Enveloping algebras of Malcev algebras

We first discuss the construction by Perez-Izquierdo and Shestakov of universal nonassociative enveloping algebras of Malcev algebras. We then describe recent results on explicit structure constants for the universal enveloping algebras (both nonassociative and alternative) of the 4-dimensional solvable Malcev algebra and the 5-dimensional nilpotent Malcev algebra. We include a proof (due to Shestakov) that the universal alternative enveloping algebra of the real 7-dimensional simple Malcev algebra is isomorphic to the 8-dimensional division algebra of real octonions. We conclude with some brief remarks on tangent algebras of analytic Bol loops and monoassociative loops. This is a revised and expanded version of the survey talk given by the first author at the Second Mile High Conference on Nonassociative Mathematics at the University of Denver (Denver, Colorado, USA, June 22 to 26, 2009).Comment: 15 page

Relativistic Tunneling Through Two Successive Barriers

We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called \emph{Generalized Hartman Effect}, an effect observed in the context of nonrelativistic tunneling as well as in its electromagnetic counterparts, and which is often associated with the possibility of superluminal velocities in the tunneling process. We discuss the behavior of both the phase (or group) tunneling time and the dwell time, and show that in the limit of opaque barriers the relativistic theory also allows the emergence of the Generalized Hartman Effect. We compare our results with the nonrelativistic ones and discuss their interpretation.Comment: 7 pages, 3 figures. Revised version, with a new appendix added. Slightly changes in the styles and captions of Figures 1 and 2. To appear in Physical Review

Magnetic-field effects in defect-controlled ferromagnetic Ga_{1-x}Mn_xAs semiconductors

We have studied the magnetic-field and concentration dependences of the magnetizations of the hole and Mn subsystems in diluted ferromagnetic semiconductor Ga_{1-x}Mn_xAs. A mean-field approximation to the hole-mediated interaction is used, in which the hole concentration p(x) is parametrized in terms of a fitting (of the hole effective mass and hole/local moment coupling) to experimental data on the Tc critical temperature. The dependence of the magnetizations with x, for a given temperature, presents a sharply peaked structure, with maxima increasing with applied magnetic field, which indicates that application to diluted-magnetic-semiconductor devices would require quality-control of the Mn-doping composition. We also compare various experimental data for Tc(x) and p(x) on different Ga_{1-x}Mn_xAs samples and stress the need of further detailed experimental work to assure that the experimental measurements are reproducible.Comment: RevTeX 4, 3 two-column pages, 4 colour figures; to appear in J Appl Phy

Disorder and the effective Mn-Mn exchange interaction in Ga1−x_{1-x}Mnx_xAs diluted magnetic semiconductors

We perform a theoretical study, using {\it ab initio} total energy density-functional calculations, of the effects of disorder on the $Mn-Mn$ exchange interactions for $Ga_{1-x}Mn_xAs$ diluted semiconductors. For a 128 atoms supercell, we consider a variety of configurations with 2, 3 and 4 Mn atoms, which correspond to concentrations of 3.1%, 4.7%, and 6.3%, respectively. In this way, the disorder is intrinsically considered in the calculations. Using a Heisenberg Hamiltonian to map the magnetic excitations, and {\it ab initio} total energy calculations, we obtain the effective \JMn, from first ($n=1$) all the way up to sixth ($n=6$) neighbors. Calculated results show a clear dependence in the magnitudes of the \JMn with the Mn concentration $x$. Also, configurational disorder and/or clustering effects lead to large dispersions in the Mn-Mn exchange interactions, in the case of fixed Mn concentration. Moreover, theoretical results for the ground-state total energies for several configurations indicate the importance of a proper consideration of disorder in treating temperature and annealing effects

Dimension formulas for the free nonassociative algebra

The free nonassociative algebra contains two subspaces closed under both the commutator and the associator: the Akivis elements and the primitive elements. Every Akivis element is primitive, but there are primitive elements which are not Akivis