Method for Finding the Exact Effective Hamiltonian of Time‐Driven Quantum Systems

Time‐driven quantum systems are important in many different fields of physics as cold atoms, solid state, optics, etc. Many of their properties are encoded in the time evolution operator or the effective Hamiltonian. Finding these operators usually requires very complex calculations that often involve some approximations. To perform this task, a systematic scheme that can be cast in the form of a symbolic computational algorithm is presented. It is suitable for periodic and non‐periodic potentials and, for convoluted systems, can also be adapted to yield numerical solutions. The method exploits the structure of the associated Lie group and a decomposition of the evolution operator on each group generator. To illustrate the use of the method, five examples are provided: harmonic oscillator with time‐dependent frequency (Paul trap), modulated optical lattice, time‐driven quantum oscillator, a step‐wise driving of a free particle, and the non‐periodic Caldirola‐Kanai Hamiltonian. To the extent of the authors' knowledge, whereas the exact form of Paul trap's evolution operator is well known, its effective Hamiltonian was until now unknown. The remaining four examples accurately reproduce previous results.     

Effect of combined polymers on the loss of efficiency caused by mechanical degradation in drag reducing flows through straight tubes

The mechanical molecular degradation in drag reducing flows is a huge problem in the effort to improve the efficiency of drag reducers, which is clearly increased when a combination of materials is used. Here, we analyze mixtures of three kinds of water-soluble polymers: Poly (ethylene oxide) (PEO), Polyacrylamide (PAM), and Xanthan Gum (XG). Two kinds of mixtures are tested: (a) PAM and XG; (b) PEO and XG. The synergy between the polymers is clearly noticeable. The values of the drag reduction (DR) obtained by the polymer–polymer combination was larger than that observed for a single polymer in a solution with the same total concentration of the mixture. Our tests are conducted in straight tubes where the total pressure is fixed. The values of DR are computed step-by-step, as the total amount of solution pass through the system. In doing so, we carefully took into account the loss of efficiency caused by the turbulent flow in the straight tubes. It is quite clear that the degradation of the flexible polymers (PEO and PAM) is delayed in the mixtures. In other words, besides the increase in the DR, the flexible polymers are more resistant when in the presence of the rigid one (XG). Such observation is the main conclusion of this work.     

Measurement of the phase behaviour of the binary systems {carbon dioxide (CO2) + non-ionic surfactants (CiEOj)}

Solubility experiments of ethoxylates surfactants denoted as C_iEO_j (where C_i = hydrocarbon tail, EO_j = oxyethylene groups, i = 6 to 8 and j = 3 to 5) in sub- and supercritical carbon dioxide were carried out at different temperatures, pressures, and concentrations in a Cailletet apparatus as a representative model for dry cleaning system. For a variety of compositions, results are reported for binary systems within temperature and pressure ranges of (260 to 310) K and (2.0 to 10) MPa respectively. In each experiment, the surfactants reach equilibrium with carbon dioxide at different concentrations. The data show that with all the surfactants upon increasing concentration, the liquid–liquid (L–L) curve shifts to lower temperatures. Therefore, the one-phase solution gap is reduced in pressure and temperature at higher concentrations. When the length of the hydrocarbon tail remains constant and the ethoxylated chain is increased from three to five groups, the L–L curve once again shifts to lower temperatures and the two phases start earlier. This effect can be attributed to the higher surfactant’s polarity due to the increase in j. On the other hand, when the number of ethoxylated groups j remains constant and the length of the hydrocarbon tail is increased from six to eight carbon atoms, no significant shift in the L–L curve is observed. That signals the fact that the appearance of two phases is directly related to the number of ethoxylated group which determine the polarity of the molecule.     

Unique green chromatography method for the determination of serotonin receptor antagonist (Ondansetron hydrochloride) related substances in a liquid formulation,robustness by quality by design-based design of experiments approach

Serotonin receptor antagonist drug Ondansetron hydrochloride injectable formulation containing all related substances was identified and quantified by a single, simple, sensitive, eco-friendly, and green high-performance liquid chromatography method. The disseverment of all impurities was achieved with the Discovery Cyano (250 × 4.6) mm, 5 μm column. The gradient program was composed of pH 5.7 phosphate buffer as mobile phase A and acetonitrile as mobile phase B. The flow rate, column compartment temperature, and detection wavelengths were 0.9 mL/min, 30°C, and 216 nm, respectively. The method was validated as per current regulatory guidelines. The obtained %relative standard deviation for the precision results was between 0.55 and 2.72% for all impurities. The correlation coefficient values from the linearity experiment for impurities and analyte were more than 0.995. The accuracy results were obtained between 88.4 and 113.0% for all impurities. Both sample and standard solutions showed 24 h stability at benchtop and refrigerator conditions. All impurities and analytes met the specificity and mass balance for all forced degradation conditions. Quality-by-design-based design of experiments was utilized to establish the method's robustness. Method greenness was assessed by using the current advanced tool green analytical procedure index, National Environmental Methods Index, and analytical eco-scale.     

Semiclassical propagator of the Wigner function

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.     

Alkaloids from stemmadenia species-I The alkaloids of S. Donnell-Smithii and S. Galeottiana

—From Stemmadenia Donnell-Smithii and S. Galeottiana, the following new alkaloids were isolated: (+)-quebrachamine (IV), an optical isomer of the known (−)-quebrachamine; isovoacangine (IIIa), a position isomer of voacangine (Ia), voacamine, tabernanthine (IIIb) and ibogamine.     

Hypervirial theorem and ladder operators. Recurrence relations for harmonic oscillator integrals

A second-quantization formalism combined with a hypervirial theorem is used to derive new recurrence relations for one-dimensional harmonic oscillator matrix elements. The most general case of 〈m|f(â, â⁺)|n〉 is considered, and the recurrence relations forf(â, â) = X^k, exp(?βX), and exp(?X²) are given as examples. The relations obtained are considerably simpler than those derived by using only the hypervirial theorem; comparatively, the recurrence relations presented here have the advantage of avoiding the use of the quantum mechanical sum-rules when determining initial matrix elements. The proposed procedure can be used to determine the recurrence relations for other potentials as well as to evaluate the two-center integrals.     

Photoacoustic method for orientation and optical characterization of nonlinear crystals

Second-harmonic conversion of the 532-nm pulsed output of a doubled Nd:YAG laser in KDP was characterized by analyzing the changes in the acoustic signals generated in the crystal at different orientation conditions and for several incident fluences. Using a piezoelectric transducer, phase-matching condition was determined by maximizing the amplitude of the acoustic signals detected. The angular orientation for optimum harmonic efficiency was obtained with the same precision compared with the conventional optical procedure. The origin of the photoacoustic signals is the relaxed energy following the absorption of 266-nm photons. To determine the mechanisms of the 266-nm absorption processes, we also performed experiments under direct illumination with the 266-nm emission of the quadrupled Nd:YAG laser. A combination of a linear and nonlinear process occurs. Direct absorption by KDP as well as the participation of transient defects produced in the material were analyzed. Received: 27 July 1998 / Revised version: 19 March 1999 / Published online: 19 August 1999