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

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...

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Bibliographic Details
Published inarXiv.org
Main Author Mallick, Kirone
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.10.2007
Subjects
Asymptotic properties
Energy dissipation
High frequencies
Noise
Physics - Chaotic Dynamics
Physics - Statistical Mechanics
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ISSN2331-8422
DOI10.48550/arxiv.0710.4063

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Summary: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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.0710.4063