Um estudo na teoria do movimento brownianno com viscosidade variável

Abstract

In this work we investigate the stochastic behavior of a large class of systems with variable damping which are described by a time-dependent Lagrangian. Our stochastic approach is based on the Langevin treatment describing the motion of a classical Brownian particle of mass m. Two situations of physical interest are considered. In the first one, we discuss in detail an application of the standard Langevin treatment (white noise) for the variable damping system. In the second one, a more general viewpoint is adopted by assuming a given expression to the so-called collored noise. For both cases, the basic diffententiaql equations are analytically solved and al the quantities physically relevant are explicitly determined. The results depend on an arbitrary q parameter measuring how the behavior of the system departs from the standard brownian particle with constant viscosity. Several types of sthocastic behavior (superdiffusive and subdiffusive) are obteinded when the free pamameter varies continuosly. However, all the results of the conventional Langevin approach with constant damping are recovered in the limit q = 1