Inhomogeneity of the phase space of the damped harmonic oscillator under Lévy noise.
The damped harmonic oscillator under symmetric Lévy white noise shows inhomogeneous phase space, which is in contrast to the homogeneous phase space of the same oscillator under the Gaussian white noise, as shown in a recent paper [Sokolov, Ebeling, and Dybiec, Phys. Rev. E 83, 041118 (2011)]. The inhomogeneity of the phase space shows correlation between the coordinate and the velocity of the damped oscillator under symmetric Lévy 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 directly demonstrate this in the reduced coordinate x[over ̃] versus velocity v[over ̃] plots and identify the physics of the antiassociation of the coordinate and velocity.
Center for Interdisciplinary Studies and Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China.
Zhan
Z
Cao
Yu-Feng
YF
Wang
Hong-Gang
HG
Luo
D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D009991:Oscillometry / Q000379:methods*