Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and gamma(5) chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

On the periodic orbits and the integrability of the regularized Hill lunar problem

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Irreducibility and compositeness in q-deformed harmonic oscillator algebras

A study of the reducibility of the Fock space representation of the q-deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is carried out by using the properties of the Gauss polynomials. When the deformation parameter is a root of unity, an interesting result comes out in the form of a reducibility scheme for the space representation which is based on the classification of the primitive or nonprimitive character of the deformation parameter. An application is carried out for a q-deformed harmonic oscillator Hamiltonian, to which the reducibility scheme is explicitly applied.

The Schrodinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Control and chaos for vibro-impact and non-ideal oscillators

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Analytical study of the nonlinear behavior of a shape memory oscillator: Part I-primary resonance and free response at low temperatures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

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.

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.

Effect of anharmonicities in the critical number of trapped condensed atoms with an attractive two-body interaction

The quantitative effect in the maximum number of particles and other static observables was determined. A deviation in the harmonic trap potential that is effective only outside the central part of the potential, with the addition of a term that is proportional to a cubic or quartic power of the distance was considered. Results showed that this study could be easily transferred to other trap geometries to estimate anharmonic effects.

Pseudospin symmetry and the relativistic harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations Σ=5+V and δ=V-S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case Σ=0, for which pseudospin symmetry is exact. We also show that the case U=δ=0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit.

Harmonic, reactive and unbalance compensation by means of CPT framework

This paper presents possible selective current compensation strategies based on the Conservative Power Theory (CPT). This recently proposed theory, introduces the concept of complex power conservation under non-sinusoidal conditions. Moreover, the related current decompositions results in several current terms, which are associated with a specific physical phenomena (power absorption P, energy storage Q, voltage and current distortion D). Such current components are used in this work for the definition of different current compensators, which can be selective in terms of minimizing particular disturbing effects. The choice of one or other current component for compensation directly affects the sizing and cost of active and/or passive devices and it will be demonstrated that it can be done to attend predefined limits for harmonic distortion, unbalances and/or power factor. Single and three-phase compensation strategies will be discussed by means of the CPT Framework. Simulation and experimental results will be demonstrated in order to validate their performance. © 2009 IEEE.

Modified radical mastectomy: A pilot clinical trial comparing the use of conventional electric scalpel and harmonic scalpel

Background: The aim of this study was to compare the rates of local postoperative complications among women undergoing modified radical mastectomy with an electric scalpel (ES) or a harmonic scalpel (HS). It is thought that HS use has less postoperative complications, mainly seroma formation. Methods: This study was a prospective non-randomised clinical trial (NCT01391988) among consecutive patients, performed in parallel. Patients underwent modified radical mastectomy using an HS or ES. We analysed the following operative variables: time, blood loss and seroma volume drainage. Postoperative complications, including seroma, flap necrosis, haematoma and infection were evaluated on the 7th and 14th days. Results: Forty-six patients underwent a MRM with ES and 49 with HS; no differences were observed between the groups. The rate of local complications was 29% in the HS group and 52% in the ES group (p=0.024). The rates of seroma (16.3% versus 28.3%; p=0.161), necrosis (4.1% vs. 21.7%; p=0.013; OR=0.15), haematoma (2.0% vs. 8.7%; p=0.195) and infection (2.0% vs. 6.5%; p=0.351) were lower in the HS group. Adding the findings of all comparative studies using HSs in MRM to the seroma rates in the current study, the seroma rate, expressed as a categorical variable, did not decrease with HS. Seroma was present in 60/219 cases using an HS and in 69/239 cases utilising an ES (p=0.72). Based on a multivariate analysis, HS decreased the risk of skin necrosis (p=0.015). Conclusions: HSs do not decrease the seroma rate. However, this method may be useful in skin sparing mastectomy because it decreases skin flap necrosis. © 2013 Surgical Associates Ltd.

Variational and perturbative schemes for a spiked harmonic oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian operator - d2/dx2 + x2 + l(l + 1)/x2 + λ|x| -α, where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schrödinger equation for the linear harmonic oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large coupling perturbative expansion is carried out and the contributions up to fourth-order to the ground state energy are explicitly evaluated. Numerical results are compared for the special case α = 5/2. © 1989 American Institute of Physics.