Exploiting physical processes for fast and energy-efficient computation bears great potential in the advancement of modern hardware components. This paper explores non-linear charge tunneling in nanoparticle networks, controlled by external voltages. The dynamics are described by a master equation, which describes the development of a distribution function over the set of charge occupation numbers. The driving force behind this evolution are charge tunneling events among nanoparticles and their associated rates. In this paper, we introduce two meanfield approximations to this master equation. By parametrization of the distribution function using its first- and second-order statistical moments, and a subsequent projection of the dynamics onto the resulting moment manifold, one can deterministically calculate expected charges and currents. Unlike a kinetic Monte Carlo approach, which extracts samples from the distribution function, this meanfield approach avoids any random elements. A comparison of results between the meanfield approximation and an already available kinetic Monte Carlo simulation demonstrates great accuracy. Our analysis also reveals that transitioning from a first-order to a second-order approximation significantly enhances the accuracy. Furthermore, we demonstrate the applicability of our approach to time-dependent simulations, using eulerian time-integration schemes.

翻译：利用物理过程实现快速、低能耗计算在现代硬件组件的发展中具有巨大潜力。本文探讨了由外部电压控制的纳米颗粒网络中的非线性电荷隧穿效应。该动力学由主方程描述，该方程刻画了电荷占据数集合上的分布函数演化过程。驱动这一演化的核心因素是纳米颗粒间的电荷隧穿事件及其相关速率。本文针对该主方程引入了两种均场近似方法。通过利用分布函数的一阶和二阶统计矩对其进行参数化，并随后将动力学投影到所得到的矩流形上，可以确定性地计算期望电荷与电流。与从分布函数中提取样本的动力学蒙特卡洛方法不同，本文提出的均场近似方法避免了任何随机元素。将均场近似结果与现有动力学蒙特卡洛模拟进行对比，显示出极高的准确性。我们的分析还表明，从一阶近似过渡到二阶近似可显著提高精度。此外，我们通过欧拉时间积分方案证明了该方法在时变模拟中的适用性。