Aspects of coherent states of nonlinear algebras

Various aspects of coherent states of nonlinear su(2) and su(1,1) algebras are studied. It is shown that the nonlinear su(1,1) Barut-Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived. (C) 2010 American Institute of Physics. doi:10.1063/1.3514118]

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Hilbert W*-modules and coherent states

Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

XANES and EXAFS of copper compounds: Studies of copper carboxylates with metal-metal bonds and of the complex formed byPseudomonas aeruginosa

X-ray absorpion near edge structure (xanes) of copper compounds with copper in 1+, 2+ and 3+ states has been studied. Extended x-ray absorption fine structure (exafs) has been employed to determine bond distances and coordination numbers in several model copper compounds. Employing bothxanes andexafs, the structure of the copper complex formed by the micro-organismPseudomonas aeruginosa has been shown to be square-planar with the Cu-O distance close to that in cupric glucuronates and cupric acetylacetonate.exafs has been shown to be useful for studying metal-metal bonds in copper carboxylates.

Lack of Cu3+, Pb4+, and Bi5+ ions in metallic and superconducting oxides

With a view to understand the oxidation states of metal ions involved in oxide superconductors, oxidation behavior of Cu, Pb, and Bi metals have been studiedi employing x-ray-photoemission and ultraviolet-photoemission spectroscopy. Pb and Bi have distinct 6p (0 to 4 eV) and 6s (7.5 to 10 eV) bands and upon oxidation, only the 6p electrons are ionized forming PbO and Bi2O3 with the simultaneous development of the O2-(2p) band (3 to 7 eV). We show that the 6s band of metals lies below the O2-(2p) band, and hence 6s electrons cannot be ionized to form Pb4+ and Bi4+ as expected in PbO2, BaPbO3, BaBiO3, and BaPb0.75Bi0.25O3. Instead these oxides are stabilized with lower valent O22- along with O2- ions with metals remaining in +2 and +3 states. Similarly, it is shown that the Cu2+(3d) band overlaps with the O2-(2p) band in the YBa2Cu3O6.95 completely and the excess oxygen can be stabilized through lower valent oxide ions instead of Cu3+.

Theoretical analysis of photoinduced H-atom elimination in thiophenol

The photoinduced hydrogen elimination reaction in thiophenol via the conical intersections of the dissociative (1)pi sigma* excited state with the bound (1)pi pi* excited state and the electronic ground state has been investigated with ab initio electronic-structure calculations and time-dependent quantum wave-packet calculations. A screening of the coupling constants of the symmetry-allowed coupling modes at the (1)pi pi*-(1)pi sigma* and (1)pi sigma*-S-0 conical intersection shows that the SH torsional mode is by far the most important coupling mode at both conical intersections. A model including three intersecting potential-energy surfaces (S-0, (1)pi pi*, (1)pi sigma*) and two nuclear degrees of freedom (SH stretch and SH torsion) has been constructed on the basis of ab initio complete-active-space self-consistent field and multireference second-order perturbation theory calculations. The nonadiabatic quantum wave-packet dynamics initiated by optical excitation of the (1)pi pi* and (1)pi sigma* states has been explored for this three-state two-coordinate model. The photodissociation dynamics is characterized in terms of snapshots of time-dependent wave packets, time-dependent electronic population probabilities, and the branching ratio of the (2)sigma/(2)pi electronic states of the thiophenoxyl radical. The dependence of the timescale of the photodissociation process and the branching ratio on the initial excitation of the SH stretching and SH torsional vibrations has been analyzed. It is shown that the node structure, which is imposed on the nuclear wave packets by the initial vibrational preparation as well as by the transitions through the conical intersections, has a profound effect on the photodissociation dynamics. The effect of additional weak coupling modes of CC twist (nu(16a)) and ring-distortion (nu(16b)) character has been investigated with three-dimensional and four-dimensional time-dependent wave-packet calculations, and has been found to be minor. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4709608]

Platinum Ion-Doped TiO2: High Catalytic Activity of Pt2+ with Oxide Ion Vacancy in Ti1-x4+Ptx2+O2-x Compared to Pt4+ without Oxide Ion Vacancy in Ti1-x4+Ptx4+O2

Ti0.97Pt0.032+O1.97 and Ti0.97Pt0.034+O2 have been synthesized by a solution combustion method using alanine and glycine as the fuels, respectively. Both crystallize in anatase TiO2 structure with 15 nm average crystallite size. X-ray photoelectron spectroscopy (XPS) confirmed Pt ions are in the 2+ state in Ti0.97Pt0.03O1.97 (alanine) and 4+ state in Ti0.97Pt0.03O2 (glycine). The rate of CO oxidation occurring over Ti0.97Pt0.032+O1.97 (0.76 mu mol.g(-1).s(-1)) is similar to 10, times more than that over Ti0.97Pt0.034+O2 at 60 degrees C (0.08 mu mol.g(-1).s(-1)). A large shift in 100% hydrocarbons conversion to lower temperature was observed for Pt2+ ion-substituted TiO2 relative 10 that for Pt4+ ion-substituted TiO2. After reoxidation of the reduced compound by H-2 as well as CO, Pt ions are stabilized in mixed valences, 2+ and 4+ states. The role of oxide ion vacancy has been demonstrated by CO oxidation and H-2 + O-2 recombination reactions in the presence and absence of O-2. We analyze the activated lattice oxygens upon substitution of Pt2+ and Pt4+ ions in TiO2, using first-principles density functional theory (DFT) calculations with supercells of Ti31Pt1O63, Ti30Pt2O62, and Ti29Pt3O61 for Pt2+ ion substitution and Ti31Pt1O64, Ti30Pt2O62, and Ti29Pt3O61 for Pt4+ ion substitution in TiO2. We find that the local structure of Pt2+ ion has a distorted square planar geometry and that of Pt4+ ion has an octahedral geometry similar to that of Ti4+ ion in pure TiO2. The change in coordination of Pt2+ ion gives rise to weakly bonded oxygens, and these oxygens are involved in high rates of catalytic reaction. Thus, the high catalytic activity results from synergistic roles of Pt2+ ion and oxide ion vacancy and weakly bonded lattice oxygen.

Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

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.

Coherent (photon) vs incoherent (current) detection of multidimensional optical signals from single molecules in open junctions

The nonlinear optical response of a current-carrying single molecule coupled to two metal leads and driven by a sequence of impulsive optical pulses with controllable phases and time delays is calculated. Coherent (stimulated, heterodyne) detection of photons and incoherent detection of the optically induced current are compared. Using a diagrammatic Liouville space superoperator formalism, the signals are recast in terms of molecular correlation functions which are then expanded in the many-body molecular states. Two dimensional signals in benzene-1,4-dithiol molecule show cross peaks involving charged states. The correlation between optical and charge current signal is also observed. (C) 2015 AIP Publishing LLC.

Valence states and magnetic properties of LaNi1-xMnxO3 (for 0≤x≤0.2 and x=0.5)

Single-phase LaNi1-xMnxO3 samples in the compositional range 0states at room temperature for x=0.1, 0.2 and 0.5. Magnetic susceptibility data suggest Mn4+ solute ions and Stoner-enhanced Pauli paramagnetism of the metallic solvent for x=0.01 with a smooth transition to Mn3+ solute ions and a spontaneously magnetised solvent conduction band at x=0.05. Below 200K, the x=0.05 sample forms superparamagnetic clusters, and below 40K there is evidence for an antiferromagnet spin-density wave. Comparisons with LaCo0.95Mn0.05O3 and La0.98Sr0.02CoO3 confirm that the long-range magnetic coupling occurs via solvent electrons in a narrow conduction band. The conductivity changes from that of a narrow-band metal for x<0.01 to that more characteristic of diffusive motion for x>0.05, but any motional enthalpy appears to remain small ( Delta Hm approximately=0). The x=0.1 sample exhibits ferrimagnetic spin glass behaviour below 40K, and the ferromagnetic interactions increase with manganese concentration. The oxide with x=0.50 is ferromagnetic with a well defined Curie temperature.

Synthesis, Structure and Optical Studies of a Family of Three-Dimensional Rare-Earth Aminoisophthalates M(mu(2)-OH)(C8H5NO4)] (M = Y3+, La3+, Pr3+, Nd3+, Sm3+, Eu3+, Gd3+, Dy3+, and Er3+)

A hydrothermal reaction of the acetate salts of the rare-earths, 5-aminoisophthalic acid (H(2)AIP), and NaOH at 150 degrees C for 3 days gave rise to a new family of three-dimensional rare-earth aminoisophthalates, M(mu(2)-OH)(C8H5NO4)] M = Y3+ (I), La3+ (II), Pr3+ (III), Nd3+ (IV), Sm3+ (V), Eu3+ (VI), Gd3+ (VII), Dy3+ (VIII), and Er3+ (IX)]. The structures contain M-O(H)-M chains connected by AIP anions. The AIP ions are connected to five metal centers and each metal center is connected with five AIP anions giving rise to a unique (5,5) net. To the best of our knowledge, this is the first observation of a (5,5) net in metal-organic frameworks that involve rare-earth elements. The doping of Eu3+/(3+) ions in place of Y3+/ La3+ in the parent structures gave rise to characteristic metal-centered emission (red = Eu3+, green = Tb3+). Life-time studies indicated that the excited emission states in the case of Eu3+ (4 mol-% doped) are in the range 0.287-0.490 ms and for Tb3+ (4 mol-% doped) are in the range of 1.265-1.702 ms. The Nd3+-containing compound exhibits up-conversion behavior based on two-photon absorption when excited using lambda = 580 nm.

Role of molecular reorientation in the vitrification of molecular liquids: A Monte Carlo study of the liquid and glassy states of 2,2-dimethylbutane

The liquid and the glassy phases of 2,2-dimethylbutane have been investigated by isothermal isobaric ensemble Monte Carlo simulation. Thermodynamic Properties and radial distribution functions for both the liquid and the glass have been obtained. The radial distribution functions have been classified into three types based on the accessibility of the group. It has been shown that the structure of the Iiquid and the glass can be understood in terms of the above classification of the radial distribution functions. Molecular reorientation plays an important role in the structural rearrangement accompanying glass formation. As much as 35% of the contribution to the increase in the intermolecular interaction energy on vitrification is due to the reorientation of the neighbouring pairs of molecules. The observed changes in the dimerisation energy and the bonding energy distribution function are consistent with the observed structural changes.