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.

High-Throughput Study of the Cu(CH3COO)(2)center dot H2O-5-Nitroisophthalic Acid Heterocyclic Ligand System: Synthesis, Structure, Magnetic, and Heterogeneous Catalytic Studies of Three Copper Nitroisophthalates

A high-throughput screening was employed to identify new compounds in Cu(CH3COO)(2)center dot H2O-NIPA-heterocyclic ligand systems. Of the compounds identified, three compounds, Cu-3{(NO2)-C6H3-(COO)(2)}(3)(C3N6H6)] (1), Cu-2(mu(3)-OH)(H2O){(NO2)-C6H3-(COO)(2)}(CN4H)]center dot-(H2O) (II), and Cu-2(mu(3)-OH)(H2O){(NO2)-C6H3-(COO)(2}-)(CN5H2)]center dot 2(H2O) (III), have been isolated as good quality single crystals by employing conventional hydrothermal methods. Three other compounds, Cu-2{(NO2)-C6H3-(COO)(2)}-(CN4H)(H2O) (IIa), Cu-2{(NO2)-C6H3-(COO)(2)}(CN5H2) (IIIa), and Cu-2{(NO2)-C6H3-(COO)(2)}{(CN5H2)(2)}2H(2)O (IIIb), were identified by a combination of elemental analysis, thermogravimetric analysis (TGA), and IR spectroscopic studies, although their structures are yet to be determined. The single crystalline compounds were also characterized by elemental analysis, TGA, IR, UV vis, magnetic, and catalytic studies. The structures of the compounds have paddle wheel (I) and infinite Cu 0(H) Cu chains (II and HI) connected with NLPA and heterocyclic ligands forming two-(II) and three-dimensional (I and III) structures. The bound and lattice water molecules in 11 and 111 could be reversibly removed/inserted without affecting the structure. In the case of II, the removal of water gives rise to a structural transition, but the dehydrated phase reverts back to the original phase on prolonged exposure to atmospheric conditions. Magnetic studies indicate an overall antiferromagnetism in all of the compounds. Lewis acid catalytic studies indicate that compounds II and HI are active for cyanosilylation of imines.

Dynamic recrystallisation during hot working of Zr-2 center dot 5Nb: Characterisation using processing maps

The characteristics of the hot deformation of Zr-2.5Nb (wt-%) in the temperature range 650-950 degrees C and in the strain rate range 0.001-100 s(-1) have been studied using hot compression testing. Two different preform microstructures: equiaxed (alpha + beta) and beta transformed have been investigated. For this study, the approach of processing maps has been adopted and their interpretation carried out using the dynamic materials model. The efficiency of power dissipation given by [2m/(m + 1)], where m is the strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. A domain of dynamic recrystallisation has been identified in the maps of equiaxed (alpha + beta) and beta transformed preforms. In the case of equiaxed (alpha + beta), the stress-strain curves are steady state and the dynamic recrystallisation domain in the map occurs with a peak efficiency of 45% at 850 degrees C and 0.001 s(-1). On the other hand the beta transformed preform exhibits stress-strain curves with continuous flow softening. The corresponding processing map shows a domain of dynamic recrystallisation occurring by the shearing of alpha platelets followed by globularisation with a peak efficiency of 54% at 750 degrees C and 0.001 s(-1). The characteristics of dynamic recrystallisation are analysed on the basis of a simple model which considers the rates of nucleation and growth of recrystallised gains. Calculations show that these two rates are nearly equal and that the nucleation of dynamic recrystallisation is essentially controlled by mechanical recovery involving the cross-slip of screw dislocations. Analysis of flow instabilities using a continuum criterion revealed that Zi-2.5Nb exhibits flow localisation at temperatures lower than 700 degrees C and strain rates higher than 1 s(-1).

Effect of magnetic field on the binding energy of a hydrogenic donor in a vertical bar z vertical bar(2/3) quantum well

We have calculated the binding energy of a hydrogenic donor in a quantum well with potential shape proportional to \z\(2/3) as a function of the width of the quantum well and the barrier height under an applied uniform magnetic field along the a axis. As the well width decreases, the binding energy increases initially up to a critical well width (which is nearly the same for all magnetic fields) at which there is a turnover. The results are qualitatively similar to those of a hydrogenic donor in a rectangular well. We have also calculated [rho(2)](1/2) and [z(2)](1/2) for the donor electron. [rho(2)](1/2) is found to be strongly dependent on the magnetic field for a given well width and weakly dependent on the well width and the barrier height, for a given value of magnetic field [z(2)](1/2) is weakly dependent on the applied magnetic field. The probability of finding the donor electron inside the well shows a rapid decrease as the well width is reduced at nearly the well width at which the binding energy shows a maximum.

Cascades of Selective Pulses on Connected Single-Quantum Transitions Leading to the Selective Excitation of Multiple-Quantum Coherences

A symmetric cascade of selective pulses applied on connected transitions leads to the excitation of a selected multiple-quantum coherence by a well-defined angle. This cascade selectively operates on the subspace of the multiple-quantum coherence and acts as a generator of rotation selectively on the multiple-quantum subspace. Single-transition operator algebra has been used to explain these experiments. Experiments have been performed on two- and three-spin systems. It is shown that such experiments can be utilized to measure the relaxation times of selected multiple-quantum coherences or of a specifically prepared initial longitudinal state of the spin system.

H-1 MAS NMR study of protonic conduction in layered HNbWO6 center dot xH(2)O (x=1.5, 0.5)

H-1 Magic Angle Spinning (MAS) NMR of layered HNbWO6 . xH(2)O (x = 1.5, 0.5) is carried out at room temperature and at various spinning speeds (1-12 kHz). Results on the fully hydrated sample (x = 1.5) are consistent with the model of diffusion of H3O+ ions within the layers. In the partially dehydrated sample (x = 0.5) an exchange between the distinctly present cage protons and H3O+ protons leads to protonic conduction.

Quantum and non-Markovian effects in the electron transfer reaction dynamics in the Marcus inverted region

Electron transfer reactions in large molecules may often be coupled to both the polar solvent modes and the intramolecular vibrational modes of the molecule. This can give rise to a complex dynamics which may in some systems, like betaine, be controlled more by vibrational rather than by solvent effects. Additionally, a significant contribution from an ultrafast relaxation component in the solvation dynamics may enhance the complexity. To explain the wide range of behavior that has been observed experimentally, Barbara et al. recently proposed that a model of an electron transfer reaction should minimally consist of a low-frequency classical solvent mode (X), a low-frequency vibrational mode (Q), and a high-frequency quantum mode (q) (J. Phys. Chem. 1991, 96, 3728). In the present work, a theoretical study of this model is described. This study generalizes earlier work by including the biphasic solvent response and the dynamics of the low-frequency vibrational mode in the presence of a delocalized, extended reaction zone. A novel Green's function technique has been developed which allowed us to study the non-Markovian dynamics on a multidimensional surface. The contributions from the high-frequency vibrational mode and the ultrafast component in the non-Markovian solvent dynamics are found to be primarily responsible for the dramatic increase in charge transfer rate over the prediction of the classical theories that neglect both these factors. These, along with a large coupling between the reactant and the product states, may combine to render the electron transfer rate both very large and constant over a wide range of solvent relaxation rates. A study on the free energy gap dependence of the electron transfer rate reveals that the rates are sensitive to changes in the quantum frequency particularly when the free energy gap is very large.

Quantum corrections to the conductivity in a perovskite oxide: A low-temperature study of LaNi1-xCoxO3 (0?x?0.75)

In this paper we propose to study the evolution of the quantum corrections to the conductivity in an oxide system as we approach the metal-insulator (M-I) transition from the metallic side. We report here the measurement of the low-temperature (0.1 K0.65), m takes on large values and ?(0)=0. We explain the temperature dependence of ?(T), for T<2 K, on the metallic side (x?0.4), as arising predominantly from electron-electron interactions, taking into account the diffusion-channel contribution (which gives m=0.5) as well as the Cooper-channel contribution. In this regime, the correction to conductivity, ??(T), is a small fraction of ?(T). However, as the M-I transition is approached (x?xc), ??(T) starts to dominate ?(T) and the above theories fail to explain the observed ?(T).