Two-component mixture of charged particles confined in a channel: melting

The melting of a binary system of charged particles confined in a {\it quasi}-one-dimensional parabolic channel is studied through Monte Carlo simulations. At zero temperature the particles are ordered in parallel chains. The melting is anisotropic and different melting temperatures are obtained according to the spatial direction, and the different types of particles present in the system. Melting is very different for the single-, two- and four-chain configurations. A temperature induced structural phase transition is found between two different four chain ordered states which is absent in the mono-disperse system. In the mixed regime, where the two types of particles are only slightly different, melting is almost isotropic and a thermally induced homogeneous distribution of the distinct types of charges is observed.Comment: To appear in Journal of Physics: condensed matter ; (13 pages, 12 figures

Magnetization profile for impurities in graphene nanoribbons

The magnetic properties of graphene-related materials and in particular the spin-polarised edge states predicted for pristine graphene nanoribbons (GNRs) with certain edge geometries have received much attention recently due to a range of possible technological applications. However, the magnetic properties of pristine GNRs are not predicted to be particularly robust in the presence of edge disorder. In this work, we examine the magnetic properties of GNRs doped with transition-metal atoms using a combination of mean-field Hubbard and Density Functional Theory techniques. The effect of impurity location on the magnetic moment of such dopants in GNRs is investigated for the two principal GNR edge geometries - armchair and zigzag. Moment profiles are calculated across the width of the ribbon for both substitutional and adsorbed impurities and regular features are observed for zigzag-edged GNRs in particular. Unlike the case of edge-state induced magnetisation, the moments of magnetic impurities embedded in GNRs are found to be particularly stable in the presence of edge disorder. Our results suggest that the magnetic properties of transition-metal doped GNRs are far more robust than those with moments arising intrinsically due to edge geometry.Comment: submitte

Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems

We associate to an arbitrary $\mathbb Z$-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer--Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.Comment: LaTeX2e, 18 page

Effects of a CPT-even and Lorentz-violating nonminimal coupling on the electron-positron scattering

We propose a new \emph{CPT}-even and Lorentz-violating nonminimal coupling between fermions and Abelian gauge fields involving the CPT-even tensor $(K_{F})_{\mu\nu\alpha\beta}$ of the standard model extension. We thus investigate its effects on the cross section of the electron-positron scattering by analyzing the process $e^{+}+e^{-}\rightarrow\mu^{+}+\mu^{-}$. Such a study was performed for the parity-odd and parity-even nonbirefringent components of the Lorentz-violating $(K_{F})_{\mu\nu\alpha\beta}$ tensor. Finally, by using experimental data available in the literature, we have imposed upper bounds as tight as $10^{-12}(eV)^{-1}$ on the magnitude of the CPT-even and Lorentz-violating parameters while nonminimally coupled.Comment: LaTeX2e, 06 pages, 01 figure