I. A. Pedrosa

Geometric phases and squeezed quantum states of relic gravitons

In this work, we investigate the quantum effects of relic gravitons from a Schrodinger-picture point of view. By considering the gravity-wave equations in the Friedmann–Robertson–Walker cosmological background, we reduce the problem to that of a generalized time-dependent harmonic oscillator and find the corresponding exact analytic wave functions with the help of the dynamical invariant operator method. Afterward, we derive the geometric phases and squeezed quantum states for this system. We also evaluate the quantum fluctuations and the uncertainty product for each mode of the quantized field.

Light propagation: From dielectrics to curved spacetimes

We investigate the light propagation through time-dependent dielectric linear media in the absence of free charges and in curved spacetimes. Remarkably, we find that the light propagation in the two cases present amazing similarities, both classically and quantum mechanically. We also establish the connection between a permittivity with an exponential time accretion and the de Sitter spacetime. Surprisingly, for the de Sitter spacetime, the properties of light propagation can be analyzed in terms of a bona fide simple harmonic oscillator.

On the quantum description of light in homogeneous conducting linear media

In this paper, we use the Coulomb gauge, linear invariants and the dynamical invariant method in the framework of the Schrodinger equation to obtain a quantum description of light propagation through homogeneous conducting linear media with no charge density. We obtain exact wavefunctions for this problem in terms of solutions of a second-order ordinary differential equation which describes the amplitude of the classical damped harmonic oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations for each mode of the quantized electromagnetic field.

Gaussian wave packet states of scalar fields in a universe of de Sitter

In this work, we study quantum effects of a massive scalar field in the de Sitter spacetime. We reduce the problem to that of a time-dependent harmonic oscillator and use exact linear invariants and the dynamic invariant method to derive the corresponding Schrodinger states in terms of solutions of a second order ordinary differential equation. Afterwards, we construct Gaussian wave packet states and calculate the quantum dispersions as well as the quantum correlations for each mode of the quantized scalar field. It is further shown that the center of the Gaussian wave packet remains trapped in the origin.

COHERENT STATES OF LIGHT PROPAGATING IN CURVED SPACETIMES

In this work we investigate classical and quantum properties of light propagating in curved spacetimes determined by the Robertson-Walker metric. As a special case we consider the classical de Sitter spacetime. Afterwards, based on a quadratic invariant and the dynamical invariant method, we solve the Schrodinger equation for this problem and write the corresponding wave functions in terms of solutions of the Milne-Pinney equation. In addition, we construct coherent states for the quantized light and employ them to study quantum properties of light in curved spacetimes. In particular, we show that the product of the quantum fluctuations of the coordinate and the momentum space does not attain its minimum value.

Quantum dynamics of a particle trapped by oscillating fields

In this work we investigate the quantum dynamics of a particle trapped by oscillating fields. With the help of quadratic invariants and of the invariant method we solve analytically and exactly the Schrödinger equation for this system and write the corresponding wave functions in terms of solutions of the Milne–Pinney equation. We also construct coherent and squeezed states for this system and evaluate the quantum fluctuations in coordinate and momentum as well as the uncertainty product between canonical coordinate and momentum.

On the quantization of the electromagnetic field in conducting media

In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulombs gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.