Anomalous diffusion due to the non-Markovian process of the dust particle velocity in complex plasmas

TL;DR

This paper models dust particle motion in complex plasmas as a non-Markovian stochastic process using fractional Langevin equations, revealing that memory effects induce anomalous diffusion characterized by power-law decay in velocity autocorrelation.

Contribution

It introduces a fractional Langevin equation approach to describe dust particle dynamics, highlighting the role of memory effects in causing anomalous diffusion in dusty plasmas.

Findings

Memory effects lead to anomalous diffusion with power-law decay in velocity autocorrelation.

The model derives mean-square displacement and velocity autocorrelation functions using Mittag-Leffler functions.

Dust particle temperature and long-time behavior are analyzed considering charge fluctuations.

Abstract

In this work, the motion of a dust particle under the influence of the random force due to dust charge fluctuations is considered as a non-Markovian stochastic process. Memory effects in the velocity process of the dust particle are studied. A model is developed based on the fractional Langevin equation for the motion of the dust grain. The fluctuation-dissipation theorem for the dust grain is derived from this equation. The mean-square displacement and the velocity autocorrelation function of the dust particle are obtained in terms of the Mittag-Leffler functions. Their asymptotic behavior and the dust particle temperature due to charge fluctuations are studied in the long-time limit. As an interesting result, it is found that the presence of memory effects in the velocity process of the dust particle as a non-Markovian process can cause an anomalous diffusion in dusty plasmas. In this case, the velocity autocorrelation function of the dust particle has a power-law decay like $t^{-\alpha-2}$, where the exponent $\alpha$ take values $0<\alpha<1$.