Level density and level-spacing distributions of random, self-adjoint, non-Hermitian matrices

We investigate the level-density $\sigma(x)$ and level-spacing distribution $p(s)$ of random matrices $M=AF\neq M^{\dagger}$ where $F$ is a (diagonal) inner-product and $A$ is a random, real symmetric or complex Hermitian matrix with independent entries drawn from a probability distribution $q(x)$ with zero mean and finite higher moments. Although not Hermitian, the matrix $M$ is self-adjoint with respect to $F$ and thus has purely real eigenvalues. We find that the level density $\sigma_F(x)$ is independent of the underlying distribution $q(x)$, is solely characterized by $F$, and therefore generalizes Wigner's semicircle distribution $\sigma_W(x)$. We find that the level-spacing distributions $p(s)$ are independent of $q(x)$, are dependent upon the inner-product $F$ and whether $A$ is real or complex, and therefore generalize the Wigner's surmise for level spacing. Our results suggest $F$-dependent generalizations of the well-known Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary Ensemble (GUE) classes.Comment: 5 pages, 5 figures, revised tex

Precision Spectroscopy of Molecular Hydrogen Ions: Towards Frequency Metrology of Particle Masses

We describe the current status of high-precision ab initio calculations of the spectra of molecular hydrogen ions (H_2^+ and HD^+) and of two experiments for vibrational spectroscopy. The perspectives for a comparison between theory and experiment at a level of 1 ppb are considered.Comment: 26 pages, 13 figures, 1 table, to appear in "Precision Physics of Simple Atomic Systems", Lecture Notes in Physics, Springer, 200

Twin polaritons in semiconductor microcavities

The quantum correlations between the beams generated by polariton pair scattering in a semiconductor microcavity above the parametric oscillation threshold are computed analytically. The influence of various parameters like the cavity-exciton detuning, the intensity mismatch between the signal and idler beams and the amount of spurious noise is analyzed. We show that very strong quantum correlations between the signal and idler polaritons can be achieved. The quantum effects on the outgoing light fields are strongly reduced due to the large mismatch in the coupling of the signal and idler polaritons to the external photons

Use of photostress and strain gages to analyze behavior of weldments and use of photostress and strain gages to analyze behavior of an aft skirt test specimen

Previous work using Photostress on TIG welded, heat treated specimens of 2219-T87 parent material and 2319 weld material indicated that behavior of the joint can be highly irregular and non-uniform. Welded joints 1.40 inches thick exhibited a totally non-uniform behavior through the weld thickness with the 'wide' side of the weld being much more ductile than the 'narrow' side. It is believed that this difference in behavior through the weld is, in part, caused by procedures used when laying the weld bead. Joints similar to weldments in references 1 and 2 are an integral part of the aft skirt of the SRB of the shuttle. Since the ultimate safety factor for the lower portion of the weld is below the minimum required safety factor, a photostress analysis of this lower portion will be conducted in the vicinity of the weld. A test program using photostress will be conducted in accordance with the project planning document entitled 'Photostress Evaluation Requirements for AFT Skirt Test Article No. 4'

Total Synthesis of Ionic Liquid Systems for Dissolution of Lunar Simulant

For purposes of Space Resource Utilization, work in the total synthesis of a new ionic liquid system for the extraction of oxygen and metals from lunar soil is studied and described. Reactions were carried out according to procedures found in the chemical literature, analyzed via Thin-Layer Chromatography and 1H Nuclear Magnetic Resonance Spectroscopy and purified via vacuum distillation and rotary evaporation. Upon final analysis via 1H NMR, it was found that while the intermediates of the synthesis had been achieved, unexpected side products were also present. The mechanisms and constraints of the synthesis are described as well as the final results of the project and recommendations for continued stud

A mid-infrared survey of the inner 2 × 1.5 degrees of the Galaxy with Spitzer/IRAC

We present a survey of Spitzer Space Telescope/IRAC observations of the central 2 × 1.5 degrees (265 × 200 pc) of the Galaxy at 3-8 μm. These data represent the highest spatial resolution and sensitivity large-scale map made to date of the Galactic Center (GC) at mid-infrared wavelengths. The IRAC data provide a census of the optically obscured stellar sources as well as a detailed map of the highly filamentary structure in the interstellar medium. The diffuse emission is dominated by PAH emission from small grains in star-forming regions. Dark clouds displaying a large variety of sizes and morphologies are imaged, many of which remain opaque at IRAC wavelengths. Using a multiwavelength comparison, we determine which objects are likely to be in the foreground and which are located at the GC. We find no counterparts at IRAC wavelengths to the unique system of linear, nonthermal radio filaments present at the GC

Convex Hull of Arithmetic Automata

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata

Metals and Oxygen Mining from Meteorites, Asteroids and Planets using Reusable Ionic Liquids

In order for humans to explore beyond Low Earth Orbit both safely and economically, it will be essential to learn how to make use of in situ materials and energy in an environment much different than on earth. Precursor robotic missions will be necessary to determine what resources will be available and to demonstrate the capabilities for their use. To that end, we have recently been studying acidic Ionic Liquid (IL) systems for use in a low temperature (< 200 C) process to solubilize regolith, and to extract, as water, the oxygen available in metal oxides. Using this method, we have solubilized lunar regolith simulant (JSC-1A), as well as extraterrestrial materials in the form of meteorites, and have extracted up to 80% of the available oxygen. Moreover, by using a hydrogen gas electrode, we have shown that the IL can be regenerated at the anode and metals (e.g. iron) can be plated onto the cathode. These results indicate that IL processing is an excellent candidate for extracting oxygen in situ, for life support and propulsion, and for extracting metals to be used as feedstock in fabrication processes. We have obtained small amounts of meteorite materials believed by meteoriticists to have originated from our moon, Mars, and the asteroid Vesta, and were able to solubilize those using acidic IL systems. From the Vesta meteorite, we were able to extract about 60% of the available oxygen as water. As far as is known, this is the first time that extraterrestrial/earth hybrid water has been obtained. NMR analysis provided proof that the liquid retrieved is indeed water. We have also been able to electro-plate nickel and iron contained in meteorite material. By varying voltage they can be plated separately (electro-winning), and we plan to soon have sufficient quantities to form usable parts utilizing the additive manufacturing process