Complementary mode analyses between sub- and super-diffusions

TL;DR

This paper introduces a mode analysis framework that reveals a duality between sub- and super-diffusive processes, using conjugated variables and polymer physics concepts, with implications for experimental force fluctuation analysis.

Contribution

It proposes a novel mode analysis approach that identifies conjugated variables exhibiting sub- and super-diffusion, enhancing understanding of diffusive behaviors in complex systems.

Findings

Identified conjugated variables undergoing sub- and super-diffusion.

Provided a polymer physics interpretation of the duality.

Suggested experimental relevance through force fluctuation analysis.

Abstract

Several sub-diffusive stochastic processes in nature, e.g., motion of tagged monomer in polymers, height fluctuation of interfaces and particle dynamics in single-file diffusion etc. can be described rigorously or approximately by the superposition of various modes whose relaxation times are broadly distributed. In this paper, we propose a mode analysis generating super-diffusion, which is paired or complementary with that for sub-diffusion. The key point in our discussion lies in the identification of a pair of conjugated variables, which undergoes sub- and super-diffusion, respectively. We provide a simple interpretation for the sub- and superdiffusion duality for these variables using the language of polymer physics. The analysis also suggests the usefulness to look at the force fluctuation in experiments, where a polymer is driven by a constant velocity.