{"title":"Second-order mean-field approximation for calculating dynamics in Au-nanoparticle networks","authors":"Evan Wonisch, Jonas Mensing, Andreas Heuer","doi":"10.1103/physreve.110.034103","DOIUrl":null,"url":null,"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.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"15 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physreve.110.034103","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
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.
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.