Inhomogeneity of the phase space of the damped harmonic oscillator under Levy noise

Details Inhomogeneity of the phase space of the damped harmonic oscillator under Levy noise Inhomogeneity of the phase space of the damped harmonic oscillator under Levy noise

2012-04-03

arxiv.org/abs/1204.0593v2

Phys. Rev. E 85,042101(2012)

Physics

Data Analysis, Statistics and Probability

7 pages,10 figures, a full version of published paper

Scientific paper

10.1103/PhysRevE.85.042101

The damped harmonic oscillator under symmetric L\'{e}vy white noise shows inhomogeneous phase space, which is in contrast to the homogeneous one of the same oscillator under the Gaussian white noise, as shown in a recent paper [I. M. Sokolov, W. Ebeling, and B. Dybiec, Phys. Rev. E \textbf{83}, 041118 (2011)]. The inhomogeneity of the phase space shows certain correlation between the coordinate and the velocity of the damped oscillator under symmetric L\'{e}vy white noise. In the present work we further explore the physical origin of these distinguished features and find that it is due to the combination of the damped effect and heavy tail of the noise. We demonstrate directly this in the reduced coordinate $\tilde{x}$ versus velocity $\tilde{v}$ plots and identify the physics of the anti-association of the coordinate and velocity.

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