Quantization of the damped harmonic oscillator revisited

We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. (C) 2011 Elsevier B.V. All rights reserved.

Field on Poincare Group and Quantum Description of Orientable Objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner`s ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincar, group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group I =GxG. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points xaG/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix ZaSpin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.

Scalar form factors and nuclear interactions

The scalar-isoscalar term in the two-pion exchange NN potential is abnormally large and does not respect the hierarchy of effects predicted by chiral perturbation theory. We argue that this anomaly is associated with non-perturbative effects, which are also present in the pi N scalar form factor.

Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S(1)(n+1)(c), n >= 3, with constant normalized scalar curvature R satisfying n-2/nc <= R <= c totally umbilical? (C) 2008 Elsevier B.V. All rights reserved.

Color Segmentation using LVQ-Learning Vector Quantization

This thesis aims to present a color segmentation approach for traffic sign recognition based on LVQ neural networks. The RGB images were converted into HSV color space, and segmented using LVQ depending on the hue and saturation values of each pixel in the HSV color space. LVQ neural network was used to segment red, blue and yellow colors on the road and traffic signs to detect and recognize them. LVQ was effectively applied to 536 sampled images taken from different countries in different conditions with 89% accuracy and the execution time of each image among 31 images was calculated in between 0.726sec to 0.844sec. The method was tested in different environmental conditions and LVQ showed its capacity to reasonably segment color despite remarkable illumination differences. The results showed high robustness.

Exact solution for a fermion in the background of a scalar inversely linear potential

The problem of a fermion subject to a general scalar potential in a two-dimensional world is mapped into a Sturm-Liouville problem for nonzero eigenenergies. The searching for possible bounded solutions is done in the circumstance of power-law potentials. The normalizable zero-eigenmode solutions are also searched. For the specific case of an inversely linear potential, which gives rise to an effective Kratzer potential, exact bounded solutions are found in closed form. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. (C) 2004 Elsevier B.V. All rights reserved.

Bounded solutions of fermions in the background of mixed vector-scalar inversely linear potentials

The problem of a fermion subject to a general mixing of vector and scalar potentials in a two-dimensional world is mapped into a Sturm-Liouville problem. Isolated bounded solutions are also searched. For the specific case of an inversely linear potential, which gives rise to an effective Kratzer potential in the Sturm-Liouville problem, exact bounded solutions are found in closed form. The case of a pure scalar potential with their isolated zero-energy solutions, already analyzed in a previous work, is obtained as a particular case. The behavior of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2004 Elsevier B.V. All rights reserved.

Effects of a mixed vector-scalar screened coulomb potential for spinless particles

The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a bona fide solitary zero-eigenmode solution, are revealed for the Klein-Gordon equation. The cases of pure vector and scalar potentials, already analyzed in previous works, are obtained as particular cases.

Bounded solutions of fermions in the background of mixed vector-scalar Poeschl-Teller-like potentials

The problem of a fermion subject to a convenient mixing of vector and scalar potentials in a two-dimensional space-time is mapped into a Sturm-Liouville problem. For a specific case which gives rise to an exactly solvable effective modified Poschl-Teller potential in the Sturm-Liouville problem, bound-state solutions are found. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The Dirac delta potential as a limit of the modified Poschl-Teller potential is also discussed. The problem is also shown to be mapped into that of massless fermions subject to classical topological scalar and pseudoscalar potentials. Copyright (C) EPLA, 2007.

Relativistic effects of mixed vector-scalar-pseudoscalar potentials for fermions in 1+1 dimensions

The problem of fermions in the presence of a pseudoscalar plus a mixing of vector and scalar potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. The cases of mixed vector and scalar Poschl-Teller-like and pseudoscalar kink-like potentials, already analyzed in previous works, are obtained as particular cases.

A fermion in a scalar inversely linear potential

The problem of a fermion subject to a a scalar inversely linear potential in a two-dimensional world is mapped into a Sturm-Liouville problem for nonzero eigenenergies. This mapping gives rise to an effective Kratzer potential and exact bounded solutions are found in closed form. The normalizable zero-eigenmode solution is also found. A few unusual results are revealed.

Klein-Gordon particles in mixed vector-scalar inversely linear potentials

The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the eigenfunctions which ensure that the effective Hamiltonian is Hermitian for all the points of the space. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2005 Elsevier B.V. All rights reserved.

Confinement of spin-0 and spin-1/2 particles in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein - Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V-v = V-s + constant. These isospectral problems are solved in the case of squared trigonometric potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfunctions are discussed in some detail. It is revealed that a spin-0 particle is better localized than a spin-1/2 particle when they have the same mass and are subjected to the same potentials.

Confinement of fermions by mixed vector-scalar linear potentials in two-dimensional space-time

The problem of confinement of fermions in 1 + 1 dimensions is approached with a linear potential in the Dirac equation by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the scalar coupling is of sufficient intensity compared to the vector coupling. (C) 2002 Elsevier B.V. B.V. All rights reserved.