Gaussian closure and dynamical mean-field theory for self-avoiding heteropolymers
Abstract
Analytical treatments of polymer dynamics have mostly been restricted to linear response theory around some steady state obtained via perturbative field theory. Here, I derive an analytical framework that yields unified access to the evolution of conformations, contact probabilities, and fluctuations within a dynamical mean-field theory. Starting with the Langevin equation of a hydrodynamically coupled and self-avoiding heteropolymer, the key idea is to focus on the two-point correlator as the lowest-order relevant observable. Truncating higher-order correlations via a Gaussian closure leads to a self-consistent diffusion equation for the chain correlations. The theory is validated by contrasting coiled, globular, and self-avoiding polymers within a single dynamical framework, and predicts hyper-compacted fractal states in hydrodynamically coupled active polymers such as chromatin.
Cite
@article{arxiv.2604.02085,
title = {Gaussian closure and dynamical mean-field theory for self-avoiding heteropolymers},
author = {Andriy Goychuk},
journal= {arXiv preprint arXiv:2604.02085},
year = {2026}
}