Second-order mean-field approximation for calculating dynamics in Au-nanoparticle networks

IF 2.4 3区 物理与天体物理 Q1 Mathematics Physical review. E Pub Date : 2024-09-03 DOI:10.1103/physreve.110.034103
Evan Wonisch, Jonas Mensing, Andreas Heuer
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Abstract

Exploiting physical processes for fast and energy-efficient computation bears great potential in the advancement of modern hardware components. This paper explores nonlinear charge tunneling in nanoparticle networks, controlled by external voltages. The dynamics are described by a master equation, which expresses the time-evolution of a distribution function over the set of charge occupation numbers. The driving force behind this evolution is charge tunneling events among nanoparticles and their associated rates. We introduce two mean-field 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 mean-field approach avoids any random elements. A comparison of results between the mean-field 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.

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计算金纳米粒子网络动态的二阶均场近似方法
利用物理过程进行快速、高能效计算,对现代硬件元件的发展具有巨大潜力。本文探讨了纳米粒子网络中由外部电压控制的非线性电荷隧穿。其动态由主方程描述,该方程表达了电荷占位数分布函数的时间演化。这种演变背后的驱动力是纳米粒子之间的电荷隧道事件及其相关速率。我们为这个主方程引入了两个均场近似值。通过使用一阶和二阶统计矩对分布函数进行参数化,并随后将动力学投影到所得到的矩流形上,就可以确定性地计算出预期电荷和电流。与从分布函数中提取样本的动力学蒙特卡罗方法不同,这种均值场方法避免了任何随机因素。对均值场近似和已有的动力学蒙特卡洛模拟结果进行比较,结果表明两者的精确度都很高。我们的分析还显示,从一阶近似过渡到二阶近似能显著提高精确度。此外,我们还利用欧拉时间积分方案证明了我们的方法适用于随时间变化的模拟。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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