On the stochastic pendulum with Ornstein-Uhlenbeck noise
Statistical Mechanics
2009-11-10 v1
Abstract
We study a frictionless pendulum subject to multiplicative random noise. Because of destructive interference between the angular displacement of the system and the noise term, the energy fluctuations are reduced when the noise has a non-zero correlation time. We derive the long time behavior of the pendulum in the case of Ornstein-Uhlenbeck noise by a recursive adiabatic elimination procedure. An analytical expression for the asymptotic probability distribution function of the energy is obtained and the results agree with numerical simulations. Lastly, we compare our method to other approximation schemes.
Keywords
Cite
@article{arxiv.cond-mat/0407198,
title = {On the stochastic pendulum with Ornstein-Uhlenbeck noise},
author = {Kirone Mallick and Philippe Marcq},
journal= {arXiv preprint arXiv:cond-mat/0407198},
year = {2009}
}
Comments
14 pages, 6 figures