A.R. Bosco de Magalhães

Classical and quantum coupled oscillators: symplectic structure

We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum regimes.

Continuous monitoring of dynamical systems and master equations

Abstract We illustrate the equivalence between the non-unitary evolution of an open quantum system governed by a Markovian master equation and a process of continuous measurements involving this system. We investigate a system of two coupled modes, only one of them interacting with external degrees of freedom, represented, in the first case, by a finite number of harmonic oscillators, and, in the second, by a sequence of atoms where each one interacts with a single mode during a limited time. Two distinct regimes appear, one of them corresponding to a Zeno-like behavior in the limit of large dissipation.

Equation-based model for the stock market

We propose a stock market model which is investigated in the forms of difference and differential equations whose variables correspond to the demand or supply of each agent and to the price. In the model, agents are driven by the behavior of their trust contact network as well by fundamental analysis. By means of the deterministic version of the model, the connection between such drive mechanisms and the price is analyzed: imitation behavior promotes market instability, finitude of resources is associated to stock index stability, and high sensitivity to the fair price provokes price oscillations. Long-range correlations in the price temporal series and heavy-tailed distribution of returns are observed for the version of the model which considers different proposals for stochasticity of microeconomic and macroeconomic origins.

Quantum erasure in the presence of a thermal bath: The effects of system–environment microscopic correlations

Abstract We investigate the role of the environment in a quantum erasure setup in the cavity quantum electrodynamics domain. Two slightly different schemes are analyzed. We show that the effects of the environment vary when a scheme is exchanged for another. This can be used to estimate the macroscopic parameters related to the system–environment microscopic correlations.

Thouless theorem for one and two degrees of freedom

Realizamos uma demonstracao acessivel do teorema de Thouless para um ou dois graus de liberdade, usando somente mecânica quântica elementar. Este teorema e especialmente util para encontrar o vacuo relativo a um conjunto de operadores bosonicos transformados. Outra motivacao e a existencia de experimentos envolvendo ions capturados ou campos em eletrodinâmica quântica de cavidades, usualmente modelados por osciladores harmonicos interagindo linearmente.