at z~0.3

As observations of molecular gas in galaxies are pushed to lower star formation rate galaxies at higher redshifts, it is becoming increasingly important to understand the conditions of the gas in these systems to properly infer their molecular gas content. The rotational transitions of the carbon monoxide (CO) molecule provide an excellent probe of the gas excitation conditions in these galaxies. In this paper we present the results from the gas excitation sample of the Evolution of molecular Gas in Normal Galaxies (EGNoG) survey at the Combined Array for Research in Millimeter-wave Astronomy (CARMA). This subset of the full EGNoG sample consists of four galaxies at z~0.3 with star formation rates of 40-65 M_Sun yr^-1 and stellar masses of ~2x10^11 M_Sun. Using the 3 mm and 1 mm bands at CARMA, we observe both the CO(1-0) and CO(3-2) transitions in these four galaxies in order to probe the excitation of the molecular gas. We report robust detections of both lines in three galaxies (and an upper limit on the fourth), with an average line ratio, r_31 = L'_CO(3-2) / L'_CO(1-0), of 0.46 \pm 0.07 (with systematic errors \lesssim 40%), which implies sub-thermal excitation of the CO(3-2) line. We conclude that the excitation of the gas in these massive, highly star-forming galaxies is consistent with normal star-forming galaxies such as local spirals, not starbursting systems like local ultra-luminous infrared galaxies. Since the EGNoG gas excitation sample galaxies are selected from the main sequence of star-forming galaxies, we suggest that this result is applicable to studies of main sequence galaxies at intermediate and high redshifts, supporting the assumptions made in studies that find molecular gas fractions in star forming galaxies at z~1-2 to be an order of magnitude larger than what is observed locally.Comment: Accepted for publication in the Astrophysical Journal, to appear January 2013; 18 pages, 10 figures, 6 table

The role of personal information sources on the decision-making process of Costa Rican dairy farmers

The attitudes of farmers in relation to the importance of different people as information and opinion sources (InfS) for different phases of the decision-making process were studied in 91 Costa Rican dairy farmers. The InfS studied were: Family members, Other farmers, Technical advisors, Farm staff and Commercial agents, while the phases were: Problem detection, Seeking for problem solutions, Seeking for new practices and Seeking for opinion. A Multidimensional Preference Analysis (MDPREF) was used to obtain a two-dimensional map of preference of the farmers. A factor analysis was used to define new variables representing the farmers' predilection towards the InfS. A canonical correlation analysis was performed to find-out simple and canonical correlation between farmers'/farms' characteristics and the InfS preferences. Informational profiles in the population were defined through a Cluster Analysis. The MDPREF suggests that Family members and Technical advisors were the most preferred InfS. However their relative importance changed throughout the phases. Farm staff were rated in third place and their role became more important in the ‘Problem detection’ phase. Other farmers and Commercial agents were, in general, the less preferred information sources. The former became slightly more important in the ‘Seeking for new practices’ phase. The canonical correlation analysis found three low-medium correlations between the farmers'/farms' characteristics and the InfS factors. These correlations showed that the farmers' age, educational level and dedication and the farms' characteristics of area, herd size and distance to population centres had significant influence on the preference of the farmers towards different information sources. The cluster analysis found nine groups of similar farmers according to their preferences towards informational sources. Some implications mainly for extension activities are also stated and discussed. The importance of different informational sources slightly change throughout the decision-making steps, the family and farm staff being the most preferred information sources