Anomalous diffusion in a random nonlinear oscillator due to high frequencies of the noise

Details Anomalous diffusion in a random nonlinear oscillator due to high frequencies of the noise Anomalous diffusion in a random nonlinear oscillator due to high frequencies of the noise

2007-10-22

arxiv.org/abs/0710.4063v1

Physica A 384, page 64 (2007)

Nonlinear Sciences

Chaotic Dynamics

Expanded version of Proceedings StatPhys-Kolkata VI

Scientific paper

10.1016/j.physa.2007.04.070

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.

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