5,334 research outputs found
Weighted Traces on Algebras of Pseudo-Differential Operators and Geometry of Loop Groups
Using {\it weighted traces} which are linear functionals of the type defined on the whole
algebra of (classical) pseudo-differential operators (P.D.O.s) and where 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
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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 with increasing
temperature, with a change in the slope of vs. at around 150 K: above
this temperature, the variation of with 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
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