Brownian Dynamics, Time-averaging and Colored Noise

D. O. Soares-Pinto, W. A. M. Morgado

Published 2006-01-18, updated 2006-05-15Version 2

We propose a method to obtain the equilibrium distribution for positions and velocities of a one-dimensional particle via time-averaging and Laplace transformations. We apply it to the case of a damped harmonic oscillator in contact with a thermal bath. The present method allows us to treat, among other cases, a Gaussian noise function exponentially correlated in time, e.g., Gaussian colored noise. We obtain the exact equilibrium solution and study some of its properties.