Effect of field quantization on Rabi oscillation of equidistant cascade four-level system

We have exactly solved a model of equidistant cascade four-level system interacting with a single-mode radiation field both semiclassically and quantum mechanically by exploiting its similarity with Jaynes-Cummings model. For the classical field, it is shown that the Rabi oscillation of the system initially in the first level (second level) is similar to that of the system when it is initially in the fourth level (third level). We then proceed to solve the quantized version of the model where the dressed state is constructed using a six-parameter four-dimensional matrix and show that the symmetry exhibited in the Rabi oscillation of the system for the semiclassical model is completely destroyed on the quantization of the cavity field. Finally, we have studied the collapse and revival of the system for the cavity field-mode in a coherent state to discuss the restoration of symmetry and its implication is discussed.      

Theory of anisotropic diamagnetism, local moment magnetization and carrier spin-polarization in Pb1−x Eu x Te

We present theoretical analyses of anisotropic lattice diamagnetism, magnetization due to magnetic ions and carrier spin-polarization in the diluted magnetic semiconductor, Pb_1-x Eu _x Te. The lattice diamagnetism results from orbital susceptibility due to inter band effects and spin-orbit contributions. The spin-orbit contribution is found to be dominant. However, both the contributions show pronounced anisotropy. With increase in x, the diamagnetism decreases. We consider contributions from randomly distributed isolated magnetic ions and clusters of pairs and triads for the local moment magnetization. The isolated magnetic-ion contribution is the dominant one.We calculate the magnetization for two typical magnetic ion concentrations: x=0.03 and x=0.06. Temperature dependence of the magnetization is also considered. Apart from lattice and localized magnetic ions, the carrier contribution to the spin-density is also calculated for a carrier density of p=10¹⁸ cm⁻³. the relative spin-density of carriers increases with increase in the magnetic field strength and magnetic ion concentration. The agreement with experiment where available is reasonably good.     

Intercalation and anisotropy of optical absorption in MoRe0.005Se1.995 single crystals

The optical energy gap of MoRe_0.005Se_1.995 single crystal has been measured at room temperature near the fundamental absorption method. The incident light was polarized along c‐axis of the crystals. Two and three dimensional models are adopted for generating the results. Direct as well as indirect transitions are involved in the absorption process. The indirect transition was found to be allowed with two phonons involved in the process. The three dimensional model could be used to describe the optical properties of the single crystal of MoRe_0.005Se_1.995. Also, the optical energy gaps depend upon the amount of the intercalating Re material, which show the anisotropy of the chemical bonds. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anisotropy of the optical absorption in layered single crystals of MoRe0.001Se1.999

Energy gap of MoRe_0.001Se_1.999 single crystal has been determined by fundamental absorption methods. The incident light was polarized along c‐axis of the crystals. The interpretion of the data is given within frameworks of two and three dimensional models. Both direct and indirect transitions are involved in the absorption process. The indirect transition was found to be allowed with two phonons participating in the process. The three dimensional model could be used to describe the optical properties of the single crystal. The energy gaps depend upon the amount of the intercalating Re material, which show the anisotropy of the chemical bonds. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Eigenvalue Bounds for the Orr–Sommerfeld Equation and Their Relevance to the Existence of Backward Wave Motion

Theoretical estimates of the phase velocity c_r of an arbitrary unstable, marginally stable or stable wave derived on the basis of the classical Orr–Sommerfeld eigenvalue problem governing the linear instability of plane Poiseuille flow or nearly parallel viscous shear flows in straight channels with velocity U(z) (=1?z², z∈[?1, +1] for plane Poiseuille flow), leave open the possibility that these phase velocities lie outside the range U_min<c_r<U_max but not a single experimental or numerical investigation, concerned with unstable waves in the context of flows with (d²U/dz²)_max≤0, has supported such a possibility as yet. U_min, U_max and (d²U/dz²)_max are, respectively, the minimum value of U(z), the maximum value of U(z), and the maximum value of (d²U/dz²) for z∈[?1, +1]. This gap between the theory on one hand and experiment and computation on the other has remained unexplained ever since Joseph [3] derived these estimates, first in 1968, and has even led to the speculation of a negative phase velocity in plane Poiseuille flow (i.e., c_r<U_min=0) and hence the possibility of a “backward” wave as in Jeffrey-Hamel flow in a diverging channel with backflow [1]. A simple mathematical proof of the nonexistence of such a possibility is given herein by showing that if (d²U/dz²)_max≤0 and (d⁴U/dz⁴)_min≥0 for z∈[?1, +1], then the phase velocity c_r of an arbitrary unstable wave must satisfy the inequality U_min<c_r<U_max, (d⁴U/dz⁴)_min is the minimum value of (d⁴U/dz⁴) for z∈[?1, +1], and therefore c_r cannot be negative when U_min=0. Another result that provides valuable insight into the general modal structure of the problem of instability of the above class of flows with U_min≥0 (e.g., plane Poiseuille flow) is that all standing waves, that is, modes for which c_r=0, are stable.     

Anisotropy of optical absorption in layered single crystals

The optical energy gap of Re doped MoSe₂ single crystal Mo_0.995Re_0.005Se₂ has been measured at room temperature near the fundamental absorption edge. The incident light was kept normal to the basal plane i.e. along the c‐axis of the grown crystals. Results have been given on the basis of two and three dimensional models. Both direct and indirect transitions are involved in the absorption process. The indirect transition was found to be allowed with two phonons involved in the process. The three dimensional model and not the two dimensional could be used to describe the optical properties of Re doped MoSe₂ single crystal. Also, the optical energy gaps depend upon the amount of the intercalating Re material. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An NHC-Stabilised Phosphinidene for Catalytic Formylation: A DFT-Guided Approach

In recent years, the applications of low-valent main group compounds have gained momentum in the field of catalysis. Owing to the accessibility of two lone pairs of electrons, NHC-stabilised phosphinidenes have been found to be excellent Lewis bases; however, they cannot yet be used as catalysts. Herein, an NHC-stabilised phosphinidene, 1,3-dimethyl-2-(phenylphosphanylidene)-2,3-dihydro-1H imidazole (1), for the activation of CO₂ is reported.A closer inspection of the CO₂ activation process by DFT calculations along with intrinsic bond orbital analysis shows that phosphinidene is associated with phenylsilane through a noncovalent π-π interaction between two phenyl rings which activates the Si−H bond facilitating hydride transfer to the CO₂ molecule. Detailed DFT studies along with spectroscopic experiments were combined to understand the mechanism of CO₂ activation and its catalytic reductive functionalisation leading to the formylation of a range of chemically inert primary amides under mild reaction conditions.     

High-Performance Thin-Layer Chromatography and Reversed-Phase High-Performance Liquid Chromatography Methods for Fingerprinting of Salvadora persica Root Powder Extract Using Benzyl Isothiocyanate as Biomarker

JPC – Journal of Planar Chromatography – Modern TLC - Salvadora persica plant having a number of antimicrobial substances and the roots of the S. persica shrub have been demonstrated to...     

A review on saturated boiling of liquids on tube bundles

A review of recent investigation on boiling of saturated liquids over plain and enhanced tube bundles has been carried out taking the earlier review works as reference point. The experimental observations of various geometry and performance parameters studied by researchers are analyzed keeping current demand of industries in design and development of compact, efficient heat exchanging devices. The study shows that tube spacing plays an important role in determination of compactness of the heat exchanger.     

A mixed anhydride approach to the preparation of sulfinate esters and allylic sulfones: Trimethylacetic p-toluenesulfinic anhydride

A reagent combination of toluenesulfinic acid and trimethylacetyl chloride affords a putative trimethylacetic p-toluenesulfinic anhydride. This reagent has been used to prepare a series of sulfinate esters from primary and secondary alcohols. In addition, the reagent was used to convert Baylis-Hillman substrates into allylic sulfones. Attempts to use the reagent to convert amines to sulfinamides were unsuccessful. In contrast, the use of 2-pyrrolidinone afforded N-p-toluenesulfinyl pyrrolidinone in 64% yield. The use of a chiral 4-benzyl-1,3-oxazolidinone or 4-benzyl-1,3-oxazolidine-2-thione led to the isolation of S-p-tolyl p-toluenethiosulfonate.