On the group of ring motions of an H-trivial link

In this paper we compute a presentation for the group of ring motions of the split union of a Hopf link with Euclidean components and a Euclidean circle. A key part of this work is the study of a short exact sequence of groups of ring motions of general ring links in R3. This sequence allowed us to build the main result from the previously known case of the ring group with one component, which a particular case of the ring groups studied by Brendle and Hatcher. This work is a first step towards the computation of a presentation for groups of motions of H-trivial links with an arbitrary number of components

Chiral dynamics in few-nucleon systems

We report on recent progress achieved in calculating various few-nucleon low-energy observables from effective field theory. Our discussion includes scattering and bound states in the 2N, 3N and 4N systems and isospin violating effects in the 2N system. We also establish a link between the nucleon-nucleon potential derived in chiral effective field theory and various modern high-precision potentials.Comment: 12 pp, uses aipproc style files, 4 figures, contribution to the conference on "Mesons and Light Nuclei", Prag, July 2001, to appear in the proceeding

Chiral dynamics in few-nucleon systems

We employ the chiral nucleon-nucleon potential derived using the method of unitary transformation up to next-to-next-to-leading order (NNLO) to study bound and scattering states in the two-nucleon system. The predicted partial wave phase shifts and mixing parameters for higher energies and higher angular momenta beyond the ones which are fitted are mostly well described for energies below 300 MeV. Various deuteron properties are discussed. We also apply the next-to-leading order (NLO) potential to 3N and 4N systems. The resulting 3N and 4N binding energies are in the same range what is found using standard NN potentials. Experimental low-energy 3N scattering observables are also very well reproduced like for standard NN forces. Surprisingly the long standing Ay-puzzle is resolved at NLO. The cut-off dependence of the scattering observables is rather mild.Comment: LaTeX2e, 8 pages; invited talk presented at the XVIIth European Conference on Few-Body Problems in Physics, Evora, Portugal, September 2000; to be published in the Proceeding

Fine structure and magneto-optics of exciton, trion, and charged biexciton states in single InAs quantum dots emitting at 1.3 um

We present a detailed investigation into the optical characteristics of individual InAs quantum dots (QDs) grown by metalorganic chemical vapor deposition, with low temperature emission in the telecoms window around 1300 nm. Using micro-photoluminescence (PL) spectroscopy we have identified neutral, positively charged, and negatively charged exciton and biexciton states. Temperature-dependent measurements reveal dot-charging effects due to differences in carrier diffusivity. We observe a pronounced linearly polarized splitting of the neutral exciton and biexciton lines (~250 ueV) resulting from asymmetry in the QD structure. This asymmetry also causes a mixing of the excited trion states which is manifested in the fine structure and polarization of the charged biexciton emission; from this data we obtain values for the ratio between the anisotropic and isotropic electron-hole exchange energies of (Delta1)/(Delta0)= 0.2--0.5. Magneto-PL spectroscopy has been used to investigate the diamagnetic response and Zeeman splitting of the various exciton complexes. We find a significant variation in g-factor between the exciton, the positive biexciton, and the negative biexciton; this is also attributed to anisotropy effects and the difference in lateral extent of the electron and hole wavefunctions.Comment: 7 pages, 6 figures, submitted to Phys. Rev.

Shadowing and Antishadowing Effects in a Model for the n+d Total Cross Section

Based on the multiple scattering series incorporated in the Faddeev scheme the high energy limit of the total n+d cross section is evaluated in a nonrelativistic model system where spins are neglected. In contrast to the naive expectation that the total n+d scattering cross section is the sum of two NN cross sections we find two additional effects resulting from rescattering processes. These additional terms have different signs (shadowing and antishadowing) and a different behavior as function of the energy. Our derivation of these results which are already known from Glauber theory is based on the analytical evaluation of elastic transition amplitudes in the high energy limit. It does not depend on the diffraction type assumptions connected with Glauber theory. In this model of spinless Yukawa type forces (with no absorption) the total n+d cross section approaches the total NN cross section multiplied by a number larger than 2 in the high energy limit. Therefore, the enhancement effect resulting from rescattering is larger than the shadowing effect, which decreases faster with energy

The Galois Complexity of Graph Drawing: Why Numerical Solutions are Ubiquitous for Force-Directed, Spectral, and Circle Packing Drawings

Many well-known graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings ubiquitously use iterative numerical approximations rather than constructing and then solving algebraic expressions representing their exact solutions. To explain this phenomenon, we use Galois theory to show that many variants of these problems have solutions that cannot be expressed by nested radicals or nested roots of low-degree polynomials. Hence, such solutions cannot be computed exactly even in extended computational models that include such operations.Comment: Graph Drawing 201

Some constructions of almost para-hyperhermitian structures on manifolds and tangent bundles

In this paper we give some examples of almost para-hyperhermitian structures on the tangent bundle of an almost product manifold, on the product manifold $M\times\mathbb{R}$, where $M$ is a manifold endowed with a mixed 3-structure and on the circle bundle over a manifold with a mixed 3-structure.Comment: 10 pages; This paper has been presented in the "4th German-Romanian Seminar on Geometry" Dortmund, Germany, 15-18 July 200

The alpha-particle based on modern nuclear forces

The Faddeev-Yakubovsky equations for the alpha-particle are solved. Accurate results are obtained for several modern NN interaction models, which include charge-symmetry breaking effects in the NN force, nucleon mass dependences as well as the Coulomb interaction. These models are augmented by three-nucleon forces of different types and adjusted to the 3N binding energy. Our results are close to the experimental binding energy with a slight overbinding. Thus there is only little room left for the contribution of possible 4N interactions to the alpha-particle binding energy. We also discuss model dependences of the binding energies and the wave functions.Comment: 22 pages REVTeX 4, 12 figures, table with TM parameters added, typos corrected, version as published in PR