Random oscillator with general Gaussian noise

Kirone Mallick (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical observables, such as the amplitude, the velocity and the energy of the oscillator grow as power-laws with time. We calculate the associated scaling exponents and we show that their values depend on the asymptotic behaviour of the external potential and on the high frequencies of the noise. Our results are generalized to include dissipative effects and additive noise.

Mots clés: Langevin dynamics; Multiplicative noise; Nonlinear oscillations

Domaines: Mécanique statistique [cond-mat.stat-mech]

Kirone Mallick. Random oscillator with general Gaussian noise. Physica A: Statistical Mechanics and its Applications, 2007, 384 (1), pp.64-68. ⟨10.1016/j.physa.2007.04.070⟩. ⟨cea-02927301⟩