A Reality Proof in PT-Symmetric Quantum Mechanics

We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral equivalences inspired by the correspondence are also discussed.     

Quantum chemistry with an attached processor

The Floating Point Systems, Inc. Model 164 Attached Processor (FPS-164) is a high-speed, pipelined, parallel processor designed for large-scale scientific computation. Benchmark studies of operations common in quantum chemistry codes are discussed and the performance of the FPS-164 is compared with other commonly available computers. A complete system of electronic structure codes has been implemented on the FPS-164 using the Fortran-77 cross-compiler and calls to optimized vector and matrix routines. The conversion of a generalized valence bond (GVB ) code illustrates the strategy adopted to adapt Fortran codes to the FPS-164. A typical production example, a large scale (GVB ) and configuration interaction calculation on the vinyl radical, shows a net throughput equivalent to nearly nine VAX 11/780 computers.     

The electronic structure of vanadium carbide, VC

Within an energy range of 2.4 eV, we have explored 29 of the 36 states of the diatomic molecule VC that arise from the atoms in their ground state, V(4s23d3;4F)+C(2s2 2p2;3P). We use multireference methods with large atomic natural orbital basis sets. The ground state is of 2Delta symmetry with the first two excited states, 4Delta and 2Sigma+, located 4.2 and 7.0 kcal/mol above the X state. All the states examined in this work are relatively strongly bound and show significant charge transfer from V to C. The binding energy of the X 2Delta state is estimated to be 95.3 kcal/mol in good agreement with the experimental value.     

Some new acridinium trifluoromethanesulfonates as spectrophotometric derivatization reagents for aromatic and aliphatic primary amines

Some new 9-substituted 10-methylacridinium trifluoromethanesuifonate (triflate) salts have been synthesized and shown to react in methanol with the model aromatic and aliphatic amines, aniline and n-butylamine, to form derivatives which absorb strongly at 445 and 439 nm, respectively. The color development is affected by heat and heating time and by the quantity of acridinium triflate used. A 10-50-fold molar excess of the triflate should be used and the solution heated at 60 degrees for 30 min. The linearity and reproducibility of the assay are improved by the presence of pyridine (for aniline) and triethylamine (for n-butylamine) in the reaction mixture. Beer's law is obeyed over the range 0-1860 ng/ml for aniline and 0-1440 ng/ml for n-butylamine, with each of the new reagents. The relative error and the precision of determination depends on the acridinium triflate used.     

Ground-state entanglement of the BCS model

The concept of local concurrence is used to quantify the entanglement between a single qubit and the remainder of a multiqubit system. For the ground state of the BCS model in the thermodynamic limit the set of local concurrences completely describes the entanglement. As a measure for the entanglement of the full system we investigate the average local concurrence (ALC). We find that the ALC satisfies a simple relation with the order parameter. We then show that for finite systems with a fixed particle number, a relation between the ALC and the condensation energy exposes a threshold coupling. Below the threshold, entanglement measures besides the ALC are significant.     

Extended formulations in mixed integer conic quadratic programming

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vielma et al. (INFORMS J Comput 20: 438–450, 2008) and Hijazi et al. (Comput Optim Appl 52: 537–558, 2012) to construct algorithms for MICQP that can provide a significant computational advantage. The first approach is based on an extended or lifted polyhedral relaxation of the Lorentz cone by Ben-Tal and Nemirovski (Math Oper Res 26(2): 193–205 2001) that is extremely economical, but whose approximation quality cannot be iteratively improved. The second is based on a lifted polyhedral relaxation of the euclidean ball that can be constructed using techniques introduced by Tawarmalani and Sahinidis (Math Programm 103(2): 225–249, 2005). This relaxation is less economical, but its approximation quality can be iteratively improved. Unfortunately, while the approach of Vielma, Ahmed and Nemhauser is applicable for general MICQP problems, the approach of Hijazi, Bonami and Ouorou can only be used for MICQP problems with convex quadratic constraints. In this paper we show how a homogenization procedure can be combined with the technique by Tawarmalani and Sahinidis to adapt the extended formulation used by Hijazi, Bonami and Ouorou to a class of conic mixed integer programming problems that include general MICQP problems. We then compare the effectiveness of this new extended formulation against traditional and extended formulation-based algorithms for MICQP. We find that this new formulation can be used to improve various LP-based algorithms. In particular, the formulation provides an easy-to-implement procedure that, in our benchmarks, significantly improved the performance of commercial MICQP solvers.     

Turbulent transport measurements with a laser Doppler velocimeter

The power spectrum of phototube current from a laser Doppler velocimeter operating in the heterodyne mode has been computed. The spectrum is obtained in terms of the space time correlation function, G(r,), of the fluid. The spectral width and shape predicted by the theory is in agreement with experiment. For normal operating parameters the time average spectrum contains information only for times shorter than the Lagrangian integral time scale of the turbulence. To examine the long time behaviour one must use either extremely small scattering angles, much longer wave-length radiation or a different mode of signal analysis, e.g. F.M. detection.     

Lifetime of C2Cl4(-) ions produced by nondissociative electron attachment to C2Cl4

The lifetimes of long-lived C2Cl4(-) ions formed by Rydberg electron transfer in K(np)/C2Cl4 collisions are investigated using a Penning ion trap. Measurements at high n, n > or = 30, show that low-energy electron attachment to C2Cl4 leads to the production of C2Cl4(-) ions with a broad range of lifetimes that extends up to at least 1 ms. This is attributed to capture by molecules in different initial vibrational states. At low n, internal-to-translational energy transfer in postattachment interactions between the product K+ and C2Cl4(-) ions becomes important and leads to a substantial increase in ion lifetimes.