R. N. Costa Filho

Displacement operator for quantum systems with position-dependent mass

A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique commutation relation for x and p{sub {gamma}}. Such a formalism naturally leads to a Schroedinger-like equation that is reminiscent of wave equations typically used to model electrons with position-dependent (effective) masses propagating through abrupt interfaces in semiconductor heterostructures. The distinctive features of our approach are demonstrated through analytical solutions calculated for particles under null and constant potentials like infinite wells in one and two dimensions and potential barriers.

Brazilian elections: voting for a scaling democracy

The proportional elections held in Brazil in 1998 and 2002 display identical statistical signatures. In particular, the distribution of votes among candidates includes a power-law regime. We suggest that the rationale behind this robust scaling invariance is a multiplicative process in which the voters choice for a candidate is governed by a product of probabilities.

A transfer matrix method for resonances in Randall-Sundrum models

In this paper we discuss in detail a numerical method to study resonances in membranes generated by domain walls in Randall-Sundrum-like scenarios. It is based on similar works to understand the quantum mechanics of electrons subject to the potential barriers that exist in heterostructures in semiconductors. This method was used recently to study resonances of a three form field and lately generalized to arbitrary forms. We apply it to a lot of important models, namely those that contain the Gauge, Gravity and Spinor fields. In many cases we find a rich structure of resonances which depends on the parameters involved.

Generalized Zipf's law in proportional voting processes

Voting data from city-councillors, state and federal deputies elections are analyzed and considered as a response function of a social system with underlying dynamics leading to complex behavior. The voting results from the last two general Brazilian elections held in 1998 and 2000 are then used as representative data sets. We show that the voting distributions follow a generalized Zipfs law which has recently been proposed within a nonextensive statistics framework. Moreover, the voting distribution for city-councillors is clearly distinct from those of state and federal deputies in the sense that the latter depicts a higher degree of nonextensivity. We relate this finding with the different degrees of complexity corresponding to local and nonlocal voting processes.

Majority-vote model on a random lattice.

The stationary critical properties of the isotropic majority vote model on random lattices with quenched connectivity disorder are calculated by using Monte Carlo simulations and finite size analysis. The critical exponents gamma and beta are found to be different from those of the Ising and majority vote on the square lattice model and the critical noise parameter is found to be q(c) =0.117+/-0.005 .

Antisymmetric tensor fields in Randall–Sundrum thick branes

Abstract In this Letter we study the issue of localization of the three-form field in a Randall–Sundrum-like scenario. We simulate our membrane by kinks embedded in D = 5 , describing the usual case (not deformed) and new models coming from a specific deformation procedure. The gravitational background regarded includes the dilaton contribution. We show that we can only localize the zero-mode of this field for a specific range of the dilaton coupling, even in the deformed case. A study about resonances is presented. We use a numerical approach for calculations of the transmission coefficients associated to the quantum mechanical problem. This gives a clear description of the physics involved in the model. We find in this way that the appearance of resonances is strongly dependent on the coupling constant. We study the cases p = 1 , 3 and 5 for α = − 1.75 and α = − 20 . The first value of α give us one resonance peak for p = 1 and no resonances for p = 3 , 5 . The second value of α give us a very rich structure of resonances, with number depending on the value of p.

A Transfer Matrix Method for Resonances in Randall-Sundrum Models II: The Deformed Case

A bstractHere we consider resonances of the Gauge, Gravity and Spinor fields in RandallSundrum-like scenarios. We consider membranes that are generated by a class of topological defects that are deformed domain walls obtained from other previously known ones. They are obtained by a deformation procedure generate different potentials to the associated Schrödinger-like equation. The resonance spectra are calculated numerically using the method of Transfer Matrix developed by the authors and presented in JHEP 1108 (2011) 071. The new deformed defects change the resonances spectra of all fields considered and the associated phenomenology as well.

On resonances of q-forms in thick p-branes

In this work we consider q form elds in a p brane embedded in a D = (p + 2) space-time. The membrane is generated by a domain wall in a RandallSundrum-like scenario. We study conditions for localization of zero modes of these elds. The expression agrees and generalizes the one found for the zero, one, two and three-forms in a 3 brane. By a generalization we mean that our expression is valid for any form in an arbitrary dimension with codimension one. We also point out that, even without the dilaton coupling, some form elds are localized in the membrane. The massive modes are considered and the resonances are calculated using a numerical method. We nd that dierent spaces have identical resonance structures, which we call dual spaces of resonances(DSR).

A transfer matrix method for resonances in Randall-Sundrum models III: an analytical comparison

A bstractThe transfer matrix method is used to analyze resonances in Randall-Sundrum models. Although it has successfully been used previously by us we provide here a comparison between the numerical and analytical models. To reach this we first find new exact solution for the scalar, gauge, Kalb-Ramond and q-form fields. Them we calculate numerically the resonances by the transfer matrix method and compare with the analytical result. For completeness, this is done for models with and without the dilaton coupling. The results show a perfect agreement between the analytical and numerical methods.

Solutions to the problem of ELKO spinor localization in brane models

Two different solutions to the problem of the zero-mode localization of the Elko spinor are presented. The first solution is given by the introduction of a mass term and by coupling the spinor with the brane through a delta function. The second solution is reached by a Yukawa geometrical coupling with the Ricci scalar. These two models consistently change the boundary condition at infinity and at the origin. For the case of the geometrical coupling, we are able to show that the zero mode is localized for any smooth version of the Randall-Sundrum model.