{"title":"Bridging classical and quantum dynamics with the Wigner–Moyal equation","authors":"Kyoung Yeon Kim","doi":"10.1007/s10825-025-02426-y","DOIUrl":null,"url":null,"abstract":"<div><p>We present a numerical framework for solving the Wigner–Moyal equation. While Moyal’s form is renowned for its similarity to classical dynamics, it has remained unusable for several decades due to severe numerical instability. This instability arises from the Moyal bracket not being constrained by the uncertainty principle, resulting in unbounded nonlocality. We demonstrate that excessive nonlocality can be suppressed by expanding the observation window to the uncertainty limit, rendering the problem well-posed. Our approach naturally reduces to the Boltzmann equation in regions where quantum effects are negligible; opening a new device simulation methodology that bridges classical and quantum dynamics.</p></div>","PeriodicalId":620,"journal":{"name":"Journal of Computational Electronics","volume":"24 6","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Electronics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10825-025-02426-y","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
We present a numerical framework for solving the Wigner–Moyal equation. While Moyal’s form is renowned for its similarity to classical dynamics, it has remained unusable for several decades due to severe numerical instability. This instability arises from the Moyal bracket not being constrained by the uncertainty principle, resulting in unbounded nonlocality. We demonstrate that excessive nonlocality can be suppressed by expanding the observation window to the uncertainty limit, rendering the problem well-posed. Our approach naturally reduces to the Boltzmann equation in regions where quantum effects are negligible; opening a new device simulation methodology that bridges classical and quantum dynamics.
期刊介绍：
he Journal of Computational Electronics brings together research on all aspects of modeling and simulation of modern electronics. This includes optical, electronic, mechanical, and quantum mechanical aspects, as well as research on the underlying mathematical algorithms and computational details. The related areas of energy conversion/storage and of molecular and biological systems, in which the thrust is on the charge transport, electronic, mechanical, and optical properties, are also covered.
In particular, we encourage manuscripts dealing with device simulation; with optical and optoelectronic systems and photonics; with energy storage (e.g. batteries, fuel cells) and harvesting (e.g. photovoltaic), with simulation of circuits, VLSI layout, logic and architecture (based on, for example, CMOS devices, quantum-cellular automata, QBITs, or single-electron transistors); with electromagnetic simulations (such as microwave electronics and components); or with molecular and biological systems. However, in all these cases, the submitted manuscripts should explicitly address the electronic properties of the relevant systems, materials, or devices and/or present novel contributions to the physical models, computational strategies, or numerical algorithms.
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