Multipoint correlation functions for continuous-time random walk models of anomalous diffusion.
Recursive relations are developed for computing the multipoint correlation functions of a particle undergoing a biased continuous-time random walk (CTRW) in an external potential. Two- and three-point correlation functions are calculated for waiting-time distributions with an anomalous power-law profile t(-alpha-1), 0 < alpha < 1, on intermediate time scales with a crossover to an exponential long time decay. Comparison of the CTRW with the Brownian harmonic oscillator model (Gaussian process) illustrates how higher-order correlation functions may be used to distinguish between dynamical models that have the same two-point correlation function.
Sanda
Frantisek
F
Department of Chemistry, University of California, Irvine, California 92697, USA.
Mukamel
Shaul
S
D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D015233:Models, Statistical; D016008:Statistical Distributions; D013223:Statistics as Topic
D003102:Colloids