A Bottom-Up Field-Theoretic Framework via Hierarchical Coarse-Graining: Generalized Mode Theory

Fuente: arXiv
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Main Authors: Jin, Jaehyeok, Han, Yining, Voth, Gregory A.
Format: Preprint
Published: 2025
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author Jin, Jaehyeok
Han, Yining
Voth, Gregory A.
author_facet Jin, Jaehyeok
Han, Yining
Voth, Gregory A.
contents Multiscale simulations facilitate the efficient exploration of large spatiotemporal scales in chemical and physical systems, yet particle-based simulations become prohibitively expensive at time and length scales beyond the molecular level. Field-theoretic simulations offer an attractive alternative, but most existing formulations rely on top-down approximations and are not systematically connected to atomistic interactions. Here, we present a hierarchical bottom-up framework for constructing auxiliary field representations of molecular liquids directly from microscopic models. We introduce a hierarchical coarse-graining framework that constructs field-theoretic models directly from atomistic liquids. The method first maps atomistic interactions to coarse-grained center-of-mass potentials and regularizes short-range divergences through a perturbative expansion in reciprocal space. Building on the auxiliary field formulation developed in polymer field-theoretic simulations, we then generalize the Hubbard-Stratonovich transformation to arbitrary pair potentials by separating positive and negative Fourier modes and introducing two auxiliary fields. The resulting generalized mode theory extends bottom-up field-theoretic modeling beyond positive-definite kernels and is compatible with existing field-theoretic sampling strategies. By combining formal derivations with numerical regularization and mode-truncation procedures, this work provides the theoretical foundation for scalable, bottom-up field-theoretic simulations of molecular systems.
format Preprint
id arxiv_https___arxiv_org_abs_2508_20025
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Bottom-Up Field-Theoretic Framework via Hierarchical Coarse-Graining: Generalized Mode Theory
Jin, Jaehyeok
Han, Yining
Voth, Gregory A.
Chemical Physics
Mesoscale and Nanoscale Physics
Soft Condensed Matter
Statistical Mechanics
Computational Physics
Multiscale simulations facilitate the efficient exploration of large spatiotemporal scales in chemical and physical systems, yet particle-based simulations become prohibitively expensive at time and length scales beyond the molecular level. Field-theoretic simulations offer an attractive alternative, but most existing formulations rely on top-down approximations and are not systematically connected to atomistic interactions. Here, we present a hierarchical bottom-up framework for constructing auxiliary field representations of molecular liquids directly from microscopic models. We introduce a hierarchical coarse-graining framework that constructs field-theoretic models directly from atomistic liquids. The method first maps atomistic interactions to coarse-grained center-of-mass potentials and regularizes short-range divergences through a perturbative expansion in reciprocal space. Building on the auxiliary field formulation developed in polymer field-theoretic simulations, we then generalize the Hubbard-Stratonovich transformation to arbitrary pair potentials by separating positive and negative Fourier modes and introducing two auxiliary fields. The resulting generalized mode theory extends bottom-up field-theoretic modeling beyond positive-definite kernels and is compatible with existing field-theoretic sampling strategies. By combining formal derivations with numerical regularization and mode-truncation procedures, this work provides the theoretical foundation for scalable, bottom-up field-theoretic simulations of molecular systems.
title A Bottom-Up Field-Theoretic Framework via Hierarchical Coarse-Graining: Generalized Mode Theory
topic Chemical Physics
Mesoscale and Nanoscale Physics
Soft Condensed Matter
Statistical Mechanics
Computational Physics
url https://arxiv.org/abs/2508.20025