Small eigenvalues of surfaces of finite type

Extending our previous work on eigenvalues of closed surfaces and work of Otal and Rosas, we show that a complete Riemannian surface $S$ of finite type and Euler characteristic \unicode[STIX]{x1D712}(S)<0 has at most -\unicode[STIX]{x1D712}(S) small eigenvalues.</jats:p

Symmetric spaces of higher rank do not admit differentiable compactifications

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry (conformal, CR or quaternionic CR depending of the space). One can ask whether such a differentiable compactification exists for higher rank spaces, hopefully leading to some knew geometry to explore. In this paper we answer negatively.Comment: 13 pages, to appear in Mathematische Annale

Resonant vibrations, peak broadening and noise in single molecule contacts: beyond the resonant tunnelling picture

We carry out experiments on single-molecule junctions at low temperatures, using the mechanically controlled break junction technique. Analyzing the results received with more than ten different molecules the nature of the first peak in the differential conductance spectra is elucidated. We observe an electronic transition with a vibronic fine structure, which is most frequently smeared out and forms a broad peak. In the usual parameter range we find strong indications that additionally fluctuations become active even at low temperatures. We conclude that the electrical field feeds instabilities, which are triggered by the onset of current. This is underscored by noise measurements that show strong anomalies at the onset of charge transport

Dual-tip-enhanced ultrafast CARS nanoscopy

Coherent anti-Stokes Raman scattering (CARS) and, in particular, femtosecond adaptive spectroscopic techniques (FAST CARS) have been successfully used for molecular spectroscopy and microscopic imaging. Recent progress in ultrafast nanooptics provides flexibility in generation and control of optical near fields, and holds promise to extend CARS techniques to the nanoscale. In this theoretical study, we demonstrate ultrafast subwavelentgh control of coherent Raman spectra of molecules in the vicinity of a plasmonic nanostructure excited by ultrashort laser pulses. The simulated nanostructure design provides localized excitation sources for CARS by focusing incident laser pulses into subwavelength hot spots via two self-similar nanolens antennas connected by a waveguide. Hot-spot-selective dual-tip-enhanced CARS (2TECARS) nanospectra of DNA nucleobases are obtained by simulating optimized pump, Stokes and probe near fields using tips, laser polarization- and pulse-shaping. This technique may be used to explore ultrafast energy and electron transfer dynamics in real space with nanometre resolution and to develop novel approaches to DNA sequencing.Comment: 11 pages, 6 figure

Vortices and Jacobian varieties

We investigate the geometry of the moduli space of N-vortices on line bundles over a closed Riemann surface of genus g > 1, in the little explored situation where 1 =< N < g. In the regime where the area of the surface is just large enough to accommodate N vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of the surface. For N = 1, we show that the metric on the moduli space converges to a natural Bergman metric on the Riemann surface. When N > 1, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel-Jacobi map at degree N. We describe consequences of this phenomenon from the point of view of multivortex dynamics.Comment: 36 pages, 2 figure

Manifolds with small Dirac eigenvalues are nilmanifolds

Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of the Dirac operator on such a manifold has $r$ small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a non-trivial spin structure, then there exists a uniform lower bound on the r-th eigenvalue of the square of the Dirac operator. If a manifold with almost nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume is not too small, then we show that the metric is close to a Ricci-flat metric on M with a parallel spinor. In dimension 4 this implies that M is either a torus or a K3-surface

Entropy of semiclassical measures for nonpositively curved surfaces

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.Comment: 20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2

Spectral instability of coverings

We study the behaviour of eigenvalues, below the bottom of the essential spectrum, of the Laplacian under finite Riemannian coverings of complete and connected Riemannian manifolds. We define spectral stability and instability of such coverings. Among others, we provide necessary conditions for stability or, equivalently, sufficient conditions for instability

Miocene waterfowl and other birds from central Otago, New Zealand

Copyright © The Natural History Museum 2007Abundant fossil bird bones from the lower Bannockburn Formation, Manuherikia Group, an Early-Middle Miocene lacustrine deposit, 16–19 Ma, from Otago in New Zealand, reveal the “St Bathans Fauna” (new name), a first Tertiary avifauna of land and freshwater birds from New Zealand. At least 23 species of birds are represented by bones, and probable moa, Aves: Dinornithiformes, by eggshell. Anatids dominate the fauna with four genera and five species described as new: a sixth and largest anatid species is represented by just one bone. This is the most diverse Early-Middle Miocene duck fauna known worldwide. Among ducks, two species of dendrochenines are most numerous in the fauna, but a tadornine is common as well. A diving petrel (Pelecanoididae: Pelecanoides) is described, so extending the geological range of this genus worldwide from the Pliocene to the Middle Miocene, at least. The remaining 16 taxa are left undescribed but include: a large species of gull (Laridae); two small waders (Charadriiformes, genus indet.), the size of Charadrius bicinctus and Calidris ruficollis, respectively; a gruiform represented by one specimen similar to Aptornis; abundant rail (Rallidae) bones, including a common flightless rail and a rarer slightly larger taxon, about the size of Gallirallus philippensis; an ?eagle (Accipitridae); a pigeon (Columbidae); three parrots (Psittacidae); an owlet nightjar (Aegothelidae: Aegotheles sp.); a swiftlet (Apodidae: Collocalia sp.); and three passerine taxa, of which the largest is a member of the Cracticidae. The absence of some waterbirds, such as anserines (including swans), grebes (Podicipedidae) and shags (Phalacrocoracidae), among the abundant bones, indicates their probable absence from New Zealand in the Early-Middle Miocene.T. H. Worthy, A. J. D. Tennyson, C. Jones, J. A. McNamara and B. J. Dougla

Factors associated with worse lung function in cystic fibrosis patients with persistent staphylococcus aureus

Background Staphylococcus aureus is an important pathogen in cystic fibrosis (CF). However, it is not clear which factors are associated with worse lung function in patients with persistent S. aureus airway cultures. Our main hypothesis was that patients with high S. aureus density in their respiratory specimens would more likely experience worsening of their lung disease than patients with low bacterial loads. Methods Therefore, we conducted an observational prospective longitudinal multi-center study and assessed the association between lung function and S. aureus bacterial density in respiratory samples, co-infection with other CF-pathogens, nasal S. aureus carriage, clinical status, antibiotic therapy, IL-6- and IgG-levels against S. aureus virulence factors. Results 195 patients from 17 centers were followed; each patient had an average of 7 visits. Data were analyzed using descriptive statistics and generalized linear mixed models. Our main hypothesis was only supported for patients providing throat specimens indicating that patients with higher density experienced a steeper lung function decline (p<0.001). Patients with exacerbations (n = 60), S. aureus small-colony variants (SCVs, n = 84) and co-infection with Stenotrophomonas maltophilia (n = 44) had worse lung function (p = 0.0068; p = 0.0011; p = 0.0103). Patients with SCVs were older (p = 0.0066) and more often treated with trimethoprim/sulfamethoxazole (p = 0.0078). IL-6 levels positively correlated with decreased lung function (p<0.001), S. aureus density in sputa (p = 0.0016), SCVs (p = 0.0209), exacerbations (p = 0.0041) and co-infections with S. maltophilia (p = 0.0195) or A. fumigatus (p = 0.0496). Conclusions In CF-patients with chronic S. aureus cultures, independent risk factors for worse lung function are high bacterial density in throat cultures, exacerbations, elevated IL-6 levels, presence of S. aureus SCVs and co-infection with S. maltophilia