Tracer Particles in Two-Dimensional Elastic Networks Diffuse Logarithmically Slow

TL;DR

This paper shows that in a two-dimensional elastic membrane, thermal fluctuations cause tracer particles to diffuse with a logarithmic time dependence, explaining extremely slow anomalous diffusion observed in experiments.

Contribution

It introduces a theoretical model demonstrating logarithmic diffusion of tracer particles due to collective modes in 2D elastic networks, differing from previous power-law models.

Findings

Tracer particles exhibit logarithmic MSD growth in 2D membranes.

Thermal fluctuations excite collective modes causing slow diffusion.

Explains experimental observations of ultra-slow particle movement.

Abstract

Several experiments on tagged molecules or particles in living systems suggest that they move anomalously slow - their mean squared displacement (MSD) increase slower than linearly with time. Leading models aimed at understanding these experiments predict that the MSD grows as a power law with a growth exponent that is smaller than unity. However, in some experiments the exponent is so small $(\sim 0.1-0.2)$ that they hint towards other mechanisms at play. In this paper, we theoretically demonstrate how in-plane collective modes excited by thermal fluctuations in a two dimensional membrane lead to logarithmic time dependence for the mean square displacement of a tracer particle.