Subdiffusive behavior in a trapping potential: mean square displacement and velocity autocorrelation function

TL;DR

This paper develops a theoretical framework based on a generalized Langevin equation to analyze subdiffusive behavior of particles in trapping potentials, providing explicit formulas for mean square displacement and velocity autocorrelation functions.

Contribution

It introduces exact solutions for particle dynamics in complex media and examines the validity of common approximations in subdiffusive systems.

Findings

Explicit expressions for MSD and VACF in subdiffusive regimes

Validation of theoretical models against approximations

Insights into particle behavior in viscoelastic and trapping environments

Abstract

A theoretical framework for analyzing stochastic data from single-particle tracking in complex or viscoelastic materials and under the influence of a trapping potential is presented. Starting from a generalized Langevin equation we found explicit expressions for the two-time dynamics of the tracer particle. The mean square displacement and the velocity autocorrelation function of the diffusing particle are given in terms of the time lag. In particular, we investigate the subdiffusive case. The exact solutions are discussed and the validity of usual approximations are examined.