Weak Gravity Conjecture for the Effective Field Theories with N Species

We conjecture an intrinsic UV cutoff for the validity of the effective field theory with a large number of species coupled to gravity. In four dimensions such a UV cutoff takes the form $\Lambda=\sqrt{\lambda/ N}M_p$ for $N$ scalar fields with the same potential $\lambda \phi_i^4$, $i=1,...,N$. This conjecture implies that the assisted chaotic inflation or N-flation might be in the swampland, not in the landscape. Similarly a UV cutoff $\Lambda=gM_p/\sqrt{N}$ is conjectured for the U(1) gauge theory with $N$ species.Comment: 12 pages; refs added and some statements clarifie

Limits from Weak Gravity Conjecture on Dark Energy Models

The weak gravity conjecture has been proposed as a criterion to distinguish the landscape from the swampland in string theory. As an application in cosmology of this conjecture, we use it to impose theoretical constraint on parameters of two types of dark energy models. Our analysis indicates that the Chaplygin-gas-type models realized in quintessence field are in the swampland, whereas the $a$ power-low decay model of the variable cosmological constant can be viable but the parameters are tightly constrained by the conjecture.Comment: Revtex4, 8 pages, 5 figures; References, minor corrections in content, and acknowledgement adde

Nanomechanical Inverse Electromagnetically Induced Transparency and Confinement of Light in Normal modes

We demonstrate the existence of the phenomenon of the inverse electromagnetically induced transparency (IEIT) in an opto mechanical system consisting of a nanomechanical mirror placed in an optical cavity. We show that two weak counter-propagating identical classical probe fields can be completely absorbed by the system in the presence of a strong coupling field so that the output probe fields are zero. The light is completely confined inside the cavity and the energy of the incoming probe fields is shared between the cavity field and creation of a coherent phonon and resides primarily in one of the polariton modes. The energy can be extracted by a perturbation of the external fields or by suddenly changing the $Q$ of the cavity.Comment: 10 pages, 5 figure

Penalized Likelihood Methods for Estimation of Sparse High Dimensional Directed Acyclic Graphs

Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges between nodes represent the influence of components of the system on each other. The general problem of estimating DAGs from observed data is computationally NP-hard, Moreover two directed graphs may be observationally equivalent. When the nodes exhibit a natural ordering, the problem of estimating directed graphs reduces to the problem of estimating the structure of the network. In this paper, we propose a penalized likelihood approach that directly estimates the adjacency matrix of DAGs. Both lasso and adaptive lasso penalties are considered and an efficient algorithm is proposed for estimation of high dimensional DAGs. We study variable selection consistency of the two penalties when the number of variables grows to infinity with the sample size. We show that although lasso can only consistently estimate the true network under stringent assumptions, adaptive lasso achieves this task under mild regularity conditions. The performance of the proposed methods is compared to alternative methods in simulated, as well as real, data examples.Comment: 19 pages, 8 figure

The Chemical Evolution of the Draco Dwarf Spheroidal Galaxy

We present an abundance analysis based on high resolution spectra of 8 stars selected to span the full range in metallicity in the Draco dwarf spheroidal galaxy. We find [Fe/H] for the sample stars ranges from -1.5 to -3.0 dex. Combining our sample with previously published work for a total of 14 luminous Draco giants, we show that the abundance ratios [Na/Fe], [Mg/Fe] and [Si/Fe] for the Draco giants overlap those of Galactic halo giants at the lowest [Fe/H] probed, but are significantly lower for the higher Fe-metallicity Draco stars. For the explosive alpha-elements Ca and Ti, the abundance ratios for Draco giants with [Fe/H] > -2.4 dex are approximately constant and slightly sub-solar, well below values characteristic of Galactic halo stars. The s-process contribution to the production of heavy elements begins at significantly lower Fe-metallicity than in the Galactic halo. Using a toy model we compare the behavior of the abundance ratios within the sample of Draco giants with those from the literature of Galactic globular clusters, and the Carina and Sgr dSph galaxies. The differences appear to be related to the timescale for buildup of the heavy elements, with Draco having the slowest rate. We note the presence of a Draco giant with [Fe/H] < -3.0 dex in our sample, and reaffirm that the inner Galactic halo could have been formed by early accretion of Galactic satellite galaxies and dissolution of young globular clusters, while the outer halo could have formed from those satellite galaxies accreted later.Comment: Submitted to ApJ Dec 22, 2008; accepted June 4, 2009. 75 pages including 22 figures and 9 table

Reactive-Coupling-Induced Normal Mode Splittings in Microdisk Resonators Coupled to Waveguides

We study the optomechanical design introduced by M. Li et al. [Phys. Rev. Lett. {\bf 103}, 223901 (2009)], which is very effective for investigation of the effects of reactive coupling. We show the normal mode splitting which is due solely to reactive coupling rather than due to dispersive coupling. We suggest feeding the waveguide with a pump field along with a probe field and scanning the output probe for evidence of reactive-coupling-induced normal mode splitting.Comment: 4 pages,6 figure