Complex Analysis of a Piece of Toda Lattice

We study a small piece of two dimensional Toda lattice as a complex dynamical system. In particular the Julia set, which appears when the piece is deformed, is shown analytically how it disappears as the system approaches to the integrable limit.Comment: 17 pages, LaTe

Metal-Semiconductor Transition and Fermi Velocity Renormalization in Metallic Carbon Nanotubes

Angular perturbations modify the band structure of armchair (and other metallic) carbon nanotubes by breaking the tube symmetry and may induce a metal-semiconductor transition when certain selection rules are satisfied. The symmetry requirements apply for both the nanotube and the perturbation potential, as studied within a nonorthogonal $\pi$-orbital tight-binding method. Perturbations of two categories are considered: an on-site electrostatic potential and a lattice deformation which changes the off-site hopping integrals. Armchair nanotubes are proved to be robust against the metal-semiconductor transition in second-order perturbation theory due to their high symmetry, but can develop a nonzero gap by extending the perturbation series to higher orders or by combining potentials of different types. An assumption of orthogonality between $\pi$ orbitals is shown to lead to an accidental electron-hole symmetry and extra selection rules that are weakly broken in the nonorthogonal theory. These results are further generalized to metallic nanotubes of arbitrary chirality.Comment: Submitted to Phys. Rev. B, 23 pages, 4 figure

Effects of Disorder and Momentum Relaxation on the Intertube Transport of Incommensurate Carbon Nanotube Ropes and Multiwall Nanotubes

We study theoretically the electrical transport between aligned carbon nanotubes in nanotube ropes, and between shells in multiwall carbon nanotubes. We focus on transport between two metallic nanotubes (or shells) of different chiralities with mismatched Fermi momenta and incommensurate periodicities. We perform numerical calculations of the transport properties of such systems within a tight-binding formalism. For clean (disorder-free) nanotubes the intertube transport is strongly suppressed as a result of momentum conservation. For clean nanotubes, the intertube transport is typically dominated by the loss of momentum conservation at the contacts. We discuss in detail the effects of disorder, which also breaks momentum conservation, and calculate the effects of localised scatterers of various types. We show that physically relevant disorder potentials lead to very dramatic enhancements of the intertube conductance. We show that recent experimental measurements of the intershell transport in multiwall nanotubes are consistent with our theoretical results for a model of short-ranged correlated disorder.Comment: References adde

Properties of solar polar coronal plumes constrained by Ultraviolet Coronagraph Spectrometer data

We investigate the plasma dynamics (outflow speed and turbulence) inside polar plumes. We compare line profiles (mainly of \ion{O}{6}) observed by the UVCS instrument on SOHO at the minimum of solar cycle 22-23 with model calculations. We consider Maxwellian velocity distributions with different widths in plume and inter-plume regions. Electron densities are assumed to be enhanced in plumes and to approach inter-plume values with increasing height. Different combinations of the outflow and turbulence velocity in the plume regions are considered. We compute line profiles and total intensities of the \ion{H}{1} Ly$\alpha$ and the \ion{O}{6} doublets. The observed profile shapes and intensities are reproduced best by a small solar wind speed at low altitudes in plumes that increases with height to reach ambient inter-plume values above roughly 3-4 R_\sun combined with a similar variation of the width of the velocity distribution of the scattering atoms/ions. We also find that plumes very close to the pole give narrow profiles at heights above 2.5 R_\sun, which are not observed. This suggests a tendency for plumes to be located away from the pole. We find that the inclusion of plumes in the model computations provides an improved correspondence with the observations and confirms previous results showing that published UVCS observations in polar coronal holes can be roughly reproduced without the need for large temperature anisotropy. The latitude distributions of plumes and magnetic flux distributions are studied by analyzing data from different instruments on SOHO and with SOLIS.Comment: 11 figure

Determination of polarized parton distribution functions with recent data on polarization asymmetries

Global analysis has been performed within the next-to-leading order in Quantum Chromodynamics (QCD) to determine polarized parton distributions with new experimental data in spin asymmetries. The new data set includes JLab, HERMES, and COMPASS measurements on spin asymmetry A_1 for the neutron and deuteron in lepton scattering. Our new analysis also utilizes the double-spin asymmetry for pi^0 production in polarized pp collisions, A_{LL}^{pi^0}, measured by the PHENIX collaboration. Because of these new data, uncertainties of the polarized PDFs are reduced. In particular, the JLab, HERMES, and COMPASS measurements are valuable for determining Delta d_v(x) at large x and Delta qbar(x) at x~0.1. The PHENIX pi^0 data significantly reduce the uncertainty of Delta g(x). Furthermore, we discuss a possible constraint on Delta g(x) at large x by using the HERMES data on g_1^d in comparison with the COMPASS ones at x~0.05.Comment: 11 pages, REVTeX, 13 eps files, Phys. Rev. D in pres

Dual Resonance Model Solves the Yang-Baxter Equation

The duality of dual resonance models is shown to imply that the four point string correlation function solves the Yang-Baxter equation. A reduction of transfer matrices to $A_l$ symmetry is described by a restriction of the KP $\tau$ function to Toda molecules.Comment: 10 pages, LaTe

Spin configurations of carbon nanotube in a nonuniform external potential

We study, theoretically, the ground state spin of a carbon nanotube in the presence of an external potential. We find that when the external potential is applied to a part of the nanotube, its variation changes the single electron spectrum significantly. This, in combination with Coulomb repulsion and the symmetry properties of a finite length armchair nanotube induces spin flips in the ground state when the external potential is varied. We discuss the possible application of our theory to recent measurements of Coulomb blocked peaks and their dependence on a weak magnetic field in armchair carbon nanotubes.Comment: RevTeX, 5 pages + two figure

On the linear representations of the symmetry groups of single-wall carbon nanotubes

The positions of atoms forming a carbon nanotube are usually described by using a system of generators of the symmetry group. Each atomic position corresponds to an element of the set Z x {0,1,...,n} x {0,1}, where n depends on the considered nanotube. We obtain an alternate rather different description by starting from a three-axes description of the honeycomb lattice. In our mathematical model, which is a factor space defined by an equivalence relation in the set {(v_0,v_1,v_2)\in Z^3 | v_0+v_1+v_2\in {0,1}}, the neighbours of an atomic position can be described in a simpler way, and the mathematical objects with geometric or physical significance have a simpler and more symmetric form. We present some results concerning the linear representations of single-wall carbon nanotubes in order to illustrate the proposed approach.Comment: Major change of content. More details will be available at http://fpcm5.fizica.unibuc.ro/~ncotfa