Tracer Particle Dynamics in Heterogeneous Many-body Systems

By use of a lattice random walk algorithm we model diffusion in a many-body system and study the mean square displacement (MSD) for a tagged particle for different distributions of crowding particles, with par-ticular emphasis on obtaining the correlation factor which contains the corrections to the mean-field result in such a system. The MSD in such a crowded environment is investigated and we find that the analytical cor-relation factor developed by Nakazato et al.[1] is not accurate for a tracer particle that is faster than the surrounding homogeneous crowding parti-cles. Simulation results for the correlation factor is found for diffusion in a heterogeneous environment, where the friction coefficients of the crowding particles were drawn from a uniform distribution, and a power-law distri-bution. The simulation results can not be fitted to Nakazato’s analytical form for the correlation factor. The MSD of a particle with the same diffusion constant as the crowding particles is investigated for a system where the particles have a probability, proportional to the corresponding Boltzmann factor, to form bonds to their nearest-neighbors. The MSD is found to be subdiffusive, (MSD ∝ tδ, δ < 1) and the exponent δ de-creases almost linearly with increasing interaction strength and is roughly independent on the concentration of crowding particles