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Anomalous diffusion in coupled viscoelastic media: A fractional Langevin equation approach

Chan Lim1 and Jae-Hyung Jeon1,2,3,*

  • *Contact author: jeonjh@postech.ac.kr
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Phys. Rev. Research 7, 043356 – Published 31 December, 2025

DOI: https://doi.org/10.1103/thv9-s9mq

Abstract

Anomalous diffusion often arises in complex environments where viscoelastic or crowded conditions influence particle motion. In many biological and soft-matter systems, distinct components of the medium exhibit unique viscoelastic responses, resulting in time-dependent changes in the observed diffusion exponents. Here, we develop a theoretical model of two particles, each embedded in a distinct viscoelastic medium, and coupled via a harmonic potential. By formulating and solving a system of coupled fractional Langevin equations (FLEs) with memory exponents 0<α<β≤1, we uncover rich transient anomalous diffusion phenomena arising from the interplay of memory kernels and bilinear coupling. Notably, we identify “recovery dynamics,” where a subdiffusive particle (α) transiently accelerates and eventually regains its intrinsic long-time mobility. This recovery emerges only when memory exponents differ (α<β), whereas identical exponents (α=β) suppress recovery. Our FLE models are further validated in comparison with Langevin dynamics simulations of polymer-based real systems. Our theoretical predictions offer insight into experimentally observed transient anomalous diffusions, such as polymer-protein complexes and cross-linked cytoskeletal networks, highlighting the critical role of memory heterogeneity and mechanical interactions in biological anomalous diffusion.

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Phys. Rev. Research 7, 043356– Published 31 December, 2025
  • Received 17 July 2025
  • Accepted 14 December 2025
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