Lattice discretization in quantum scattering

The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin in two- and three-space dimensions. This shows that the lattice discretization technique could be a useful tool for the numerical solution of scattering problems in general. The approach is illustrated in the case of the Dirac delta function potential.

Energy-transfer mechanisms and emission quantum yields in Eu3+-based siloxane-poly(oxyethylene) nanohybrids

We report the energy-transfer mechanisms and emission quantum yield measurements of sol-gel-derived Eu3+-based nanohybrids. The matrix of these materials, classified as diureasils and termed U(2000) and U(600), includes urea cross-links between a siliceous backbone and polyether-based segments of two molecular weights, 2000 and 600, respectively. These materials are full-color emitters in which the Eu3+ (5)Do --> F-7(0-4) lines merge with the broad green-blue emission of the nanoscopic matrix's backbone. The excitation spectra show the presence of a large broad band (similar to 27000-29000 cm(-1)) undoubtedly assigned to a ligand-to-metal charge-transfer state. Emission quantum yields range from 2% to 13.0% depending on the polymer molecular weight and Eu3+ concentration. Energy transfer between the hybrid hosts and the cations arises from two different and independent processes: the charge-transfer band and energy transfer from the hybrid's emitting centers. The activation of the latter mechanisms induces a decrease in the emission quantum yields (relative to undoped nanohybrids) and permits a fine-tuning of the emission chromaticity across the Comission Internacionalle d'Eclairage diagram, e.g., (x, y) color coordinates from (0.21, 0.24) to (0.39, 0.36). Moreover, that activation depends noticeably on the ion local coordination. For the diureasils with longer polymer chains, energy transfer occurs as the Eu3+ coordination involves the carbonyl-type oxygen atoms of the urea bridges, which are located near the hybrid's host emitting centers. on the contrary, in the U(600)-based diureasils, the Eu3+ ions are coordinated to the polymer chains, and therefore, the distance between the hybrid's emitting centers and the metal ions is large enough to allow efficient energy-transfer mechanisms.

GENERATING FUNCTION FOR CLEBSCH-GORDAN-COEFFICIENTS, OF THE SUQ(2) QUANTUM ALGEBRA

Some methods have been developed to calculate the su(q)(2) Clebsch-Gordan coefficients (CGC). Here we develop a method based on the calculation of Clebsch-Gordan generating functions through the use of 'quantum algebraic' coherent states. Calculating the su(q)(2) CGC by means of this generating function is an easy and straightforward task.

In situ UV-vis and EXAFS studies of ZnO quantum-sized nanocrystals and Zn-HDS formations from sol-gel route

We have pointed Out that. zinc-based particles obtained from zinc acetate sol-gel route is a mixture of quantum-sized ZnO nanoparticles, zinc acetate, and zinc hydroxide double salt (Zn-HDS). Aiming the knowledge of the mechanisms involved in the formation of ZnO and Zn-HDS phases, the thermohydrolysis of ethanolic zinc acetate solutions induced by lithium hydroxide ([LiOH]/[Zn2+] = 0.1) or water ([H2O]/[Zn2+] = 0.05) addition was investigated at different isothermal temperatures (40, 50, 60 and 70 degrees C) by in situ measurements of turbidity, UV-vis absorption spectra and extended X-ray absorption fine structures (EXAFS). Only the growth of ZnO nanoparticles was observed in sol prepared with LiOH, while a two-step process was observed in that prepared with water addition, leading the fast growth of Zn-HDS and the formation of ZnO nanoparticles at advanced stage. A mechanism of dissolution/reprecipitation governed by the water/ethanol proportion is proposed to account for relative amount of ZnO. (c) 2007 Elsevier Ltd. All rights reserved.

An application of the Element Free Galerkin Method to the analysis of quantum well structures

In order to obtain the quantum-mechanical properties of layered semicondutor structures (quantum well and superlattice structures, for instance), solutions of the Schrodinger equation should be obtained for arbitrary potential profiles. In this paper, it is shown that such problems may be also studied by the Element Free Galerkin Method.

2-DIMENSIONAL QUANTUM GAS

Identical impenetrable particles in a 2-dimensional configuration space obey braid statistics, intermediate between bosons and fermions. This statistics, based on braid groups, is introduced as a generalization of the usual statistics founded on the symmetric groups. The main properties of an ideal gas of such particles are presented. They do interpolate the properties of bosons and fermions but include classical particles as a special case. Restriction to 2 dimensions precludes lambda points but originates a peculiar symmetry, responsible in particular for the identity of boson and fermion specific heats.

Renormalization in non-relativistic quantum mechanics

The importance and usefulness of renormalization are emphasized in non-relativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin exhibits ultraviolet divergence. The use of renormalization techniques in these problems leads to finite converged results for both the exact and perturbative solutions. The renormalization procedure is carried out for the quantum two-body problem in different partial waves for a minimal potential possessing only the threshold behaviour and no form factors. The renormalized perturbative and exact solutions for this problem are found to be consistent with each other. The useful role of the renormalization group equations for this problem is also pointed out.

A neural approach for determination of global energetic efficiency indicator in groundwater wells

In most of the cases, the systems of water distribution from groundwater wells use electrical submersible pumps. All electrical energy is applied to the pumps; however, other components (pipes, valves, etc.) of these systems are also responsible by the higher or lower consumption of electric energy. The supervisors and operators of the systems should thus have knowledge of the global energetic behavior of the process in order to administrate it properly. This work suggests a 'Global Energetic Efficiency Indicator' for groundwater wells by using mathematical equations and neural networks. Simulation results will be presented in order to demonstrate the validity of the proposed approach.

Generalized point interactions in one-dimensional quantum mechanics

There is a four-parameter family of point interactions in one-dimensional quantum mechanics. They represent all possible self-adjoint extensions of the kinetic energy operator. If time-reversal invariance is imposed, the number of parameters is reduced to three. One of these point interactions is the familiar delta function potential but the other generalized ones do not seem to be widely known. We present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so-called delta' interaction. We emphasize that there is little resemblance between the delta' interaction and what its name suggests.

Nanoscale manipulation of CdSe quantum dots in layer-by-layer films: influence of the host polyelectrolyte on the luminescent properties

Thioglycolic acid-capped Use quantum dots (QDs) were assembled on glass substrates with two distinct polyelectrolytes, viz poly(allylamine hydrochloride) (PAH) and poly(amidoamine) (PAMAM), generation 4 dendrimer, via the layer-by-layer (LbL) technique. Films containing up to 30 polyelectrolyte/QD bilayers were prepared. The growth of the multilayers was monitored with UV-vis spectroscopy, which showed an almost linear increase in the absorbance of the 2.8 nm QDs at 535 nm with the number of deposited bilayers. AFM measurements estimated a film thickness of 3 nm per bilayer for the PAH/Cdse films. The adsorption process and the optical properties of the PAMAM/CdSe LbL films were further analyzed layer-by-layer using surface plasmon resonance (SPR), from which a thickness of 3.2 nm was found for a PAMAM/CdSe bilayer. Photoluminescence measurements revealed higher photooxidation of the quantum dots in PAH/CdSe than in PAMAM/CdSe films. (c) 2004 Elsevier B.V. All rights reserved.

A Bethe ansatz solution for the closed U-q[sl(2)] Temperley-Lieb quantum spin chains

We solve the spectrum of the closed Temperley-Lieb quantum spin chains using the coordinate Bethe ansatz. These models are invariant under the quantum group U-q[sl(2)].

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

Quantum equivalence between the self-dual and the Maxwell-Chern-Simons models nonlinearly coupled to U(1) scalar fields

The use of master actions to prove duality at quantum level becomes cumbersome if one of the dual fields interacts nonlinearly with other fields. This is the case of the theory considered here consisting of U(1) scalar fields coupled to a self-dual field through a linear and a quadratic term in the self-dual field. Integrating perturbatively over the scalar fields and deriving effective actions for the self-dual and the gauge field we are able to consistently neglect awkward extra terms generated via master action and establish quantum duality up to cubic terms in the coupling constant. The duality holds for the partition function and some correlation functions. The absence of ghosts imposes restrictions on the coupling with the scalar fields.

GENERAL POTENTIALS DESCRIBED BY SO(2,1) DYNAMIC ALGEBRA IN PARABOLIC-COORDINATE SYSTEMS

We propose general three-dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the SO(2, 1) dynamical group. Then we construct their Green functions algebraically and find their spectra. Particular cases of these potentials which appear in the literature are also briefly discussed.

Supersymmetric quantum mechanics and partially solvable potential

Supersymmetric quantum mechanics can be used to obtain the spectrum and eigenstates of one-dimensional Hamiltonians. It is particularly useful when applied to partially solvable potentials because a superalgebra allows us to compute the spectrum state by state. Some solutions for the truncated Coulomb potential, an asymptotically linear potential, and a nonpolynomial potential are shown to exemplify the method.