Underdamped stochastic harmonic oscillator

Abstract

We investigate stationary states of the linear damped stochastic oscillator driven by Lévy noises. In the long time limit kinetic and potential energies of the oscillator do not fulfill the equipartition theorem and their distributions follow the power-law asymptotics. At the same time, partition of the mechanical energy is controlled by the damping coefficient. We show that in the limit of vanishing damping a stochastic analogue of the equipartition theorem can be proposed, namely the statistical properties of potential and kinetic energies attain distributions characterized by the same width. Finally, we demonstrate that the ratio of instantaneous kinetic and potential energies which signifies departure from the mechanical energy equipartition, follows universal power-law asymptotics.

8 pages. 3 figures

References in corpus (6)

• The scaling laws of human travel
• Stationary states in Langevin dynamics under asymmetric Lévy noises
• Harmonic oscillator under Levy noise: Unexpected properties in the phase space
• Fluctuation relations for anomalous dynamics
• Fluctuation relation for a Lévy particle
• Stationary states in 2D systems driven by bi-variate Lévy noises

Cited by in corpus (8)

• Hydrodynamics of Random-Organizing Hyperuniform Fluids
• How to define temperature in active systems?
• Non-equilibrium dynamic hyperuniform states
• Closed-form solutions for the Lévy-stable distribution
• Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
• Probing the limits of effective temperature consistency in actively driven systems
• Bounding energy growth in friction-less stochastic oscillators
• Energy partition for anharmonic, undamped, classical oscillators