Variational supersymmetric approach to evaluate Fokker-Planck probability

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolution. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Quantum description of spin tunneling in magnetic molecules

Starting from a phenomenological Hamiltonian originally written in terms of angular momentum operators we derive a new quantum angle-based Hamiltonian that allows for a discussion on the quantum spin tunneling. The study of the applicability of the present approach, carried out in calculations with a soluble quasi-spin model, shows that we are allowed to use our method in the description of physical systems such as the Mn12-acetate molecule, as well as the octanuclear iron cluster, Fe8, in a reliable way. With the present description the interpretation of the spin tunneling is seen to be direct, the spectra and energy barriers of those systems are obtained, and it is shown that they agree with the experimental ones. (c) 2006 Elsevier B.V. All rights reserved.

Electromagnetic field at finite temperature: A first order approach

In this work we study the electromagnetic field at finite temperature via the massless DKP formalism. The constraint analysis is performed and the partition function for the theory is constructed and computed. When it is specialized to the spin 1 sector we obtain the well-known result for the thermodynamic equilibrium of the electromagnetic field. (c) 2006 Elsevier B.V. All rights reserved.

Cosmological term and fundamental physics

A nonvanishing cosmological term in Einstein's equations implies a nonvanishing spacetime curvature even in the absence of any kind of matter. It would, in consequence, affect many of the underlying kinematic tenets of physical theory. The usual commutative spacetime translations of the Poincare group would be replaced by the mixed conformal translations of the de Sitter group, leading to obvious alterations in elementary concepts such as time, energy and momentum. Although negligible at small scales, such modifications may come to have important consequences both in the large and for the inflationary picture of the early Universe. A qualitative discussion is presented, which suggests deep changes in Hamiltonian, Quantum and Statistical Mechanics. In the primeval universe as described by the standard cosmological model, in particular, the equations of state of the matter sources could be quite different from those usually introduced.

Operator ordering in quantum radiative processes

In this work we reexamine quantum electrodynamics of atomic electrons in the Coulomb gauge in the dipole approximation and calculate the shift of atomic energy levels in the context of Dalibard, Dupont-Roc and Cohen-Tannoudji formalism by considering the variation rates of physical observable. We then analyze the physical interpretation of the ordering of operators in the dipole approximation interaction Hamiltonian in terms of field fluctuations and self-reaction of atomic electrons, discussing the arbitrariness in the statistical functions in second-order bound-state perturbation theory. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Dressed coordinates: the path-integral approach

The recently introduced dressed coordinates are studied in the path-integral approach. These coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path-integral functional measure. The analysis also generalizes the sum rules established in a previous work. (c) 2006 Elsevier B.V. All rights reserved.

Quantum spin tunneling in a soluble quasi-spin model: an angle-based potential description

We propose an approach which allows one to construct and use a potential function written in terms of an angle variable to describe interacting spin systems. We show how this can be implemented in the Lipkin-Meshkov-Glick, here considered a paradigmatic spin model. It is shown how some features of the energy gap can be interpreted in terms of a spin tunneling. A discrete Wigner function is constructed for a symmetric combination of two states of the model and its time evolution is obtained. The physical information extracted from that function reinforces our description of phase oscillations in a potential. (c) 2004 Elsevier B.V. All rights reserved.

Ploidy, sex and crossing over in an evolutionary aging model

Nowadays, many forms of reproduction coexist in nature: Asexual, Sexual, apomictic and meiotic parthenogenesis, hermaphroditism and parasex. The mechanisms of their evolution and what made them successful reproductive alternatives are very challenging and debated questions. Here, using a simple evolutionary aging model, we give I possible scenario. By studying the performance of Populations where individuals may have diverse characteristics-different ploidies, sex with or without crossing over, as well as the absence of sex-we find all evolution sequence that may explain why there are actually two major or leading groups: Sexual and asexual. We also investigate the dependence of these characteristics on different conditions of fertility and deleterious mutations. Finally, if the primeval organisms oil Earth were, in fact, asexual individuals we conjecture that the sexual form of reproduction could have more easily been set and found its niche during a period of low-intensity mutations. (c) 2005 Elsevier B.V. All rights reserved.

The impossibility of a universal relativistic temperature transformation

The non-existence of a relativistic temperature transformation is due to the fact that an observer moving in a heat reservoir cannot detect a blackbody spectrum. (C) 2004 Published by Elsevier B.V.

Testing option pricing with the Edgeworth expansion

There is a well-developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is flawed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black-Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more efficient hedging strategies of these instruments. (C) 2004 Elsevier B.V. All rights reserved.

Quantum spin tunneling of magnetization in small ferromagnetic particles

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

Interacting constituents in cosmology

Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure x energy density equations of state p(p). The usual approach in cosmology considers equations of state accounting only for kinematic terms, ignoring the contribution from the interactions between the particles constituting the source fluid. In this work the importance of these neglected terms is emphasized. A systematic method, based on the statistical mechanics of real fluids, is proposed to include them. A toy model is presented which shows how such interaction terms could be applied to engender significant cosmological effects.

Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)