Tóthová Jana, Lisý Vladimír
Department of Physics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Park Komenského 2, Košice 042 00, Slovakia.
Chaos. 2024 Dec 1;34(12). doi: 10.1063/5.0241335.
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.
研究了在外部交流电场影响下，带电粒子液体中标记粒子的广义朗之万方程（GLE）。对于GLE中的分数记忆核，在欠阻尼和过阻尼两种情况下，对粒子的均方位移（MSD）进行了解析研究。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来表示。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。自爱因斯坦和朗之万时代以来，布朗运动理论经历了蓬勃发展，描述溶液中小颗粒不规则运动的方法已在多个科学领域得到应用。在许多实验观察中，该理论中关键量的时间依赖性，如凝聚态物理中粒子MSD，已被证明是反常的，即不同于线性关系。观测粒子的运动表现出周围环境热噪声的相关特性，在不同系统中可能有很大差异，并且与粒子动力学中的记忆效应相关。一种通过GLE方法有效描述复杂系统的选择是使用其摩擦记忆积分的分数核，它取代了原始朗之万运动方程中的斯托克斯摩擦力。在我们的工作中，首次求解了外部振荡电场中浴中粒子系统（粒子可以与周围粒子相同）具有分数记忆的GLE。所有粒子都带电，例如在等离子体或液体电解质中就是这种情况，所以被监测粒子及其周围环境都受到外部场的影响。在整个时间尺度上对GLE进行了解析求解。结果包括经典无记忆朗之万方程的解以及MSD时间依赖性的新特征，包括异常的近弹道或超弹道粒子输运，这取决于外部交流场的施加方式。
