Nonlinear friction in underdamped anharmonic stochastic oscillators

Capała, Karol; Dybiec, Bartłomiej; Gudowska–Nowak, Ewa

doi:10.1063/5.0007581

Cited by 2 publications

(1 citation statement)

References 56 publications

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“…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.…”

Section: Discussionmentioning

confidence: 99%

Energy partition for anharmonic, undamped, classical oscillators

Mandrysz¹,

Dybiec²

2020

J. Phys. A: Math. Theor.

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Using stochastic methods, general formulas for average kinetic and potential energies for anharmonic, undamped (frictionless), classical oscillators are derived. It is demonstrated that for potentials of |x| ν (ν > 0) type energies are equipartitioned for the harmonic potential only. For potential wells weaker than parabolic potential energy dominates, while for potentials stronger than parabolic kinetic energy prevails. Due to energy conservation, the variances of kinetic and potential energies are equal. In the limiting case of the infinite rectangular potential well (ν → ∞) the whole energy is stored in the form of the kinetic energy and variances of energy distributions vanish.

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Section: Discussionmentioning

confidence: 99%

Energy partition for anharmonic, undamped, classical oscillators

Mandrysz¹,

Dybiec²

2020

J. Phys. A: Math. Theor.

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Resetting induced multimodality

Pogorzelec

Dybiec

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Properties of stochastic systems are defined by the noise type and deterministic forces acting on the system. In out-of-equilibrium setups, e.g., for motions under action of Lévy noises, the existence of the stationary state is not only determined by the potential but also by the noise. Potential wells need to be steeper than parabolic in order to assure the existence of stationary states. The existence of stationary states, in sub-harmonic potential wells, can be restored by stochastic resetting, which is the protocol of starting over at random times. Herein, we demonstrate that the combined action of Lévy noise and Poissonian stochastic resetting can result in the phase transition between non-equilibrium stationary states of various multimodality in the overdamped system in super-harmonic potentials. Fine-tuned resetting rates can increase the modality of stationary states, while for high resetting rates, the multimodality is destroyed as the stochastic resetting limits the spread of particles.

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Role of long jumps in Lévy noise-induced multimodality

Pogorzelec,

Dybiec

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Lévy noise is a paradigmatic noise used to describe out-of-equilibrium systems. Typically, properties of Lévy noise driven systems are very different from their Gaussian white noise driven counterparts. In particular, under action of Lévy noise, stationary states in single-well, super-harmonic, potentials are no longer unimodal. Typically, they are bimodal; however, for fine-tuned potentials, the number of modes can be further increased. The multimodality arises as a consequence of the competition between long displacements induced by the non-equilibrium stochastic driving and action of the deterministic force. Here, we explore robustness of bimodality in the quartic potential under action of the Lévy noise. We explore various scenarios of bounding long jumps and assess their ability to weaken and destroy multimodality. In general, we demonstrate that despite its robustness it is possible to destroy the bimodality, however it requires drastic reduction in the length of noise-induced jumps.

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Nonlinear friction in underdamped anharmonic stochastic oscillators

Cited by 2 publications

References 56 publications

Energy partition for anharmonic, undamped, classical oscillators

Energy partition for anharmonic, undamped, classical oscillators

Resetting induced multimodality

Role of long jumps in Lévy noise-induced multimodality

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