Stefan E. Schmidt

Finite-Ring Combinatorics and MacWilliams' Equivalence Theorem

F. J. MacWilliams proved that Hamming isometries between linear codes extend to monomial transformations. This theorem has recently been genera- lized by J. Wood who proved it for Frobenius rings using character theoretic methods. The present paper provides a combinatorial approach: First we extend I. Constantinescus concept of homogeneous weights on arbitrary finite rings and prove MacWilliams equivalence theorem to hold with respect to these weights for all finite Frobenius rings. As a central tool we then establish a general inversion principle for real functions on finite modules that involves Mobius inversion on partially ordered sets. An application of the latter yields the aforementioned result of Wood.

Gray isometries for finite chain rings and a nonlinear ternary (36, 3/sup 12/, 15) code

Using tensor product constructions for the first-order generalized Reed-Muller codes, we extend the well-established concept of the Gray isometry between (Z/sub 4/, /spl delta//sub L/) and (Z/sub 2//sup 2/, /spl delta//sub H/) to the context of finite chain rings. Our approach covers previous results by Carlet (see ibid., vol.44, p.1543-7, 1998), Constantinescu (see Probl. Pered. Inform., vol.33, no.3, p.22-8, 1997 and Ph.D. dissertation, Tech. Univ. Munchen, Munchen, Germany, 1995), Nechaev et al. (see Proc. IEEE Int. Symp. Information Theory and its Applications, p.31-4, 1996) and overlaps with Heise et al. (see Proc. ACCT 6, Pskov, Russia, p.123-9, 1998) and Honold et al. (see Proc. ACCT 6, Pskov, Russia, p.135-41, 1998). Applying the Gray isometry on Z/sub 9/ we obtain a previously unknown nonlinear ternary (36, 3/sup 12/, 15) code.

Electron-phonon coupling and its evidence in the photoemission spectra of lead.

We present a detailed study of the influence of strong electron-phonon coupling on the photoemission spectra of lead. Representing the strong-coupling regime of superconductivity, the spectra of lead show characteristic features that demonstrate the correspondence of physical properties in the normal and the superconducting state, as predicted by the Eliashberg theory. These features appear on an energy scale of a few meV and are accessible for photoemission only by using modern spectrometers with high-resolution in energy and angle.

A unified approach to projective lattice geometries

The interest in pursuing projective geometry on modules has led to several lattice theoretic generalizations of the classical synthetic concept of projective geometry on vector spaces.Introduced in this paper is an approach that is capable of unifying various attempts within a new conceptual frame. This approach reflects algebraic properties from a lattice-geometric point of view. Together with new results we are presenting results from previous publications which have been improved in the frame of this work.

High precision hyperfine measurements in Bismuth challenge bound-state strong-field QED

Electrons bound in highly charged heavy ions such as hydrogen-like bismuth 209Bi82+ experience electromagnetic fields that are a million times stronger than in light atoms. Measuring the wavelength of light emitted and absorbed by these ions is therefore a sensitive testing ground for quantum electrodynamical (QED) effects and especially the electron–nucleus interaction under such extreme conditions. However, insufficient knowledge of the nuclear structure has prevented a rigorous test of strong-field QED. Here we present a measurement of the so-called specific difference between the hyperfine splittings in hydrogen-like and lithium-like bismuth 209Bi82+,80+ with a precision that is improved by more than an order of magnitude. Even though this quantity is believed to be largely insensitive to nuclear structure and therefore the most decisive test of QED in the strong magnetic field regime, we find a 7-σ discrepancy compared with the theoretical prediction.

Projective Geometry on Modular Lattices

Publisher Summary This chapter focuses on projective geometry on modular lattices. Incidence and Order are basic concepts for a foundation of modern synthetic geometry. These concepts describe the relative location or containment of geometric objects and have led to different lines of geometry, an incidence-geometric and a lattice-theoretic one. Modularity is one of the fundamental properties of classical projective geometry. It makes projections into join-preserving mappings and yields perspectivities to be (interval) isomorphisms. It is therefore natural that order-theoretic generalizations of projective geometry are based on modular lattices and even more, the theory of modular lattices may be considered as a most general concept of projective geometry. In particular, the partially ordered set of all submodules of a module forms a (complete) modular lattice; even more general, any sublattice of the lattice of all normal subgroups of a group is a modular lattice. It considers that lattice-geometric approaches are complete geometrical structures whose geometrical objects form complete (modular) lattices.

An improved value for the hyperfine splitting of hydrogen-like 209Bi82+

We report an improved measurement of the hyperfine splitting in hydrogen-like bismuth (209Bi82+) at the experimental storage ring ESR at GSI by laser spectroscopy on a coasting beam. Accuracy was improved by about an order of magnitude compared to the first observation in 1994. The most important improvement is an in situ high voltage measurement at the electron cooler (EC) platform with an accuracy at the 10 ppm level. Furthermore, the space charge effect of the EC current on the ion velocity was determined with two independent techniques that provided consistent results. The result of nm provides an important reference value for experiments testing bound-state quantum electrodynamics in the strong magnetic field regime by evaluating the specific difference between the splittings in the hydrogen-like and lithium-like ions.

Fundamentalsatz für affine Räume über Moduln

Within the conceptual frame of [1] a general fundamental theorem for mappings between affine spaces over modules is obtained.

Rapid crystallization of externally produced ions in a Penning trap

We have studied the cooling dynamics, formation process and geometric structure of mesoscopic crystals of externally produced magnesium ions in a Penning trap. We present a cooling model and measurements for a combination of buffer gas cooling and laser cooling which has been found to reduce the ion kinetic energy by eight orders of magnitude from several hundreds of eV to micro-eV and below within seconds. With ion numbers of the order of 1000 to 100000, such cooling leads to the formation of ion Coulomb crystals which display a characteristic shell structure in agreement with theory of non-neutral plasmas. We show the production and characterization of two-species ion crystals as a means of sympathetic cooling of ions lacking a suitable laser-cooling transition.

Non-destructive single-pass low-noise detection of ions in a beamline

We have conceived, built, and operated a device for the non-destructive single-pass detection of charged particles in a beamline. The detector is based on the non-resonant pick-up and subsequent low-noise amplification of the image charges induced in a cylindrical electrode surrounding the particles beam path. The first stage of the amplification electronics is designed to be operated from room temperature down to liquid helium temperature. The device represents a non-destructive charge counter as well as a sensitive timing circuit. We present the concept and design details of the device. We have characterized its performance and show measurements with low-energy highly charged ions (such as Ar(13+)) passing through one of the electrodes of a cylindrical Penning trap. This work demonstrates a novel approach of non-destructive, low noise detection of charged particles which is, depending on the bunch structure, suitable, e.g., for ion traps, low-energy beamlines or accelerator transfer sections.