Nonlinear friction in underdamped anharmonic stochastic oscillators.

Area of Science:

• Statistical physics
• Nonlinear dynamics
• Stochastic processes

Background:

• Non-equilibrium stationary states of stochastic oscillators driven by Lévy noise often exhibit multimodal distributions.
• This multimodality is observed in both overdamped systems and underdamped systems with linear friction in single-well potentials.

Purpose of the Study:

• To investigate the influence of nonlinear friction on the behavior of underdamped stochastic oscillators driven by Lévy noise.
• To determine if multimodality can be induced in the position and velocity distributions under nonlinear friction.

Main Methods:

• The study employed computer simulations to model underdamped motions in single-well potentials.
• The focus was on systems experiencing nonlinear friction, relaxing the assumption of linear friction.

Main Results:

• Multimodality in the velocity distribution is readily observed and is analogous to the overdamped case with similar deterministic forces.
• Inducing multimodality in the position distribution is more challenging but achievable with specifically tuned nonlinear friction.

Conclusions:

• Nonlinear friction significantly impacts the multimodality of stochastic oscillator distributions.
• Velocity distributions are more susceptible to multimodality than position distributions, which require precise tuning of friction parameters.