Simulation of Brownian Motion Driven Internally by White Noise and an External Electric Oscillator

Abstract

Understanding the Brownian motion of a random particle caused by the contribution of randomness can lead to a great physical interpretation into the behavior of any stochastic phenomena. In this study, we used a mathematical and analytical modeling of realistic stochastic processes with a numerical treatment on the random force addressed as white noise term. The transition of motion from the classical Langevin equation was treated; and the ballistic to diffusive regime due to the inertial term on the Langevin equation for a short time was then considered. Furthermore, we examined the diffusive regime without the inertial term and subjected it to a varying electric oscillator with fixed fluctuation of frequency for a short time. Lastly, plots for the displacements, and mean squared displacements, when with or without inertial term and when it is subjected to an electric oscillator were obtained.