New bounds on the Lieb-Thirring constants

Improved estimates on the constants $L_{\gamma,d}$, for $1/2<\gamma<3/2$, $d\in N$ in the inequalities for the eigenvalue moments of Schr\"{o}dinger operators are established

LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States

We prove general comparison theorems for eigenvalues of perturbed Schrodinger operators that allow proof of Lieb--Thirring bounds for suitable non-free Schrodinger operators and Jacobi matrices.Comment: 11 page

Weighted Supermembrane Toy Model

A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient weights. This follows from a bound for the number of negative eigenvalues of an associated matrix-valued Schr\"odinger operator.Comment: 18 pages, 2 figures; to appear in Lett. Math. Phys

Lieb-Thirring inequalities for geometrically induced bound states

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page

Localization criteria for Anderson models on locally finite graphs

We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on \ZZ^d. We establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently large disorder

The Thresher : lucky imaging without the waste

JAH acknowledges funding from the Science and Technology Facilities Council of the United Kingdom.In traditional lucky imaging (TLI), many consecutive images of the same scene are taken with a high frame-rate camera, and all but the sharpest images are discarded before constructing the final shift-and-add image. Here, we present an alternative image analysis pipeline – The Thresher – for these kinds of data, based on online multi-frame blind deconvolution. It makes use of all available data to obtain the best estimate of the astronomical scene in the context of reasonable computational limits; it does not require prior estimates of the point-spread functions in the images, or knowledge of point sources in the scene that could provide such estimates. Most importantly, the scene it aims to return is the optimum of a justified scalar objective based on the likelihood function. Because it uses the full set of images in the stack, The Thresher outperforms TLI in signal-to-noise ratio; as it accounts for the individual-frame PSFs, it does this without loss of angular resolution. We demonstrate the effectiveness of our algorithm on both simulated data and real Electron-Multiplying CCD images obtained at the Danish 1.54-m telescope (hosted by ESO, La Silla). We also explore the current limitations of the algorithm, and find that for the choice of image model presented here, non-linearities in flux are introduced into the returned scene. Ongoing development of the software can be viewed at https://github.com/jah1994/TheThresher.Publisher PDFPeer reviewe

On the negative spectrum of two-dimensional Schr\"odinger operators with radial potentials

For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V$ with the radial potential $V(x)=F(|x|), F(r)\ge 0$, we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues, as the coupling parameter $\alpha$ tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth $N_-(H_{\alpha V})=O(\alpha)$ and for the validity of the Weyl asymptotic law.Comment: 13 page

Simulator for Microlens Planet Surveys

We summarize the status of a computer simulator for microlens planet surveys. The simulator generates synthetic light curves of microlensing events observed with specified networks of telescopes over specified periods of time. Particular attention is paid to models for sky brightness and seeing, calibrated by fitting to data from the OGLE survey and RoboNet observations in 2011. Time intervals during which events are observable are identified by accounting for positions of the Sun and the Moon, and other restrictions on telescope pointing. Simulated observations are then generated for an algorithm that adjusts target priorities in real time with the aim of maximizing planet detection zone area summed over all the available events. The exoplanet detection capability of observations was compared for several telescopes.Comment: Proc. IAU Symp. No. 293 "Formation, detection, and characterization of extrasolar habitable planets", ed. by N. Haghighipour. 4 pages, in pres