Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the hardy space H¹ on products of half-spaces

We show that the Hardy space H¹ anal (R2+ x R2+) can be identified with the class of functions f such that f and all its double and partial Hubert transforms Hk f belong to L¹ (R2). A basic tool used in the proof is the bisubharmonicity of |F|q, where F is a vector field that satisfies a generalized conjugate system of Cauchy-Riemann type.

LARGE-ORDER PERTURBATION EXPANSIONS FOR THE CHARGED HARMONIC-OSCILLATOR

The charged oscillator, defined by the Hamiltonian H = -d2/dr2+ r2 + lambda/r in the domain [0, infinity], is a particular case of the family of spiked oscillators, which does not behave as a supersingular Hamiltonian. This problem is analysed around the three regions lambda --> infinity, lambda --> 0 and lambda --> -infinity by using Rayleigh-Ritz large-order perturbative expansions. A path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda. Finally, the Riccati-Pade method is used to construct an implicit expansion around lambda --> 0 which extends to very large values of Absolute value of lambda.

A new three-phase transformer modeling for three-phase harmonic analysis in distribution systems

This work presents a new three-phase transformer modeling suitable for simulations in Pspice environment, which until now represents the electrical characteristics of a real transformer. It is proposed the model comparison to a three-phase transformer modeling present in EMTP - ATP program, which includes the electrical and magnetic characteristics. In addition, a set including non-linear loads and a real three-phase transformer was prepared in order to compare and validate the results of this new proposed model. The three-phase Pspice transformer modeling, different from the conventional one using inductance coupling, is remarkable for its simplicity and ease in simulation process, since it uses available voltage and current sources present in Pspice program, enabling simulations of three-phase network system including the most common configuration, three wires in the primary side and four wires in the secondary side (three-phases and neutral). Finally, the proposed modeling becomes a powerful tool for three-phase network simulations due to its simplicity and accuracy, able to simulate and analyze harmonic flow in three-phase systems under balanced and unbalanced conditions.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

CLOSED SPACES IN COSMOLOGY

This paper deals with two aspects of relativistic cosmologies with closed spatial sections. These spacetimes are based on the theory of general relativity, and admit a foliation into space sections S(t), which are spacelike hypersurfaces satisfying the postulate of the closure of space: each S(t) is a three-dimensional closed Riemannian manifold. The topics discussed are: (i) a comparison, previously obtained, between Thurston geometries and Bianchi-Kantowski-Sachs metrics for such three-manifolds is here clarified and developed; and (ii) the implications of global inhomogeneity for locally homogeneous three-spaces of constant curvature are analyzed from an observational viewpoint.

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Perturbative breaking of the pseudospin symmetry in the relativistic harmonic oscillator

We show that relativistic mean fields theories with scalar S, and vector V, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S = -V. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this, symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.

Harmonic identification using parallel neural networks in single-phase systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An extended Weyl-Wigner transformation for special finite spaces

We extend the Weyl-Wigner transformation to those particular degrees of freedom described by a finite number of states using a technique of constructing operator bases developed by Schwinger. Discrete transformation kernels are presented instead of continuous coordinate-momentum pair system and systems such as the one-dimensional canonical continuous coordinate-momentum pair system and the two-dimensional rotation system are described by special limits. Expressions are explicitly given for the spin one-half case. © 1988.

Nonsingular spiked harmonic oscillator

A perturbative study of a class of nonsingular spiked harmonic oscillators defined by the Hamiltonian H= -d2/dr2 + r2 + λ/rα in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. © 1991 American Institute of Physics.

On the quantum mechanical propagator for driven coupled harmonic oscillators

The exact propagator beyond and at caustics for a pair of coupled and driven oscillators with different frequencies and masses is calculated using the path-integral approach. The exact wavefunctions and energies are also presented. Finally the propagator is re-calculated through an alternative method, using the δfunction. © 1992 IOP Publishing Ltd.

Exact solution for a three-dimensional three-body problem with harmonic interactions

The three-dimensional three-body problem with non-equal masses interacting through pairwise harmonic forces of non-equal strengths is analysed. It is shown that the Jacobi coordinates per se do not decouple this problem but lead to the problem of two coupled three-dimensional harmonic oscillators which becomes exactly soluble through the use of an additional coordinate set.

Symmetries and time evolution in discrete phase spaces: a soluble model calculation

Using the flexibility and constructive definition of the Schwinger bases, we developed different mapping procedures to enhance different aspects of the dynamics and of the symmetries of an extended version of the two-level Lipkin model. The classical limits of the dynamics are discussed in connection with the different mappings. Discrete Wigner functions are also calculated. © 1995.