Sistemas dinâmicos e caos: do clássico ao quântico

Abstract

In the second half of the 20th century, a set of advances in various areas of science, catalyzed by the invention of the modern computer, resulted in the emergence of Chaos Theory. The great milestone for this development was the work of Edward Lorenz, developed from his studies in atmospheric modeling, and which he had with one of the bases the geometric method of analysis developed by Poincaré. Shortly thereafter, in the early 1970s, Gutzwiller resolved the issue of quantization in chaotic systems through his trace formula, and in the following decade, the Random Matrices formalism was introduced to the Quantum Chaos approach. Despite being part of an interdisciplinary field of study today, both Chaos and the study of dynamical systems and nonlinearity have their earliest origins in physics. Through this work, we will discuss how dynamical systems are represented in physics through the formalism of classical mechanics, which provides space for the geometric analysis of dynamical systems in general. And we will see how deterministic Chaos arises from a forced and dampened pendulum system, and briefly introduce Quantum Chaos through the Random Matrix Theory.