Nonlinear friction in underdamped anharmonic stochastic oscillators

Abstract

Non-equilibrium stationary states of overdamped anharmonic stochastic oscillators driven by Lévy noise are typically multimodal. The very same situation is recorded for an underdamped Lévy noise driven motion in single-well potentials with linear friction. Within current manuscript we relax the assumption that the friction experienced by a particle is linear. Using computer simulations, we study underdamped motions in single-well potentials in the regime of nonlinear friction. We demonstrate that it is relatively easy to observe multimodality in the velocity distribution as it is determined by the friction itself and it is the same as the multimodality in the overdamped case with the analogous deterministic force. Contrary to the velocity marginal density, it is more difficult to induce multimodality in the position. Nevertheless, for a fine-tuned nonlinear friction, the spatial multimodality can be recorded.

Energy partition for anharmonic, undamped, classical oscillators

“…Consequently, there is no classical energy equipartition relation [36]. Nevertheless, systems driven by Lévy noise require further studies especially in the regime of nonlinear friction [37], which is capable of bounding average energies.…”