Movimento browniano e difração

Abstract

The present work aims a theoretical study of Brownian Motion (MB). MB theory have many applications. In the branch of Mathematics and Statistics, have applicability for the study of sistems the evolve in a ramdomic way. In the branch of Physics, MB theoretical model serves as the basis to approach other natural phenomena which have similar behavior. In the branch of Economy, among many applications, we can emphasize Macroeconomics situations. MB theory is studied in this work in 4 different ways, each one requiring a specific prior knowledge. Thats why, in first chapters, we introduce some useful concepts that later will be clear. An introductory approach is made about stochastic process, since in MB study we obtain an equation one of its variables is random in time. We also obtain the Fokker-Planck equation, which describes the time evolution of a given probability distribution, being then of great importance to MB study. We also introduce the Random Walk problem, where we note the versatility of this model in the description of MB. Will be seen Einstein’s approach to MB theory. All these approaches will lead us to equations with the same physical foundation, which is called diffusion. This phenomenon, also discussed in MB study, will be also displayed starting from Fick’s Law, which is an empirical observation. All approaches lead us to a broader vision about the system under study.