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

Kirone Mallick (1) , Philippe Marcq (2)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

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.

Domaines: Mécanique des fluides [physics.class-ph]

Kirone Mallick, Philippe Marcq. Scaling behavior of a nonlinear oscillator with additive noise, white and colored. The European Physical Journal B: Condensed Matter and Complex Systems, 2003, 31 (4), pp.553 - 561. ⟨10.1140/epjb/e2003-00065-y⟩. ⟨hal-00014827⟩