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Asymptotic behavior of a harmonic oscillator driven by a generalized Mittag-Leffler noise. (English) Zbl 1217.82056

Summary: The asymptotic behavior of a harmonic oscillator driven by a generalized Mittag-Leffler noise was studied by analyzing the generalized Langevin equation. The mean square displacement (MSD) and the velocity autocorrelation function (VACF) of a diffusing particle were obtained by using the Laplace transform method and Tauberian theorem. It was found that the MSD and VACF for various values of the parameters show a power-law decay, i.e. an anomalous diffusive behavior of the oscillator.

MSC:

82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
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