Schwinger and Pegg-Barnett approaches and a relationship between angular and Cartesian quantum descriptions: II. Phase spaces

Following the discussion-in state-space language-presented in a preceding paper, we work on the passage from the phase-space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labelled) number of states. With this it is possible to relate an original Schwinger idea to the Pegg-Barnett approach to the phase problem. In phase-space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian and angular coordinates, as limiting elements of the discrete phase-space formalism.

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

QUASIDISTRIBUTIONS and COHERENT STATES FOR FINITE-DIMENSIONAL QUANTUM SYSTEMS

In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber-Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism.

Dimensional Compactification and Two-Particle Binding

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

Dynamical properties for the problem of a particle in an electric field of wave packet: Low velocity and relativistic approach

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

The generator coordinate Hartree-Fock method as strategy for building Gaussian basis sets to ab initio study of the process of adsorption of sulfur on platinum (200) surface

The scheme named generator coordinate Hartree-Fock method (GCHF) is used to build (22s14p) and (33s22p16d9f) gaussian basis sets to S ((3)P) and Pt ((3)D) atoms, respectively. Theses basis sets are contracted to [13s10p] and [19s13p9d5f] through of Dunning's segmented contraction scheme and are enriched with d and g polarization functions, [13s10p1d] and [19s13p9d5flg]. Finally, the [19s13p9d5f1g] basis Set to Pt ((3)D) was supplemented with s and d diffuse functions, [20s13p10d5flg], and used in combination with [13s10p1d] to study the effects of adsorption of S ((3)D) atom on a pt ((3)D) atom belonged to infinite Pt (200) surface. Atom-atom overlap population, bond order, and infrared spectrum of [pt(_)S](2 -) were calculated properties and were carried out at Hartree-Fock-Roothaan level. The results indicate that the process of adsorption of S ((3)P) on pt ((3)D) in the infinite Pt (200) surface is mainly caused by a strong contribution of sigma between the 3p(z) orbital of S ((3)P) and the 6s orbital of pt ((3)D). (c) 2004 Elsevier 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.

Unfolding of plasmon-polariton modes in one-dimensional layered systems containing anisotropic left-handed materials

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.

Higher-dimensional twistor transforms using pure spinors

Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (euclidean) dimension d = 2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on ℝ2n. For d = 4 and d = 6, these spaces are ℂℙ1 and ℂℙ3 and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d > 6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations. © SISSA/ISAS 2005.

Locating invariant tori for a family of two-dimensional Hamiltonian mappings

The location of invariant tori for a two-dimensional Hamiltonian mapping exhibiting mixed phase space is discussed. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori. Given the mapping considered is parameterised by an exponent γ in one of the dynamical variables, a connection with the standard mapping near a transition from local to global chaos is used to estimate the position of the invariant tori limiting the size of the chaotic sea for different values of the parameter γ. © 2011 Elsevier B.V. All rights reserved.

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

Spin squeezing and entanglement via finite-dimensional discrete phase-space description

We show how mapping techniques inherent to N2-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson- Schrödinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects, as well as allow to investigate the basic role of spin correlations through the discrete representatives of quasiprobability distribution functions. Entropy functionals are also discussed in this context. The main sequence correlations → entanglement → squeezing of quantum effects embraces a new set of insights and interpretations in this framework, which represents an effective gain for future researches in different spin systems. © 2013 World Scientific Publishing Company.

A redução de Liapunov-Schmidt e a bifurcação de Hopf

Pós-graduação em Matemática - IBILCE

Cohomologia de grupos e invariante algébricos

Pós-graduação em Matemática - IBILCE