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

Abstract

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 Lévy 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.

arXiv comment7 pages, 4 figures

References in corpus (7)

• The scaling laws of human travel
• Levy Flight Superdiffusion: An Introduction
• Non-diffusive transport in plasma turbulence: a fractional diffusion approach
• Optimal target search on a fast folding polymer chain with volume exchange
• Lévy flights in a steep potential well
• Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field
• Ornstein-Uhlenbeck-Cauchy Process

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