Anomalous Diffusion In Microrheology: A Comparative Study

TL;DR

This paper compares two theoretical models for microrheology, analyzing anomalous diffusion and viscoelastic media, and validates the theories with experimental data.

Contribution

It introduces a comparative analysis of GLE and GFPE models for microrheology, linking fractional kinetics to physical properties.

Findings

GLE explains power-law behavior in viscoelastic media

GFPE is equivalent to GLE under certain conditions

Experimental data supports the theoretical models

Abstract

We present a comparative study on two theoretical descriptions of microrheological experiments. Using a generalized Langevin equation (GLE), we analyze the origin of the power-law behavior of the main properties of a viscoelastic medium. Then, we discuss the equivalence of the GLE with a generalized Fokker-Planck equation (GFPE), and how more general GFPE's can be derived from a thermo-kinetic formalism. These complementary theories lead to a justification for the physical nature of the Hurst exponent of fractional kinetics. Theory is compared with experiments.