PT symmetry and large-N models

Recently developed methods for PT-symmetric models can be applied to quantum-mechanical matrix and vector models. In matrix models, the calculation of all singlet wave functions can be reduced to the solution a one-dimensional PT-symmetric model. The large-N limit of a wide class of matrix models exists, and properties of the lowest-lying singlet state can be computed using WKB. For models with cubic and quartic interactions, the ground state energy appears to show rapid convergence to the large-N limit. For the special case of a quartic model, we find explicitly an isospectral Hermitian matrix model. The Hermitian form for a vector model with O(N) symmetry can also be found, and shows many unusual features. The effective potential obtained in the large-N limit of the Hermitian form is shown to be identical to the form obtained from the original PT-symmetric model using familiar constraint field methods. The analogous constraint field prescription in four dimensions suggests that PT-symmetric scalar field theories are asymptotically free.Comment: 15 pages, to be published in J. Phys. A special issue on Pseudo Hermitian Hamiltonians in Quantum Physic

Line-profile variations in radial-velocity measurements: Two alternative indicators for planetary searches

Aims. We introduce two methods to identify false-positive planetary signals in the context of radial-velocity exoplanet searches. The first is the bi-Gaussian cross-correlation function fitting, and the second is the measurement of asymmetry in radial-velocity spectral line information content, Vasy. Methods. We make a systematic analysis of the most used common line profile diagnosis, Bisector Inverse Slope and Velocity Span, along with the two proposed ones. We evaluate all these diagnosis methods following a set of well-defined common criteria and using both simulated and real data. We apply them to simulated cross-correlation functions created with the program SOAP and which are affected by the presence of stellar spots, and to real cross-correlation functions, calculated from HARPS spectra, for stars with a signal originating both in activity and created by a planet. Results. We demonstrate that the bi-Gaussian method allows a more precise characterization of the deformation of line profiles than the standard bisector inverse slope. The calculation of the deformation indicator is simpler and its interpretation more straightforward. More importantly, its amplitude can be up to 30% larger than that of the bisector span, allowing the detection of smaller-amplitude correlations with radial-velocity variations. However, a particular parametrization of the bisector inverse slope is shown to be more efficient on high-signal-to-noise data than both the standard bisector and the bi-Gaussian. The results of the Vasy method show that this indicator is more effective than any of the previous ones, being correlated with the radial-velocity with more significance for signals resulting from a line deformation. Moreover, it provides a qualitative advantage over the bisector, showing significant correlations with RV for active stars for which bisector analysis is inconclusive. (abridged)Comment: 12 pages, 7 figures, accepted for publication in Astronomy and Astrophysics, comments welcom

Quasi-Langmuir-Blodgett Thin Film Deposition of Carbon Nanotubes

The handling and manipulation of carbon nanotubes continues to be a challenge to those interested in the application potential of these promising materials. To this end, we have developed a method to deposit pure nanotube films over large flat areas on substrates of arbitrary composition. The method bears some resemblance to the Langmuir-Blodgett deposition method used to lay down thin organic layers. We show that this redeposition technique causes no major changes in the films' microstructure and that they retain the electronic properties of as-deposited film laid down on an alumina membrane.Comment: 3 pages, 3 figures, submitted Journal of Applied Physic

Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers

Motivated by recent experiments showing nonlinear elasticity of in vitro networks of the biopolymer actin cross-linked with filamin, we present an effective medium theory of flexibly cross-linked stiff polymer networks. We model such networks by randomly oriented elastic rods connected by flexible connectors to a surrounding elastic continuum, which self-consistently represents the behavior of the rest of the network. This model yields a crossover from a linear elastic regime to a highly nonlinear elastic regime that stiffens in a way quantitatively consistent with experiment.Comment: 4 pages, 3 figure