Scaling behaviour of Brownian motion interacting with an external field

Abstract

Scaling properties of Brownian trajectories under the effect of a constant force are studied using Brownian dynamic simulations. The field is found to have a strong influence on the randomness of the trajectories, and as consequence on the properties associated with it, e.g., the fractal dimension, the Kolmogorov entropy, or the diffusive character of the motion. By increasing the external field it is possible to observe the change from diffusive motion to ballistic motion, which occurs in the values of the scaling properties of trajectories, i.e., there are decreases in the ideal fractal dimension, the entropy of the trajectories and the scaling parameter between the time and the trajectory distance. These changes in the scaling parameters take place very quickly for relatively low fields, and converge very slowly to the values corresponding to ballistic motion for very high fields. In general, some of these parameters scale in a power relationship with the value of the field for intermediate values. Als...