Quatro abordagens para o movimento browniano

Abstract

The random trajectory of small particles in suspension within a liquid, a phenomenon known as brownian motion, was firstly explained by Einstein in his famous doctorate thesis. From a historical perspective, we show how such a phenomenon can be described in four different ways, namely: the Einstein diffusive treatment, the stochastic variant or fluctuating force proposed by Paul Langevin, the approach through the Fokker-Planck equation, and, finally, the random walks by Mark Kac. Some limitations present in the standard diffusive approach are also discussed. In particular, we show that the parabolic equation in which Einstein based his explanation should be replaced by a hyperbolic equation of motion which also appears naturally in the treatment of random walks. The general solution of the generalized diffusion equation is obtained and compared to the standard result. For short times, in comparison with the characteristic time scales of the system, the motion of the particles is described by a wave behavior. Copyright by the Sociedade Brasileira de Física.