On the reversible quadratic polynomial vector fields on S-2

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

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

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

Discrete dimorphism among castes of the bald-faced hornet Dolichovespula maculata (Hymenoptera: Vespidae) in different phases of the colony cycle

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

Naturally light invisible axion in models with large local discrete symmetries

We show that by introducing appropriate local Z(N)(Ngreater than or equal to13) symmetries in electroweak models it is possible to implement an automatic Peccei-Quinn symmetry, at the same time keeping the axion protected against gravitational effects. Although we consider here only an extension of the standard model and a particular 3-3-1 model, the strategy can be used in any kind of electroweak model. An interesting feature of this 3-3-1 model is that if we add (i) right-handed neutrinos, (ii) the conservation of the total lepton number, and (iii) a Z(2) symmetry, the Z(13) and the chiral Peccei-Quinn U(1)P-Q symmetries are both accidental symmetries in the sense that they are not imposed on the Lagrangian but are just a consequence of the particle content of the model, its gauge invariance, renormalizability, and Lorentz invariance. In addition, this model has no domain wall problem.

Determining the shape of the universe using discrete sources

Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our universe? It is shown here that, if our universe has flat spatial sections, these multiple images can be accommodated within any of the six classes of compact orientable three-dimensional flat space forms. Moreover, the discovery of two more triples of multiple images in the neighbourhood of the first one would allow the determination of the topology of the universe, and in most cases the determination of its size.

Discrete symmetries, invisible axion, and lepton number symmetry in an economic 3-3-1 model

We show that Peccei-Quinn and lepton number symmetries can be a natural outcome in a 3-3-1 model with right-handed neutrinos after imposing a Z(11)circle timesZ(2) symmetry. This symmetry is suitably accommodated in this model when we augment its spectrum by including merely one singlet scalar field. We work out the breaking of the Peccei-Quinn symmetry, yielding the axion, and study the phenomenological consequences. The main result of this work is that the solution to the strong CP problem can be implemented in a natural way, implying an invisible axion phenomenologically unconstrained, free of domain wall formation, and constituting a good candidate for the cold dark matter.

Quantum discrete phase space dynamics and its continuous limit

The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.

Time evolution of the Wigner function in discrete quantum phase space for a soluble quasi-spin model

The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wi:ner function is written for some chosen states associated to discrete angle and angular momentum variables, and the rime evolution is numerically calculated using the discrete von Neumnnn-Liouville equation. Direct evidences in the lime evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU(2)-based semiclassical continuous approach to the Lipkin model is also presented.

Discrete squeezed states for finite-dimensional spaces

We show how discrete squeezed states in an N-2-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum information theory with the aim of establishing an initial study on the interference effects between discrete variables in a finite phase space. Moreover, the interpretation of the squeezing effects is seen to be direct in the present approach, and has some potential applications in different branches of physics.

Discrete and canonical quantum variables

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The flavor problem and discrete symmetries

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A discrete finite-dimensional phase space approach for the description of Fe8 magnetic clusters: Wigner and Husimi functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stability of differential equations with piecewise constant argument via discrete equations

Lyapunov stability for a class of differential equation with piecewise constant argument (EPCA) is considered by means of the stability of a discrete equation. Applications to some nonlinear autonomous equations are given improving some linear known cases.