Electron correlation forms in the LiH molecule—fermi correlation

Correlation forms for electrons of the same spin small molecules are analyzed by taking the LiH molecule as an example. The analyses are carried out on the basis of the reduced density matrix theory and for both the ground state and the first excited state. It turns out that although there is a certain similarity, the correlated motions of parallel-spin electrons in this four-electron molecule are more complicated than those found for the two-electron molecule. The correlation forms are not always constant. They vary essentially from one state to another, but are insensitive to fairly large changes of the internuclear distance for a given state.     

Characterization of an actively linearized ultrabroadband chirped laser with a fiber-laser optical frequency comb

The optical frequency sweep of an actively linearized, ultrabroadband, chirped laser source is characterized through optical heterodyne detection against a fiber-laser frequency comb. Frequency sweeps were measured over approximately 5 THz bandwidths from 1530 nm to 1570 nm. The dominant deviation from linearity resulted from the nonzero dispersion of the fiber delay used as a reference for the sweep linearization. Removing the low-order dispersion effects, the residual sweep nonlinearity was less than 60 kHz rms, corresponding to a constant chirp with less than 15 ppb deviation across the 5 THz sweep.     

Nanosecond laser ablation and deposition of silicon

Nanosecond-pulsed KrF (248 nm, 25 ns) and Nd:YAG (1064 nm, 532 nm, 355 nm, 5 ns) lasers were used to ablate a polycrystalline Si target in a background pressure of <10⁻⁴ Pa. Si films were deposited on Si and GaAs substrates at room temperature. The surface morphology of the films was characterized using scanning electron microscopy (SEM) and atomic force microscopy (AFM). Round droplets from 20 nm to 5 μm were detected on the deposited films. Raman Spectroscopy indicated that the micron-sized droplets were crystalline and the films were amorphous. The dependence of the properties of the films on laser wavelengths and fluence is discussed.     

Insider Trading in Convergent Markets

Optimal trading strategies are found for an insider who is trading in two convergent stocks and is bound by margin constraints.     

Ammonia synthesis and decomposition on a Ru-based catalyst modeled by first-principles

A recently published first-principles model for the ammonia synthesis on an unpromoted Ru-based catalyst is extended to also describe ammonia decomposition. In addition, further analysis concerning trends in ammonia productivity, surface conditions during the reaction, and macro-properties, such as apparent activation energies and reaction orders are provided. All observed trends in activity are captured by the model and the absolute value of ammonia synthesis/decomposition productivity is predicted to within a factor of 1–100 depending on the experimental conditions. Moreover it is shown: (i) that small changes in the relative adsorption potential energies are sufficient to get a quantitative agreement between theory and experiment (Appendix A) and (ii) that it is possible to reproduce results from the first-principles model by a simple micro-kinetic model (Appendix B).     

Non-existence of a minimizer to the magnetic Hartree-Fock functional

In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization.