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Field-theoretic simulation of Dean-Kawasaki dynamics for interacting particles

Jaehyeok Jin*, Chen Liu†, and David R. Reichman‡

  • *Contact author: jj3296@columbia.edu
  • †Present address: Innovation and Research Division, Ge-Room, Inc., 93160 Noisy le Grand, France.
  • ‡Contact author: drr2103@columbia.edu
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Phys. Rev. E 113, 044138 – Published 29 April, 2026

DOI: https://doi.org/10.1103/d1xd-9tw3

Abstract

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. 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.

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Phys. Rev. E 113, 044138– Published 29 April, 2026
  • Received 6 October 2025
  • Accepted 31 March 2026
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