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

M. DESPÓSITO; ANGEL DANIEL VIÑALES

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Año: 2009 vol. 80 p. 1 - 7

1063-651X

A  theoretical framework for analyzing stochastic data from single-particle tracking in viscoelastic materials and  under the influence of a trapping potential is presented. Starting from a generalized Langevin equation we found analytical expressions for thetwo-time dynamics of a  particle subjected to a harmonic potential. The mean square displacement and the velocity autocorrelation function of the diffusing particleare given in terms of the time lag. In particular, we investigate the subdiffusive case.Using a power-law memory kernel, exact expressions for the mean square displacement and the velocity autocorrelation function are obtained in terms of Mittag-Leffler functions and their derivatives. The behavior for short, intermediate and long time lags are investigated in terms of the involved parameters. Finally, the validity of usual approximations are examined.