Solvable Lie algebras are not that hypo

We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3). The choice of a splitting g^*=V_1 + V_2, and the vanishing of certain associated cohomology groups, determine a first obstruction. We also construct necessary conditions for the existence of a hypo structure with a fixed almost-contact form. For non-unimodular Lie algebras, we derive an obstruction to the existence of a hypo structure, with no choice involved. We apply these methods to classify solvable Lie algebras that admit a hypo structure.Comment: 21 pages; v2: presentation improved, typos corrected, notational conflicts eliminated. To appear in Transformation Group

Calabi-Yau cones from contact reduction

We consider a generalization of Einstein-Sasaki manifolds, which we characterize in terms both of spinors and differential forms, that in the real analytic case corresponds to contact manifolds whose symplectic cone is Calabi-Yau. We construct solvable examples in seven dimensions. Then, we consider circle actions that preserve the structure, and determine conditions for the contact reduction to carry an induced structure of the same type. We apply this construction to obtain a new hypo-contact structure on S^2\times T^3.Comment: 30 pages; v2: typos corrected, presentation improved, one reference added. To appear in Ann. Glob. Analysis and Geometr

Experimental measurement of photothermal effect in Fabry-Perot cavities

We report the experimental observation of the photothermal effect. The measurements are performed by modulating the laser power absorbed by the mirrors of two high-finesse Fabry-Perot cavities. The results are very well described by a recently proposed theoretical model [M. Cerdonio, L. Conti, A. Heidmann and M. Pinard, Phys. Rev. D 63 (2001) 082003], confirming the correctness of such calculations. Our observations and quantitative characterization of the photothermal effect demonstrate its critical importance for high sensitivity interferometric displacement measurements, as those necessary for gravitational wave detection.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Infrared Observations of the Candidate LBV 1806-20 & Nearby Cluster Stars

We report near-infrared photometry, spectroscopy, and speckle imaging of the hot, luminous star we identify as candidate LBV 1806-20. We also present photometry and spectroscopy of 3 nearby stars, which are members of the same star cluster containing LBV 1806-20 and SGR 1806-20. The spectroscopy and photometry show that LBV 1806-20 is similar in many respects to the luminous ``Pistol Star'', albeit with some important differences. They also provide estimates of the effective temperature and reddening of LBV 1806-20, and confirm distance estimates, leading to a best estimate for the luminosity of this star of $> 5 \times 10^6 L_{\odot}$. The nearby cluster stars have spectral types and inferred absolute magnitudes which confirm the distance (and thus luminosity) estimate for LBV 1806-20. If we drop kinematic measurements of the distance ($15.1 ^{+1.8}_{-1.3}$ kpc), we have a lower limit on the distance of $>9.5$ kpc, and on the luminosity of $>2 \times 10^6 L_{\odot}$, based on the cluster stars. If we drop both the kinematic and cluster star indicators for distance, an ammonia absorption feature sets yet another lower limit to the distance of $>5.7$ kpc, with a corresponding luminosity estimate of $>7 \times 10^5 L_{\odot}$ for the candidate LBV 1806-20. Furthermore, based on very high angular-resolution speckle images, we determine that LBV 1806-20 is not a cluster of stars, but is rather a single star or binary system. Simple arguments based on the Eddington luminosity lead to an estimate of the total mass of LBV 1806-20 (single or binary) exceeding $190 M_{\odot}$. We discuss the possible uncertainties in these results, and their implications for the star formation history of this cluster.Comment: 36 pages, including 8 figures (Figures 1 and 7 in JPG format due to space); Accepted for publication in Ap

Harmonic damped oscillators with feedback. A Langevin study

We consider a system in direct contact with a thermal reservoir and which, if left unperturbed, is well described by a memory-less equilibrium Langevin equation of the second order in the time coordinate. In such conditions, the strength of the noise fluctuations is set by the damping factor, in accordance with the Fluctuation and Dissipation theorem. We study the system when it is subject to a feedback mechanism, by modifying the Langevin equation accordingly. Memory terms now arise in the time evolution, which we study in a non-equilibrium steady state. Two types of feedback schemes are considered, one focusing on time shifts and one on phase shifts, and for both cases we evaluate the power spectrum of the system's fluctuations. Our analysis finds application in feedback cooled oscillators, such as the Gravitational Wave detector AURIGA.Comment: 17 page

Interaction of N solitons in the massive Thirring model and optical gap system: the Complex Toda Chain Model

Using the Karpman-Solov''ev quasiparticle approach for soliton-soliton interaction I show that the train propagation of N well separated solitons of the massive Thirring model is described by the complex Toda chain with N nodes. For the optical gap system a generalised (non-integrable) complex Toda chain is derived for description of the train propagation of well separated gap solitons. These results are in favor of the recently proposed conjecture of universality of the complex Toda chain.Comment: RevTex, 23 pages, no figures. Submitted to Physical Review

Dissipative continuous Euler flows

We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy

Green's Function Approach to the Edge Spectral Density

It is shown that the conventional many-body techniques to calculate the Green's functions can be applied to the wide, compressible edge of a quantum Hall bar. The only ansatz we need is the existence of stable density modes that yields a simple equation of motion of the density operators. We derive the spectral density at a finite temperature and show how the tunneling characteristics of a sharp edge can be deduced as a limiting case.Comment: Revised and Enlarged. Submitted to Phys. Rev.

Observability of counterpropagating modes at fractional-quantum-Hall edges

When the bulk filling factor is equal to 1 - 1/m with m odd, at least one counterpropagating chiral collective mode occurs simultaneously with magnetoplasmons at the edge of fractional-quantum-Hall samples. Initial experimental searches for an additional mode were unsuccessful. In this paper, we address conditions under which its observation should be expected in experiments where the electronic system is excited and probed by capacitive coupling. We derive realistic expressions for the velocity of the slow counterpropagating mode, starting from a microscopic calculation which is simplified by a Landau-Silin-like separation between long-range Hartree and residual interactions. The microscopic calculation determines the stiffness of the edge to long-wavelength neutral excitations, which fixes the slow-mode velocity, and the effective width of the edge region, which influences the magnetoplasmon dispersion.Comment: 18 pages, RevTex, 6 figures, final version to be published in Physical Review