168 resultados para Elliptical Quantum Group And Quantum Group
em Indian Institute of Science - Bangalore - Índia
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The H-1 NMR spectroscopic discrimination of enantiomers in the solution state and the measurement of enantiomeric composition is most often hindered due to either very small chemical shift differences between the discriminated peaks or severe overlap of transitions from other chemically non-equivalent protons. In addition the use of chiral auxiliaries such as, crown ether and chiral lanthanide shift reagent may often cause enormous line broadening or give little degree of discrimination beyond the crown ether substrate ratio, hampering the discrimination. In circumventing such problems we are proposing the utilization of the difference in the additive values of all the chemical shifts of a scalar coupled spin system. The excitation and detection of appropriate highest quantum coherence yields the measurable difference in the frequencies between two transitions, one pertaining to each enantiomer in the maximum quantum dimension permitting their discrimination and the F-2 cross section at each of these frequencies yields an enantiopure spectrum. The advantage of the utility of the proposed method is demonstrated on several chiral compounds where the conventional one dimensional H-1 NMR spectra fail to differentiate the enantiomers.
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This is the report of the QCD working sub-group at the Tenth Workshop on High Energy Physics Phenomenology (WHEPP-X).
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1H NMR spin-lattice relaxation time (T1) studies have been carried out in the temperature range 100 K to 4 K, at two Larmor frequencies 11.4 and 23.3 MHz, in the mixed system of betaine phosphate and glycine phosphite (BPxGPI(1-x)), to study the effects of disorder on the proton group dynamics. Analysis of T1 data indicates the presence of a number of inequivalent methyl groups and a gradual transition from classical reorientations to quantum tunneling rotations. At lower temperatures, microstructural disorder in the local environments of the methyl groups, result in a distribution in the activation energy (Ea) and the torsional energy gap (E01). For certain values of x, the magnetisation recovery shows biexponential behaviour at lower temperatures.
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Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.
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The possible nonplanar distortions of the amide group in formamide, acetamide, N-methylacetamide, and N-ethylacetamide have been examined using CNDO/2 and INDO methods. The predictions from these methods are compared with the results obtained from X-ray and neutron diffraction studies on crystals of small open peptides, cyclic peptides, and amides. It is shown that the INDO results are in good agreement with observations, and that the dihedral angles N and defining the nonplanarity of the amide unit are correlated approximately by the relation N = -2, while C is small and uncorrelated with . The present study indicates that the nonplanar distortions at the nitrogen atom of the peptide unit may have to be taken into consideration, in addition to the variation in the dihedral angles (,), in working out polypeptide and protein structures.
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We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.
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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
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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.
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The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D(4h) symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3671946]
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Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.
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Groups exhibit properties that either are not perceived to exist, or perhaps cannot exist, at the individual level. Such `emergent' properties depend on how individuals interact, both among themselves and with their surroundings. The world of everyday objects consists of material entities. These are, ultimately, groups of elementary particles that organize themselves into atoms and molecules, occupy space, and so on. It turns out that an explanation of even the most commonplace features of this world requires relativistic quantum field theory and the fact that Planck's constant is discrete, not zero. Groups of molecules in solution, in particular polymers ('sols'), can form viscous clusters that behave like elastic solids ('gels'). Sol-gel transitions are examples of cooperative phenomena. Their occurrence is explained by modelling the statistics of inter-unit interactions: the likelihood of either state varies sharply as a critical parameter crosses a threshold value. Group behaviour among cells or organisms is often heritable and therefore can evolve. This permits an additional, typically biological, explanation for it in terms of reproductive advantage, whether of the individual or of the group. There is no general agreement on the appropriate explanatory framework for understanding group-level phenomena in biology.
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Given the recent reports pertaining to novel optical properties of ultra-small quantum dots (QDs) (r <2 nm), this nanomaterial is of relevance to both technology and science. However it is well known that in these size regimes most chalocogenide QD dispersions are unstable. Since applications often require use of QD dispersions (e.g. for deployment on a substrate), stabilizing these ultra-small particles is of practical relevance. In this work we demonstrate a facile, green, solution approach for synthesis of stable, ultra-small ZnO QDs having radius less than 2 nm. The particle size is calculated using Brits' equation and confirmed by transmission electron micrographs. ZnO QDs reported remain stable for > 120 days in ethanol (at similar to 298-303 K). We report digestive ripening (DR) in TEA capped ZnO QDs; this occurs rapidly over a short duration of 5 min. To explain this observation we propose a suitable mechanism based on the Lee's theory, which correlates the tendency of DR with the observed zeta potentials of the dispersed medium. To the best of our knowledge this is the (i) first report on DR in oxide QDs, as well as the first direct experimental verification of Lee's theory, and (ii) most rapid DR reported so far. The facile nature of the method presented here makes ultra-small ZnO readily accessible for fundamental exploration and technologically relevant applications. (C) 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
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The existence of three centered C=O...H(N)...X-C hydrogen bonds (H-bonds) involving organic fluorine and other halogens in diphenyloxamide derivatives has been explored by NMR spectroscopy and quantum theoretical studies. The three centered H-bond with the participation of a rotating CF3 group and the F...H-N intramolecular hydrogen bonds, a rare observation of its kind in organofluorine compounds, has been detected. It is also unambiguously established by a number of one and two dimensional NMR experiments, such as temperature perturbation, solvent titration, N-15-H-1 HSQC, and F-19-H-1 HOESY, and is also confirmed by theoretical calculations, such as quantum theory of atoms in molecules (QTAIM), natural bond orbital (NBO) and non-covalent interaction (NCI).
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An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 approximate to 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with N-A not equal N-B. The ground state (GS) and spin densities rho(r) = < S-r(z)> at site r are quite different for junctions with S = 1/2, 1, 3/2, and 2. The GS has finite total spin S-G = 2S(S) for even (odd) N and for M-G = S-G in the S-G spin manifold, rho(r) > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized S-z = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.
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Several mechanisms have been proposed to explain the action of enzymes at the atomic level. Among them, the recent proposals involving short hydrogen bonds as a step in catalysis by Gerlt and Gassman [1] and proton transfer through low barrier hydrogen bonds (LBHBs) [2, 3] have attracted attention. There are several limitations to experimentally testing such hypotheses, Recent developments in computational methods facilitate the study of active site-ligand complexes to high levels of accuracy, Our previous studies, which involved the docking of the dinucleotide substrate UpA to the active site of RNase A [4, 5], enabled us to obtain a realistic model of the ligand-bound active site of RNase A. From these studies, based on empirical potential functions, we were able to obtain the molecular dynamics averaged coordinates of RNase A, bound to the ligand UpA. A quantum mechanical study is required to investigate the catalytic process which involves the cleavage and formation of covalent bonds. In the present study, we have investigated the strengths of some of the hydrogen bonds between the active site residues of RNase A and UpA at the ab initio quantum chemical level using the molecular dynamics averaged coordinates as the starting point. The 49 atom system and other model systems were optimized at the 3-21G level and the energies of the optimized systems were obtained at the 6-31G* level. The results clearly indicate the strengthening of hydrogen bonds between neutral residues due to the presence of charged species at appropriate positions. Such a strengthening manifests itself in the form of short hydrogen bonds and a low barrier for proton transfer. In the present study, the proton transfer between the 2'-OH of ribose (from the substrate) and the imidazole group from the H12 of RNase A is influenced by K41, which plays a crucial role in strengthening the neutral hydrogen bond, reducing the barrier for proton transfer.