Squeezed states, metaplectic group, and operator möbius transformations

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically

Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

Automatic identification of modal damping from Floquet analysis

A practical method is proposed to identify the mode associated with the frequency part of the eigenvalue of the Floquet transition matrix (FTM). From the FTM eigenvector, which contains the states and their derivatives, the ratio of the derivative and the state corresponding to the largest component is computed. The method exploits the fact that the imaginary part of this (complex) ratio closely approximates the frequency of the mode. It also lends itself well to automation and has been tested over a large number of FTMs of order as high as 250.

Comparative studies on the effects of specific immunoneutralization of endogenous FSH or LH on testicular germ cell transformations in the adult bonnet monkey (Macaca radiata)

PROBLEM: It is yet to be determined clearly whether the two hormones FSH and T act synergistically in the same cell type-the Sertoli cells-to control overall spermatogenesis or influence independently the transformation of specific germ cell types during spermatogenesis in the adult mammal. METHOD: Adult male bonnet monkeys specifically deprived of either FSH or LH using immunoneutralization techniques were monitored for changes in testicular germ cell transformation by DNA flow cytometry. RESULTS: FSH deprivation caused a significant reduction (>40%; P < 0.05) in [H-3] thymidine incorporation into DNA of proliferating 2C (spermatogonial) cells, a marked inhibition (>50%) in the transformation of 2C to primary spermatocytes (4C) and a concomitant, belated reduction (50%) in the formation of round spermatids (1C). In contrast, specific LH/T deprivation led to an immediate arrest in the meiotic transformation of 4C to 1C/HC leading to an effective and significant block (<90%; P < 0.01) in sperm production. CONCLUSION: Thus, LH rather than FSH deprivation has a more pronounced and immediate effect as the former primarily blocks meiosis (4C --> 1C/HC) which controls production of spermatids. These data provide evidence for LH/T and FSH regulating spermatogenic process in the adult primate by primarily acting at specific germ cell transformation steps.

Thermally induced transformations in GexAsyTe100-x-y glasses

Chalcogenide glasses with compositions Ge7.5AsyTe92.5-y (y = 20, 40, 45, 47.5, 50, 52.5, 55) and Ge10AsyTe90-y (y = 15, 20, 22.5, 35, 40, 45, 50) have been prepared by the melt-quenching technique. The amorphous nature of these glasses has been confirmed by X-ray powder diffractometry. The thermal stability of these glasses has been studied using differential scanning calorimetry (DSC). The compositional dependence of the glass transition temperature, T(g), the crystallization temperatures, T(c1) and T(c2), and the melting temperature, T(m), are reported. The glass-forming tendency, K(gl), and the activation energy of crystallization, E, are calculated. The activation energy decreases with increasing tellurium content for both sets of glasses.

Transformations of morphine, codeine and their analogues by Bacillus sp

A bacterial strain belonging to the genus Bacillus isolated by enrichment culture technique using morphine as a sole source of carbon transforms morphine and codeine into 14-hydroxymorphinone and 14-hydroxycodeinone as major and 14-hydroxymorphine and 14-hydroxycodeine as minor metabolites, respectively. When the N-methyl group in morphine and codeine are replaced by higher alkyl groups, the organism still retains its ability to carry out 14-hydroxylation as well as oxidation of the C-6-hydroxyl group in these N-variants, although the level of metabolites formed are considerably low. The organism readily transforms dihydromorphine and dihydrocodeine into only dihydromorphinone and dihydrocodeinone, respectively; suggesting that the 7,8-double bond is a necessary structural feature to carry out 14-hydroxylation reaction. The cell free extract (20,000 x g supernatant), prepared from morphine grown cells, transforms morphine into 14-hydroxymorphinone in the presence of NAD(+), but fails to show activity against testosterone. However, the cell free extract prepared from testosterone grown cells contains significant levels of 17 beta- hydroxysteroid dehydrogenase but shows no activity against morphine.

Transformations of two-dimensional layered zinc phosphates to three-dimensional and one-dimensional structures

Transformations of the layered zinc phosphates of the compositions [C6N4H22](0.5) [Zn-2 (HPO4)(3)], I, [C3N2H12][Zn-2 (HPO4)(3)], II and [C3N2OH12][Zn-2 (HPO4)(3)], III, containing triethylenetetramine, 1,3-diaminopropane, and 1,3-diamino-2-hydroxypropane, respectively, have been investigated under different conditions. On heating in water, I transforms to a one-dimensional (1-D) ladder and a three-dimensional (3-D) structure, while II gives rise to only a two-dimensional (2-D) layered structure. In the transformation reaction of I with zinc acetate, the same ladder and 3-D structures are obtained along with a tubular layer. Under similar conditions II gives a layered structure formed by the joining of two ladder motifs. III, on the other hand, is essentially unreactive when heated with water and zinc acetate, probably because the presence of the hydroxy group in the amine which hydrogen bonds to the framework. In the presence of piperazine, I, II and III give rise to a four-membered, corner-shared linear chain which is likely to be formed via the ladder structure. In addition, 2-D and 3-D structures derived from the 1-D linear chain or ladder structures are also formed. The primary result from the study is that the layers produce 1-D ladders, which then undergo other transformations. It is noteworthy that in the various transformations carried out, most of the products are single-crystalline.

A kinetic study of the phase transformations in Al2O3 and Na2O · 6Al2O3 by a combined use of 27Al MAS NMR spectroscopy and x-ray diffraction: Importance of nucleation

Phase transformations of Al2O3 and Na2O · 6Al2O3 prepared by the gel route have been investigated for the first time by 27Al MAS NMR spectroscopy in combination with x-ray diffraction. Of particular interest in the study is the kinetics of the γ → α and γ → β transformations, respectively, in these two systems. Analysis of the kinetic data shows the important role of nucleation in both these transformations.

Biochemistry of water-logged soils. Part IV. Carbon and nitrogen transformations

1. During the fermentation of water-logged soil containing added substances with different carbon-nitrogen ratios, the reaction first turns slightly acid, but soon returns to the original hydrogen-ion concentration (pH 7·6). 2. The quantities of ammonia present in the medium increase up to a point, after which there is steady decrease. 3. There is nitrification only in the case of substances with narrow C/N ratios. The production of nitrate generally commences only after about a month, when the vigour of the initial fermentation has subsided and fairly large quantities of ammonia have accumulated in the medium. 4. The extent of mineralisation of nitrogen is determined chiefly by the C/N ratio, though in the cases of substances like mahua and lantana the presence of other constituents may also influence the processes. The quantities of mineralised nitrogen present in the soil system generally tend to decrease after about two months.

Structural Transformations, Composition Anomalies and a Dramatic Collapse of Linear Polymer Chains in Dilute Ethanol-Water Mixtures

Water-ethanol mixtures exhibit many interesting anomalies, such as negative excess partial molar volume of ethanol, excess sound absorption coefficient at low concentrations, and positive deviation from Raoult's law for vapor pressure, to mention a few. These anomalies have been attributed to different, often contradictory origins, but a quantitative understanding is still lacking. We show by computer simulation and theoretical analyses that these anomalies arise from the sudden emergence of a bicontinuous phase that occurs at a relatively low ethanol concentration of x(eth) approximate to 0.06-0.10 (that amounts to a volume fraction of 0.17-0.26, which is a significant range!). The bicontinuous phase is formed by aggregation of ethanol molecules, resulting in a weak phase transition whose nature is elucidated. We find that the microheterogeneous structure of the mixture gives rise to a pronounced nonmonotonic composition dependence of local compressibility and nonmonotonic dependence in the peak value of the radial distribution function of ethyl groups. A multidimensional free energy surface of pair association is shown to provide a molecular explanation of the known negative excess partial volume of ethanol in terms of parallel orientation and hence better packing of the ethyl groups in the mixture due to hydrophobic interactions. The energy distribution of the ethanol molecules indicates additional energy decay channels that explain the excess sound attenuation coefficient in aqueous alcohol mixtures. We studied the dependence of the solvation of a linear polymer chain on the composition of the water-ethanol solvent. We find that there is a sudden collapse of the polymer at x(eth) approximate to 0.05-a phenomenon which we attribute to the formation of the microheterogeneous structures in the binary mixture at low ethanol concentrations. Together with recent single molecule pulling experiments, these results provide new insight into the behavior of polymer chain and foreign solutes, such as enzymes, in aqueous binary mixtures.