Squeezed “atomic” states,pseudo-Hermitian operators and Wigner D-matrices

The states of N two-level atoms can be mapped onto the eigenvectors of angular momentum (with j=N/2) and this system in interaction with a radiation field constitutes a fundamental model in Quantum Optics. There from one may construct atomic coherent states and minimum uncertainty packets. The squeezing of such states is of considerable contemporary interest. We show that the properties of squeezed atomic states are most elegantly and economically expressed in terms of pseudo-Hermitian operators and through Wigner D-matrices and their analytical continuation.     

Influence of turbulence model constants and boundary conditions on the computed hydrodynamic variables in gas-stirred reactors

A finite difference procedure has been employed to obtain numerical predictions of recirculating flows in gas-stirred reactors. Sensitivity of alternative boundary conditions at gas-liquid interface as well as empirical constants of the turbulence model on the predicted flow field have been investigated.     

Self-affine multiplicity fluctuation of target residues in relativistic nuclear collisions at a few GeV to a few hundred GeV

Self-affine multiplicity scaling is investigated in the framework of two-dimensional factorial moment methodology using the concept of the Hurst exponent (H). Our investigation on experimental data of the target-evaporated slow particles emitted in ³²S-AgBr interactions at 200 AGeV and ²⁸Si-AgBr interactions at 14.5 AGeV reveals that a better power law behavior is exhibited in self-affine analysis than self-similar analysis. This work shows a clear evidence of self-affine target fragmentation. Received: 22 October 2001 / Accepted: 6 March 2002     

A link between the second-order Jahn-Teller effect and the highest occupied molecular orbital postulate for molecular shapes

For a closed-shell molecule, a connection is drawn between two recent models for molecular shapes, namely, those based on the second-order Jahn-Teller (SOJT) effect and the highest occupied molecular orbital (HOMO) postulate respectively. Two necessary and sufficient conditions are derived within the molecular orbital framework for the approximation inherent in the SOJT model to be valid. One of these conditions is akin to the HOMO postulate.     

The Extractive-Spectrophotometric Determination of Iron(III) As a Mixed-Ligand Complex with N-Hydroxy-N,N′DI-p-Tolyl-p-Toluamidine and Thiocyanate

The extractive-photometric determination or iron(III) as a mixed-ligand complex with N -hydroxy-N, N′ -di-p -tolyl-p -toluamidine (HDTTA) and thiocyanate is described. The orange-red Waterinsoluble 1:1:2 (metal: HDTTA: SCN^?) ternary complex formed in 0.1–0.6 M hydrochloric acid solutions is quantitatively extractable into benzene. The wavelength of maximum absorption, molar absorptivity and sensitivity of the colour system are 460nm, 12000 l. mole^?1 cm^?1 and 0.0046 μg Fe/cm ²respectively. The influence or foreign ions on the determination of iron has been studied. This method has also been applied to determine the iron content of several alloys.     

Nonlinear goal programming using multi-objective genetic algorithms

Goal programming is a technique often used in engineering design activities primarily to find a compromised solution which will simultaneously satisfy a number of design goals. In solving goal programming problems, classical methods reduce the multiple goal-attainment problem into a single objective of minimizing a weighted sum of deviations from goals. This procedure has a number of known difficulties. First, the obtained solution to the goal programming problem is sensitive to the chosen weight vector. Second, the conversion to a single-objective optimization problem involves additional constraints. Third, since most real-world goal programming problems involve nonlinear criterion functions, the resulting single-objective optimization problem becomes a nonlinear programming problem, which is difficult to solve using classical optimization methods. In tackling nonlinear goal programming problems, although successive linearization techniques have been suggested, they are found to be sensitive to the chosen starting solution. In this paper, we pose the goal programming problem as a multi-objective optimization problem of minimizing deviations from individual goals and then suggest an evolutionary optimization algorithm to find multiple Pareto-optimal solutions of the resulting multi-objective optimization problem. The proposed approach alleviates all the above difficulties. It does not need any weight vector. It eliminates the need of having extra constraints needed with the classical formulations. The proposed approach is also suitable for solving goal programming problems having nonlinear criterion functions and having a non-convex trade-off region. The efficacy of the proposed approach is demonstrated by solving a number of nonlinear goal programming test problems and an engineering design problem. In all problems, multiple solutions (each corresponding to a different weight vector) to the goal programming problem are found in one single simulation run. The results suggest that the proposed approach is an effective and practical tool for solving real-world goal programming problems.     

Broadband second-harmonic generation in a double-tapered gallium arsenide slab using total internal reflection quasiphase matching

This article analytically describes broadband second-harmonic generation in a double-tapered gallium arsenide (GaAs) slab using total internal reflection quasi-phase matching technique. This double-tapered configuration ensures a combination of increasing and then decreasing bounce lengths which provides an extremely wide 3 dB bandwidth of 573.6 nm with a conversion efficiency of 1.929%, after considering reflection and absorption losses. Effect of varying the slab dimensions, viz., length and tapering angles, as well as the operating temperature on the performance parameters has also been incorporated in the analysis.     

Langevin-Bloch equations for a spin bath

We derive the Bloch equations for a two-level system coupled to a spin bath of infinitely many two-level atoms to examine phase and energy relaxation of an optically excited system. We show that increasing temperature assists coherence. This is reflected in a number of anomalous features of relaxation of the system, e.g., decrease of integrated absorption coefficient with temperature, nonlinear variation of linewidth with incident power. We also predict that thermally induced coherence may result in anomalous narrowing of linewidth, reminiscent (but distinct) of "motional narrowing" of spectral line. The theoretical results are discussed in the light of absorption-emission experiments on single quantum dots.