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

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 $0<\alpha <\beta \le 1$, 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 ($\alpha$) transiently accelerates and eventually regains its intrinsic long-time mobility. This recovery emerges only when memory exponents differ ($\alpha <\beta$), whereas identical exponents ($\alpha =\beta$) suppress recovery. 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.

References in corpus (9)

• Why the Mittag-Leffler function can be considered the Queen function of the Fractional Calculus?
• Anomalous Polymer Dynamics Is Non-Markovian: Memory Effects and The Generalized Langevin Equation Formulation
• Generalized Elastic Model yields Fractional Langevin Equation
• Intracellular microrheology of motile Amoeba proteus
• On the generalized Langevin equation for a Rouse bead in a nonequilibrium bath
• Single cell visualization of transcription kinetics variance of highly mobile identical genes using 3D nanoimaging
• Diffusion of intrinsically disordered proteins within viscoelastic membraneless droplets
• Nonequilibrium diffusion of active particles bound to a semi-flexible polymer network: simulations and fractional Langevin equation
• Hyperphosphorylation-Induced Phase Transition in Vesicle Delivery Dynamics of Motor Proteins in Neuronal Cells