标题： 场论模拟相互作用粒子的Dean-Kawasaki动力学 显示英文标题

标题： Field-Theoretic Simulation of Dean-Kawasaki Dynamics for Interacting Particles

摘要： 对相互作用粒子的波动流体动力学理论的建立是液体理论描述中的关键步骤。 几十年前Dean和Kawasaki提出的微观映射在这些问题的分析处理中发挥了核心作用。 然而，这些推导中使用的密度分布的奇异数学性质引发了对所得随机偏微分方程的有效性和实际适用性的担忧，特别是在直接数值模拟中。 最近的努力集中在建立一种严格的粗粒化过程，以使有效的Dean-Kawasaki方程规范化。 在此基础上，我们首次在这样的规范化框架内对弱相互作用流体进行了数值研究。 我们的工作揭示了在结构相关性层面，正则化对Dean-Kawasaki形式化的影响，并为改进液体中波动流体动力学的数值方法铺平了道路。 显示英文摘要

摘要： The formulation of a fluctuating hydrodynamic theory for interacting particles is a crucial step in the theoretical description of liquids. The microscopic mappings proposed decades ago by Dean and Kawasaki have played a central role in the analytical treatment of such problems. However, the singular mathematical nature of the density distributions used in these derivations raises concerns about the validity and practical utility of the resulting stochastic partial differential equations, particularly for direct numerical simulations. Recent efforts have centered on establishing a rigorous coarse-graining procedure to regularize the effective Dean-Kawasaki equation. Building on this foundation, we numerically investigate weakly interacting fluids within such a regularized framework for the first time. Our work reveals, at the level of structural correlations, the effects of regularization on the Dean-Kawasaki formalism and paves the way for improved numerical approaches to simulate fluctuating hydrodynamics in liquids.