Symmetry operators and separation of variables in the (2+1)(2+1)-dimensional Dirac equation with external electromagnetic field

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a $(2+1)$-dimensional Minkowski (flat) space. For each of the sets we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.Comment: 24 pages, version accepted for publication in Int. J. Geom. Methods Mod. Phy

Electronic Green's functions in a T-shaped multi-quantum dot system

We developed a set of equations to calculate the electronic Green's functions in a T-shaped multi-quantum dot system using the equation of motion method. We model the system using a generalized Anderson Hamiltonian which accounts for {\em finite} intradot on-site Coulomb interaction in all component dots as well as for the interdot electron tunneling between adjacent quantum dots. Our results are obtained within and beyond the Hartree-Fock approximation and provide a path to evaluate all the electronic correlations in the multi-quantum dot system in the Coulomb blockade regime. Both approximations provide information on the physical effects related to the finite intradot on-site Coulomb interaction. As a particular example for our generalized results, we considered the simplest T-shaped system consisting of two dots and proved that our approximation introduces important corrections in the detector and side dots Green's functions, and implicitly in the evaluation of the system's transport properties. The multi-quantum dot T-shaped setup may be of interest for the practical realization of qubit states in quantum dots systems.Comment: 13 pages, 2 figure

The lepton pair production in heavy ion collisions in perturbation theory

We derive the first terms in the amplitude of lepton pair production in the Coulomb fields of two relativistic heavy ions. Using the Sudakov technique, which very simplify the calculations in momentum space for the processes at high energies, we get the compact analytical expressions for differential cross section of the process under consideration in the lowest order in fine structure constant (Born approximation) valid for any momentum transfer and in a wide kinematics region for produced particles. Exploiting the same technique we consider the next terms of perturbation series (up to fourth order in fine structure constant) and investigate their energy dependence and limiting cases. It has been shown that taking in account all relevant terms in corresponding order one obtains the expressions which are gauge invariant and finite. We estimate the contribution of the Coulomb corrections to the total cross section and discuss the cancellations of the different terms which holds in the total cross section.Comment: LaTeX2e, 18 pages, 4 eps figure

How Can Reasoner Performance of ABox Intensive Ontologies Be Predicted?

Reasoner performance prediction of ontologies in OWL 2 language has been studied so far from different dimensions. One key aspect of these studies has been the prediction of how much time a particular task for a given ontology will consume. Several approaches have adopted different machine learning techniques to predict time consumption of ontologies already. However, these studies focused on capturing general aspects of the ontologies (i.e., mainly the complexity of their TBoxes), while paying little attention to ABox intensive ontologies. To address this issue, in this paper, we propose to improve the representativeness of ontology metrics by developing new metrics which focus on the ABox features of ontologies. Our experiments show that the proposed metrics contribute to overall prediction accuracy for all ontologies in general without causing side-effects

A light-fronts approach to electron-positron pair production in ultrarelativistic heavy-ion collisions

We perform a gauge-transformation on the time-dependent Dirac equation describing the evolution of an electron in a heavy-ion collision to remove the explicit dependence on the long-range part of the interaction. We solve, in an ultra-relativistic limit, the gauged-transformed Dirac equation using light-front variables and a light-fronts representation, obtaining non-perturbative results for the free pair-creation amplitudes in the collider frame. Our result reproduces the result of second-order perturbation theory in the small charge limit while non-perturbative effects arise for realistic charges of the ions.Comment: 39 pages, Revtex, 7 figures, submitted to PR

Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence.Comment: 10 pages, 12 figures, additional references adde

Phytochemical and nutritional properties of sumac (Rhus coriaria): a potential ingredient for developing functional foods

This is the final version. Available on open access from Elsevier via the DOI in this recordSumac (Rhus coriaria) is a flowering plant that is widely consumed for its promoting health benefits and used in food preparations as a spice in the Mediterranean region. It is a high shrub or small tree with imparipinnate leaves, villus and red fruits with one-seeded drupe, and small greenish-white flowers. The nutraceutical and pharmaceutical potential of sumac makes it a remarkable functional food. In this review, the phytochemical and nutritional properties of sumac as an under valorized functional food have been discussed. Flavonoids, anthocyanins, phenolic acids, and organic acids have been reported as dominant phytochemicals in sumac, which are well known for their pharmacological properties that attract many consumers to commonly choose sumac in their diet as well as food preparations. The remarkable volatile compounds present in sumac give it a unique aroma that increases its acceptance by consumers and potential use in the food industry. Sumac has been evaluated for a broad range of nutritional and pharmacological activities such as antioxidant, antinociceptive, anti-inflammatory, anti-diabetic, hepatoprotective, cardioprotective, anticancer, anti-infertility, and neuroprotective potential. This review has also briefly outlined the safety concerns concerning the use of sumac in terms of toxicology and interactions

Wigner crystal physics in quantum wires

The physics of interacting quantum wires has attracted a lot of attention recently. When the density of electrons in the wire is very low, the strong repulsion between electrons leads to the formation of a Wigner crystal. We review the rich spin and orbital properties of the Wigner crystal, both in the one-dimensional and quasi-one-dimensional regime. In the one-dimensional Wigner crystal the electron spins form an antiferromagnetic Heisenberg chain with exponentially small exchange coupling. In the presence of leads the resulting inhomogeneity of the electron density causes a violation of spin-charge separation. As a consequence the spin degrees of freedom affect the conductance of the wire. Upon increasing the electron density, the Wigner crystal starts deviating from the strictly one-dimensional geometry, forming a zigzag structure instead. Spin interactions in this regime are dominated by ring exchanges, and the phase diagram of the resulting zigzag spin chain has a number of unpolarized phases as well as regions of complete and partial spin polarization. Finally we address the orbital properties in the vicinity of the transition from a one-dimensional to a quasi-one-dimensional state. Due to the locking between chains in the zigzag Wigner crystal, only one gapless mode exists. Manifestations of Wigner crystal physics at weak interactions are explored by studying the fate of the additional gapped low-energy mode as a function of interaction strength.Comment: 37 pages, 15 figures; v2: references adde