Weighted Traces on Algebras of Pseudo-Differential Operators and Geometry of Loop Groups

Using {\it weighted traces} which are linear functionals of the type $$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$ defined on the whole algebra of (classical) pseudo-differential operators (P.D.O.s) and where $Q$ is some positive invertible elliptic operator, we investigate the geometry of loop groups in the light of the cohomology of pseudo-differential operators. We set up a geometric framework to study a class of infinite dimensional manifolds in which we recover some results on the geometry of loop groups, using again weighted traces. Along the way, we investigate properties of extensions of the Radul and Schwinger cocycles defined with the help of weighted traces.Comment: 36 page

Trinets encode tree-child and level-2 phylogenetic networks

Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in trying to develop methods to construct rooted phylogenetic networks from triplets, that is rooted trees on three species. However, although triplets determine or encode rooted phylogenetic trees, they do not in general encode rooted phylogenetic networks, which is a potential issue for any such method. Motivated by this fact, Huber and Moulton recently introduced trinets as a natural extension of rooted triplets to networks. In particular, they showed that level-1 level-1 phylogenetic networks are encoded by their trinets, and also conjectured that all “recoverable” rooted phylogenetic networks are encoded by their trinets. Here we prove that recoverable binary level-2 networks and binary tree-child networks are also encoded by their trinets. To do this we prove two decomposition theorems based on trinets which hold for all recoverable binary rooted phylogenetic networks. Our results provide some additional evidence in support of the conjecture that trinets encode all recoverable rooted phylogenetic networks, and could also lead to new approaches to construct phylogenetic networks from trinets

Isotope effects on the lattice parameter of cubic SiC

Path-integral molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble have been carried out to study the dependence of the lattice parameter of 3C-SiC upon isotope mass. This computational method allows a quantitative and nonperturbative study of such anharmonic effect. Atomic nuclei were treated as quantum particles interacting via a tight-binding-type potential. At 300 K, the difference Delta a between lattice parameters of 3C-SiC crystals with 12C and 13C amounts to 2.1 x 10^{-4} A. The effect due to Si isotopes is smaller, and amounts to 3.5 x 10^{-5} A when replacing 28Si by 29Si. Results of the PIMD simulations are interpreted in terms of a quasiharmonic approximation for the lattice vibrations.Comment: 4 pages, 3 figure

Chemical Raman Enhancement of Organic Adsorbates on Metal Surfaces

Using a combination of first-principles theory and experiments, we provide a quantitative explanation for chemical contributions to surface-enhanced Raman spectroscopy for a well-studied organic molecule, benzene thiol, chemisorbed on planar Au(111) surfaces. With density functional theory calculations of the static Raman tensor, we demonstrate and quantify a strong mode-dependent modification of benzene thiol Raman spectra by Au substrates. Raman active modes with the largest enhancements result from stronger contributions from Au to their electron-vibron coupling, as quantified through a deformation potential, a well-defined property of each vibrational mode. A straightforward and general analysis is introduced that allows extraction of chemical enhancement from experiments for specific vibrational modes; measured values are in excellent agreement with our calculations.Comment: 5 pages, 4 figures and Supplementary material included as ancillary fil

Fermi surface of MoO2 studied by angle-resolved photoemission spectroscopy, de Haas-van Alphen measurements, and electronic structure calculations

A comprehensive study of the electronic properties of monoclinic MoO2 from both an experimental and a theoretical point of view is presented. We focus on the investigation of the Fermi body and the band structure using angle resolved photoemission spectroscopy, de Haas-van Alphen measurements, and electronic structure calculations. For the latter, the new full-potential augmented spherical wave (ASW) method has been applied. Very good agreement between the experimental and theoretical results is found. In particular, all Fermi surface sheets are correctly identified by all three approaches. Previous controversies concerning additional hole-like surfaces centered around the Z- and B-point could be resolved; these surfaces were an artefact of the atomic-sphere approximation used in the old calculations. Our results underline the importance of electronic structure calculations for the understanding of MoO2 and the neighbouring rutile-type early transition-metal dioxides. This includes the low-temperature insulating phases of VO2 and NbO2, which have crystal structures very similar to that of molybdenum dioxide and display the well-known prominent metal-insulator transitions.Comment: 17 pages, 21 figures, more information at http://www.physik.uni-augsburg.de/~eyert

Electron-phonon renormalization of the absorption edge of the cuprous halides

Compared to most tetrahedral semiconductors, the temperature dependence of the absorption edges of the cuprous halides (CuCl, CuBr, CuI) is very small. CuCl and CuBr show a small increase of the gap $E_0$ with increasing temperature, with a change in the slope of $E_0$ vs. $T$ at around 150 K: above this temperature, the variation of $E_0$ with $T$ becomes even smaller. This unusual behavior has been clarified for CuCl by measurements of the low temperature gap vs. the isotopic masses of both constituents, yielding an anomalous negative shift with increasing copper mass. Here we report the isotope effects of Cu and Br on the gap of CuBr, and that of Cu on the gap of CuI. The measured isotope effects allow us to understand the corresponding temperature dependences, which we also report, to our knowledge for the first time, in the case of CuI. These results enable us to develop a more quantitative understanding of the phenomena mentioned for the three halides, and to interpret other anomalies reported for the temperature dependence of the absorption gap in copper and silver chalcogenides; similarities to the behavior observed for the copper chalcopyrites are also pointed out.Comment: 14 pages, 5 figures, submitted to Phys. Rev.

Implications of Charge Ordering for Single-Particle Properties of High-Tc Superconductors

The consequences of disordered charge stripes and antiphase spin domains for the properties of the high-temperature superconductors are studied. We focus on angle-resolved photoemission spectroscopy and optical conductivity, and show that the many unusual features of the experimentally observed spectra can be understood naturally in this way. This interpretation of the data, when combined with evidence from neutron scattering and NMR, suggests that disordered and fluctuating stripe phases are a common feature of high-temperature superconductors.Comment: 4 pages, figures by fax or mai

Structure and cluster formation in size asymmetric soft electrolyte

We examine the structure and thermodynamic properties of systems composed ions with rigid Gaussian charge distributions of differing widths that only interact electrostatically. These ultrasoft electrolytes [1,2] provide insight into the role of electrostatics in colloidal systems and have been observed to exhibit a liquid-vapor phase transition, as well as aggregation. We perform molecular dynamics and Monte Carlo simulations over a broad range of ion densities and electrostatic coupling strengths for systems containing ions with different width charge distributions. Under certain conditions, these systems are observed to form large, finite sized clusters in an isotropic phase. The structure of these clusters, their charge and electrostatic potential distribution, and energetics of formation are analyzed in detail. We compare and interpret the simulation results with a splitting field theory [3] framework that focuses on fluctuations in the electrostatic potential. Within this approach, the short wavelength and long wavelength fluctuations are treated within different approximation schemes. This theory can accurately describe the counterion mediated attractive interactions between like-charged plates [3,4] and the one-component plasma (OCP) [5] from the weak, intermediate, and strong coupling regimes. As the charge distribution of one of the ion species in the ultrasoft electrolyte broadens, the system more closely resembles the OCP, where the splitting theory is known to work well. We carefully examine the evolution of ultrasoft electrolyte as the width of one of the ions changes from being infinitely broad to smaller sizes. In particular, we present spatial correlations in the fluctuations of the electrostatic potential, decomposing them into short and long wavelength contributions. This information is used to extend the splitting theory to capture the region of cluster formation