Uniqueness of the ground state in the Feshbach renormalization analysis

In the operator theoretic renormalization analysis introduced by Bach, Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page

Constraints on the Space Density of Methane Dwarfs and the Substellar Mass Function from a Deep Near-Infrared Survey

We report preliminary results of a deep near-infrared search for methane-absorbing brown dwarfs; almost five years after the discovery of Gl 229b, there are only a few confirmed examples of this type of object. New J band, wide-field images, combined with pre-existing R band observations, allow efficient identification of candidates by their extreme (R-J) colours. Follow-up measurements with custom filters can then confirm objects with methane absorption. To date, we have surveyed a total of 11.4 square degrees to J~20.5 and R~25. Follow-up CH_4 filter observations of promising candidates in 1/4 of these fields have turned up no methane absorbing brown dwarfs. With 90% confidence, this implies that the space density of objects similar to Gl 229b is less than 0.012 per cubic parsec. These calculations account for the vertical structure of the Galaxy, which can be important for sensitive measurements. Combining published theoretical atmospheric models with our observations sets an upper limit of alpha <= 0.8 for the exponent of the initial mass function power law in this domain.Comment: 11 pages + 2 figures To be published in Astrophysical Journal Letter

Ground States in the Spin Boson Model

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory

Reaction Networks For Interstellar Chemical Modelling: Improvements and Challenges

We survey the current situation regarding chemical modelling of the synthesis of molecules in the interstellar medium. The present state of knowledge concerning the rate coefficients and their uncertainties for the major gas-phase processes -- ion-neutral reactions, neutral-neutral reactions, radiative association, and dissociative recombination -- is reviewed. Emphasis is placed on those reactions that have been identified, by sensitivity analyses, as 'crucial' in determining the predicted abundances of the species observed in the interstellar medium. These sensitivity analyses have been carried out for gas-phase models of three representative, molecule-rich, astronomical sources: the cold dense molecular clouds TMC-1 and L134N, and the expanding circumstellar envelope IRC +10216. Our review has led to the proposal of new values and uncertainties for the rate coefficients of many of the key reactions. The impact of these new data on the predicted abundances in TMC-1 and L134N is reported. Interstellar dust particles also influence the observed abundances of molecules in the interstellar medium. Their role is included in gas-grain, as distinct from gas-phase only, models. We review the methods for incorporating both accretion onto, and reactions on, the surfaces of grains in such models, as well as describing some recent experimental efforts to simulate and examine relevant processes in the laboratory. These efforts include experiments on the surface-catalysed recombination of hydrogen atoms, on chemical processing on and in the ices that are known to exist on the surface of interstellar grains, and on desorption processes, which may enable species formed on grains to return to the gas-phase.Comment: Accepted for publication in Space Science Review

Moduli Webs and Superpotentials for Five-Branes

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli space and use this to compute effective open-closed superpotentials to all orders in the open string couplings. The fixed points of D5-brane moduli under bulk deformations are determined.Comment: 41 pages, 1 figur

Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED

We consider a class of translation invariant models of non-relativistic QED with net charge. Under certain natural assumptions we prove that ground states do not exist in the Fock space

An evolution equation as the WKB correction in long-time asymptotics of Schrodinger dynamics

We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the standard WKB correction should be replaced by the solution to certain evolution equation.Comment: This is a preprint of an article whose final and definitive form has been published in Comm. Partial Differential Equations, available online at http://www.informaworld.co

The Disappearing Act of KH 15D: Photometric Results from 1995 to 2004

We present results from the most recent (2002-2004) observing campaigns of the eclipsing system KH 15D, in addition to re-reduced data obtained at Van Vleck Observatory (VVO) between 1995 and 2000. Phasing nine years of photometric data shows substantial evolution in the width and depth of the eclipses. The most recent data indicate that the eclipses are now approximately 24 days in length, or half the orbital period. These results are interpreted and discussed in the context of the recent models for this system put forward by Winn et al. and Chiang & Murray-Clay. A periodogram of the entire data set yields a highly significant peak at 48.37 +/- 0.01 days, which is in accord with the spectroscopic period of 48.38 +/- 0.01 days determined by Johnson et al. Another significant peak, at 9.6 days, was found in the periodogram of the out-of-eclipse data at two different epochs. We interpret this as the rotation period of the visible star and argue that it may be tidally locked in pseudosynchronism with its orbital motion. If so, application of Hut's theory implies that the eccentricity of the orbit is e = 0.65 +/- 0.01. Analysis of the UVES/VLT spectra obtained by Hamilton et al. shows that the v sin(i) of the visible star in this system is 6.9 +/- 0.3 km/sec. Using this value of v sin(i) and the measured rotation period of the star, we calculate the lower limit on the radius to be R = (1.3 +/- 0.1), R_Sun, which concurs with the value obtained by Hamilton et al. from its luminosity and effective temperature. Here we assume that i = 90 degrees since it is likely that the spin and orbital angular momenta vectors are nearly aligned.Comment: 55 pages, 18 figures, 1 color figure, to appear the September issue of the Astronomical Journa

Molecular Evolution in Collapsing Prestellar Cores

We have investigated the evolution and distribution of molecules in collapsing prestellar cores via numerical chemical models, adopting the Larson-Penston solution and its delayed analogues to study collapse. Molecular abundances and distributions in a collapsing core are determined by the balance among the dynamical, chemical and adsorption time scales. When the central density n_H of a prestellar core with the Larson-Penston flow rises to 3 10^6 cm^{-3}, the CCS and CO column densities are calculated to show central holes of radius 7000 AU and 4000 AU, respectively, while the column density of N2H+ is centrally peaked. These predictions are consistent with observations of L1544. If the dynamical time scale of the core is larger than that of the Larson-Penston solution owing to magnetic fields, rotation, or turbulence, the column densities of CO and CCS are smaller, and their holes are larger than in the Larson-Penston core with the same central gas density. On the other hand, N2H+ and NH3 are more abundant in the more slowly collapsing core. Therefore, molecular distributions can probe the collapse time scale of prestellar cores. Deuterium fractionation has also been studied via numerical calculations. The deuterium fraction in molecules increases as a core evolves and molecular depletion onto grains proceeds. When the central density of the core is n_H=3 10^6 cm^{-3}, the ratio DCO+/HCO+ at the center is in the range 0.06-0.27, depending on the collapse time scale and adsorption energy; this range is in reasonable agreement with the observed value in L1544.Comment: 21 pages, 17 figure

Alignment and preliminary outcomes of an ELT-size instrument to a very large telescope: LINC-NIRVANA at LBT

LINC-NIRVANA (LN) is a high resolution, near infrared imager that uses a multiple field-of-view, layer-oriented, multi-conjugate AO system, consisting of four multi-pyramid wavefront sensors (two for each arm of the Large Binocular Telescope, each conjugated to a different altitude). The system employs up to 40 star probes, looking at up to 20 natural guide stars simultaneously. Its final goal is to perform Fizeau interferometric imaging, thereby achieving ELT-like spatial resolution (22.8 m baseline resolution). For this reason, LN is also equipped with a fringe tracker, a beam combiner and a NIR science camera, for a total of more than 250 optical components and an overall size of approximately 6x4x4.5 meters. This paper describes the tradeoffs evaluated in order to achieve the alignment of the system to the telescope. We note that LN is comparable in size to planned ELT instrumentation. The impact of such alignment strategies will be compared and the selected procedure, where the LBT telescope is, in fact, aligned to the instrument, will be described. Furthermore, results coming from early night-time commissioning of the system will be presented.Comment: 8 pages, 6 pages, AO4ELT5 Proceedings, 201