Eur. Phys. J. B 31, 553-561 (2003)
https://doi.org/10.1140/epjb/e2003-00065-y

Scaling behavior of a nonlinear oscillator with additive noise, white and colored

¹ Service de Physique Théorique, Centre d'Études de Saclay, 91191 Gif-sur-Yvette Cedex, France
² Institut de Recherche sur les Phénomènes Hors Équilibre, Université de Provence, 49 rue Joliot-Curie, BP 146, 13384 Marseille Cedex 13, France

Corresponding author: ^a mallick@spht.saclay.cea.fr

Received: 10 October 2002
Published online: 6 March 2003

Abstract

We study analytically and numerically the problem of a nonlinear mechanical oscillator with additive noise in the absence of damping. We show that the amplitude, the velocity and the energy of the oscillator grow algebraically with time. For Gaussian white noise, an analytical expression for the probability distribution function of the energy is obtained in the long-time limit. In the case of colored, Ornstein-Uhlenbeck noise, a self-consistent calculation leads to (different) anomalous diffusion exponents. Dimensional analysis yields the qualitative behavior of the prefactors (generalized diffusion constants) as a function of the correlation time.