Moduli Spaces and Formal Operads

Let overline{M}_{g,n} be the moduli space of stable algebraic curves of genus g with n marked points. With the operations which relate the different moduli spaces identifying marked points, the family (overline{M}_{g,n})_{g,n} is a modular operad of projective smooth Deligne-Mumford stacks, overline{M}. In this paper we prove that the modular operad of singular chains C_*(overline{M};Q) is formal; so it is weakly equivalent to the modular operad of its homology H_*(overline{M};Q). As a consequence, the "up to homotopy" algebras of these two operads are the same. To obtain this result we prove a formality theorem for operads analogous to Deligne-Griffiths-Morgan-Sullivan formality theorem, the existence of minimal models of modular operads, and a characterization of formality for operads which shows that formality is independent of the ground field.Comment: 36 pages (v3: some typographical corrections

TELEPENSOUTH project: Measurement of the Earth gravitomagnetic field in a terrestrial laboratory

We will expose a preliminary study on the feasibility of an experiment leading to a direct measurement of the gravitomagnetic field generated by the rotational motion of the Earth. This measurement would be achieved by means of an appropriate coupling of a TELEscope and a Foucault PENdulum in a laboratory on ground, preferably at the SOUTH pole. An experiment of this kind was firstly proposed by Braginski, Polnarev and Thorne, 18 years ago, but it was never re-analyzed.Comment: 7 pages, LaTeX, Springer style files included. Contribution to the Proceedings of the Spanish Relativity Meeting-ERE-2001 (Madrid, September 2001). To appear in the book "Relativistic Astrophysics", Lecture Notes in Physics, Springer Verlag (2002), edited by L. Fernandez-Jambrina, L.M. Gonzalez-Romer

Ferromagnetic coupling of mononuclear Fe centers in a self-assembled metal-organic network on Au(111)

The magnetic state and magnetic coupling of individual atoms in nanoscale structures relies on a delicate balance between different interactions with the atomic-scale surrounding. Using scanning tunneling microscopy, we resolve the self-assembled formation of highly ordered bilayer structures of Fe atoms and organic linker molecules (T4PT) when deposited on a Au(111) surface. The Fe atoms are encaged in a three-dimensional coordination motif by three T4PT molecules in the surface plane and an additional T4PT unit on top. Within this crystal field, the Fe atoms retain a magnetic ground state with easy-axis anisotropy, as evidenced by X-ray absorption spectroscopy and X-ray magnetic circular dichroism. The magnetization curves reveal the existence of ferromagnetic coupling between the Fe centers

Pion Interactions in Chiral Field Theories

We study in various chiral models the pion charge radius, $\pi_{e3}$ form factor ratio, $\pi^\circ \to \gamma \gamma$ amplitude, charge pion polarizabilities, $\gamma\gamma \to \pi^\circ \pi^\circ$ amplitude at low energies and the $\pi\pi$ s-wave I = 0 scattering length. We find that a quark-level linear sigma-model approach (also being consistent with tree-level vector meson dominance) is quite compatible with all of the above data.Comment: 12 pages, 9 eps figure

On the Reliability of Cross Correlation Function Lag Determinations in Active Galactic Nuclei

Many AGN exhibit a highly variable luminosity. Some AGN also show a pronounced time delay between variations seen in their optical continuum and in their emission lines. In effect, the emission lines are light echoes of the continuum. This light travel-time delay provides a characteristic radius of the region producing the emission lines. The cross correlation function (CCF) is the standard tool used to measure the time lag between the continuum and line variations. For the few well-sampled AGN, the lag ranges from 1-100 days, depending upon which line is used and the luminosity of the AGN. In the best sampled AGN, NGC 5548, the H_beta lag shows year-to-year changes, ranging from about 8.7 days to about 22.9 days over a span of 8 years. In this paper it is demonstrated that, in the context of AGN variability studies, the lag estimate using the CCF is biased too low and subject to a large variance. Thus the year-to-year changes of the measured lag in NGC 5548 do not necessarily imply changes in the AGN structure. The bias and large variance are consequences of finite duration sampling and the dominance of long timescale trends in the light curves, not due to noise or irregular sampling. Lag estimates can be substantially improved by removing low frequency power from the light curves prior to computing the CCF.Comment: To appear in the PASP, vol 111, 1999 Nov; 37 pages; 10 figure

Recombination limited energy relaxation in a BCS superconductor

We study quasiparticle energy relaxation at sub-kelvin temperatures by injecting hot electrons into an aluminium island and measuring the energy flux from electrons into phonons both in the superconducting and in the normal state. The data show strong reduction of the flux at low temperatures in the superconducting state, in qualitative agreement with the presented quasiclassical theory for clean superconductors. Quantitatively, the energy flux exceeds that from the theory both in the superconducting and in the normal state, possibly suggesting an enhanced or additional relaxation process

Three loop MSbar renormalization of QED in the 't~Hooft-Veltman gauge

Quantum electrodynamics (QED) fixed in the 't~Hooft-Veltman gauge is renormalized to three loops in the MSbar scheme. The beta-functions and anomalous dimensions are computed as functions of the usual QED coupling and the additional coupling, xi, which is introduced as part of the nonlinear gauge fixing condition. Similar to the maximal abelian gauge of quantum chromodynamics, the renormalization of the gauge parameter is singular.Comment: 8 latex page