Harmonic oscillator under Levy noise: Unexpected properties in the phase space

Details Harmonic oscillator under Levy noise: Unexpected properties in the phase space Harmonic oscillator under Levy noise: Unexpected properties in the phase space

2010-10-13

arxiv.org/abs/1010.2657v2

Phys. Rev. E 83, 041118 (2011)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 figures

Scientific paper

10.1103/PhysRevE.83.041118

A harmonic oscillator under influence of the noise is a basic model of various physical phenomena. Under Gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to the bivariate Gaussian distribution with elliptic level lines. The distribution of phase is homogeneous. None of these properties hold in the general L\'evy case. Thus, the level lines of the joint probability density are not elliptic. The coordinate and the velocity of the oscillator are strongly dependent, and this dependence is quantified by introducing the corresponding parameter ("width deficit"). The distribution of the phase is inhomogeneous and highly nontrivial.

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