The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case

We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be the spectra of two different self-adjoint extensions of a Jacobi operator in the limit circle case.Comment: 26 pages. Changes in the presentation of some result

On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices

We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg-Marchenko theorem for Schr{\"o}dinger operators in the half-line. Furthermore, we give necessary and sufficient conditions for two real sequences to be the spectra of a Jacobi operator with different boundary conditions.Comment: In this slightly revised version we have reworded some of the theorems, and we updated two reference

The signed loop approach to the Ising model: foundations and critical point

The signed loop method is a beautiful way to rigorously study the two-dimensional Ising model with no external field. In this paper, we explore the foundations of the method, including details that have so far been neglected or overlooked in the literature. We demonstrate how the method can be applied to the Ising model on the square lattice to derive explicit formal expressions for the free energy density and two-point functions in terms of sums over loops, valid all the way up to the self-dual point. As a corollary, it follows that the self-dual point is critical both for the behaviour of the free energy density, and for the decay of the two-point functions.Comment: 38 pages, 7 figures, with an improved Introduction. The final publication is available at link.springer.co

Mechanistic in situ and ex situ studies of phase transformations in molecular co-crystals

Co‐crystallisation is widely explored as a route to improve the physical properties of pharmaceutical active ingredients, but little is known about the fundamental mechanisms of the process. Herein, we apply a hyphenated differential scanning calorimetry—X‐ray diffraction technique to mimic the commercial hot melt extrusion process, and explore the heat‐induced synthesis of a series of new co‐crystals containing isonicotinamide. These comprise a 1:1 co‐crystal with 4‐hydroxybenzoic acid, 2:1 and 1:2 systems with 4‐hydroxyphenylacetic acid and a 1:1 crystal with 3,4‐dihydroxyphenylactic acid. The formation of co‐crystals during heating is complex mechanistically. In addition to co‐crystallisation, conversions between polymorphs of the co‐former starting materials and co‐crystal products are also observed. A subsequent study exploring the use of inkjet printing and milling to generate co‐crystals revealed that the synthetic approach has a major effect on the co‐crystal species and polymorphs produced

A device for feasible fidelity, purity, Hilbert-Schmidt distance and entanglement witness measurements

A generic model of measurement device which is able to directly measure commonly used quantum-state characteristics such as fidelity, overlap, purity and Hilbert-Schmidt distance for two general uncorrelated mixed states is proposed. In addition, for two correlated mixed states, the measurement realizes an entanglement witness for Werner's separability criterion. To determine these observables, the estimation only one parameter - the visibility of interference, is needed. The implementations in cavity QED, trapped ion and electromagnetically induced transparency experiments are discussed.Comment: 6 pages, 3 figure

Western oceanus procellarum as seen by c1xs on chandrayaan-1

We present the analysis of an X-ray fluorescence (XRF) observation of the western part of Oceanus Procellarum on the Moon’s nearside made by the Chandrayaan-1 X-ray Spectrometer on 10th February 2009. Through forward modelling of the X-ray spectra, we provide estimates of the MgO/SiO2 and Al2O3/SiO2 ratios for seven regions along the flare’s ground track. These results are combined with FeO and TiO2 contents derived from Clementine multispectral reflectance data in order to investigate the compositional diversity of this region of the Moon. The ground track observed consists mainly of low-Ti basaltic units, and the XRF data are largely consistent with this expectation. However, we obtain higher Al2O3/SiO2 ratios for these units than for most basalts in the Apollo sample collection. The widest compositional variation between the different lava flows is in wt% FeO content. A footprint that occurs in a predominantly highland region, immediately to the north of Oceanus Procellarum, has a composition that is consistent with mixing between low-Ti mare basaltic and more feldspathic regoliths. In contrast to some previous studies, we find no evidence for systematic differences in surface composition, as determined through X-ray and gamma-ray spectroscopy techniques

Detecting genuine multipartite continuous-variable entanglement

We derive necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multi-party multi-mode continuous-variable state. Their violations can be sufficient for genuine multipartite entanglement, provided the combinations contain both conjugate variables of all modes. Hence a complete state determination, for example by detecting the entire correlation matrix of a Gaussian state, is not needed.Comment: 13 pages, 3 figure

Constraining warm dark matter with cosmic shear power spectra

We investigate potential constraints from cosmic shear on the dark matter particle mass, assuming all dark matter is made up of light thermal relic particles. Given the theoretical uncertainties involved in making cosmological predictions in such warm dark matter scenarios we use analytical fits to linear warm dark matter power spectra and compare (i) the halo model using a mass function evaluated from these linear power spectra and (ii) an analytical fit to the non-linear evolution of the linear power spectra. We optimistically ignore the competing effect of baryons for this work. We find approach (ii) to be conservative compared to approach (i). We evaluate cosmological constraints using these methods, marginalising over four other cosmological parameters. Using the more conservative method we find that a Euclid-like weak lensing survey together with constraints from the Planck cosmic microwave background mission primary anisotropies could achieve a lower limit on the particle mass of 2.5 keV.Comment: 26 pages, 9 figures, minor changes to match the version accepted for publication in JCA

Non-minimally coupled dark matter: effective pressure and structure formation

We propose a phenomenological model in which a non-minimal coupling between gravity and dark matter is present in order to address some of the apparent small scales issues of \lcdm model. When described in a frame in which gravity dynamics is given by the standard Einstein-Hilbert action, the non-minimal coupling translates into an effective pressure for the dark matter component. We consider some phenomenological examples and describe both background and linear perturbations. We show that the presence of an effective pressure may lead these scenarios to differ from \lcdm at the scales where the non-minimal coupling (and therefore the pressure) is active. In particular two effects are present: a pressure term for the dark matter component that is able to reduce the growth of structures at galactic scales, possibly reconciling simulations and observations; an effective interaction term between dark matter and baryons that could explain observed correlations between the two components of the cosmic fluid within Tully-Fisher analysis.Comment: 18 pages, 6 figures, references added. Published in JCA

Boundary States for D-branes with Traveling Waves

We construct boundary states for D-branes which carry traveling waves in the covariant formalism. We compute their vacuum amplitudes to investigate their interactions. In non-compact space, the vacuum amplitudes become trivial as is common in plane wave geometries. However, we found that if they are compactified in the traveling direction, then the amplitudes are affected by non-trivial time dependent effects. The interaction between D-branes with waves traveling in the opposite directions (`pulse-antipulse scattering') are also computed. Furthermore, we apply these ideas to open string tachyon condensation with traveling waves.Comment: 30 pages. 1 figure, Latex, minor corrections, references adde