Fractional hyper-ballistic transport under external oscillating electric fields.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED Chaos Pub Date : 2024-12-01 DOI:10.1063/5.0241335
Jana Tóthová, Vladimír Lisý
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Abstract

The generalized Langevin equation (GLE) for a tagged particle in a liquid of charged particles under the influence of external AC electric fields is studied. For the fractional memory kernel in the GLE, the mean square displacement (MSD) of the particle is studied analytically in both the underdamped and overdamped regimes. The MSD consists of a part corresponding to the absence of the external field and a part affected by the external field, which is expressed through the mean velocity of the particle. We have identified the time windows when the particle shows unusual behaviors in the oscillating fields including hyper-ballistic diffusion, thus generalizing the results for the memoryless Brownian motion. The theory of Brownian motion, since the time of Einstein and Langevin, has overcome a stormy development and the methods of the description of the irregular movement of small particles in solutions have found use in several areas of science. The time dependence of the key quantities in this theory, such as the particle's MSD in condensed matter physics, has been shown to be anomalous, that is, different from linear, in many experimental observations. The movement of the observed particle shows correlation properties of the thermal noise of the surrounding environment, which can be very different in different systems and are associated with memory effects in the dynamics of the particle. One option, effective in describing complex systems by the method of the GLE, is the use of the fractional kernel of its frictional memory integral that replaces the Stokes friction force in the original Langevin equation of motion. In our work, for the first time, we solve such a GLE with a fractional memory for a particle-in-bath system (the particle can be identical with the surrounding particles) in an external oscillating electric field. All particles are charged, as is the case, for example, in plasma or liquid electrolytes, so both the monitored particle and its surroundings are affected by the external field. The GLE is solved analytically for the entire time scale. The results include solutions to the classical memoryless Langevin equation and new features in the time dependence of the MSD, including unusual near-ballistic or hyper-ballistic particle transport, depending on the way the external AC field is applied.

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研究了在外部交流电场影响下,带电粒子液体中的标记粒子的广义朗格文方程(GLE)。对于 GLE 中的分数记忆核,粒子的均方根位移 (MSD) 在欠阻尼和过阻尼两种情况下都是通过分析来研究的。MSD 由对应于无外部场的部分和受外部场影响的部分组成,后者通过粒子的平均速度表示。我们确定了粒子在振荡场中表现出异常行为(包括超弹道扩散)的时间窗口,从而推广了无记忆布朗运动的结果。自爱因斯坦和朗格文时代以来,布朗运动理论经历了风风雨雨的发展,描述溶液中微小粒子不规则运动的方法已在多个科学领域得到应用。这一理论中关键量的时间依赖性,如凝聚态物理学中粒子的 MSD,在许多实验观测中被证明是反常的,即不同于线性。观察到的粒子运动显示了周围环境热噪声的相关特性,这些特性在不同的系统中可能非常不同,并与粒子动力学中的记忆效应有关。在用 GLE 方法描述复杂系统时,一种有效的方法是使用其摩擦记忆积分的分数内核来替代原始朗之文运动方程中的斯托克斯摩擦力。在我们的工作中,我们首次求解了外部振荡电场中的 "浴中粒子 "系统(粒子可以与周围的粒子相同)的分数记忆 GLE。所有粒子都带电,例如在等离子体或液体电解质中,因此被监测粒子及其周围环境都会受到外部电场的影响。GLE 在整个时间尺度上都是通过分析求解的。结果包括经典无记忆朗格文方程的解法和 MSD 随时间变化的新特征,包括不寻常的近弹道或超弹道粒子传输,这取决于外部交流场的应用方式。
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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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