Gamba Daniele, Cui Bingyu, Zaccone Alessio
Department of Physics "A. Pontremoli," <a href="https://ror.org/00wjc7c48">University of Milan</a>, via Celoria 16, 20133 Milan, Italy.
Institute of Theoretical Physics, <a href="https://ror.org/01y9bpm73">University of Göttingen</a>, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
Phys Rev E. 2024 Nov;110(5-1):054137. doi: 10.1103/PhysRevE.110.054137.
The Langevin equation is ubiquitously employed to numerically simulate plasmas, colloids, and electrolytes. However, the usual assumption of white noise becomes untenable when the system is subject to an external ac electric field. This is because the charged particles in the system, which provide the thermal bath for the particle transport, become themselves responsive to the ac field and the thermal noise is field dependent and non-Markovian. We theoretically study the particle diffusivity in a Langevin transport model for a tagged charged particle immersed in a dense system of charged particles (plus also, possibly, other neutral particles) that act as the thermal bath, under an external ac electric field. This is done by properly accounting for the effects of the ac field on the thermal bath statistics. We analytically derive the time-dependent generalized diffusivity D(t) for different initial conditions. The generalized diffusivity exhibits damped oscillatory-like behavior with initial very large peaks, where the generalized diffusion coefficient is enhanced by orders of magnitude with respect to the infinite-time steady-state value. The latter coincides with the Stokes-Einstein diffusivity in the absence of an external field. For initial conditions where the external field is already on at t=0 and the system is thermalized under dc conditions for t≤0, the short-time behavior is hyperballistic, MSD∼t^{4} (where MSD is the mean-squared displacement), leading to giant enhancement of the particle transport. Finally, the theory elucidates the role of medium polarization on the local Lorentz field, and allows for estimates of the effective electric charge due to polarization by the surrounding charges.
朗之万方程被广泛用于对等离子体、胶体和电解质进行数值模拟。然而，当系统受到外部交流电场作用时，通常的白噪声假设就变得站不住脚了。这是因为系统中的带电粒子为粒子输运提供了热库，它们自身会对交流电场产生响应，热噪声与场相关且是非马尔可夫的。我们从理论上研究了在外部交流电场作用下，一个标记带电粒子浸没在充当热库的带电粒子（可能还包括其他中性粒子）密集系统中的朗之万输运模型中的粒子扩散率。这是通过恰当地考虑交流电场对热库统计特性的影响来实现的。我们针对不同的初始条件解析推导了随时间变化的广义扩散率D(t)。广义扩散率呈现出带有初始非常大峰值的阻尼振荡状行为，其中广义扩散系数相对于无限时间稳态值提高了几个数量级。在没有外部场的情况下，后者与斯托克斯 - 爱因斯坦扩散率一致。对于在t = 0时外部场已经开启且系统在t≤0时在直流条件下热化的初始条件，短时间行为是超弹道的，平均平方位移MSD∼t⁴，导致粒子输运大幅增强。最后该理论阐明了介质极化对局部洛伦兹场的作用，并允许对周围电荷极化引起的有效电荷进行估计。
