Tracer Particle Dynamics in Heterogeneous Many-body Systems

Abstract: 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 particular 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 correlation factor developed by Nakazato et al.1 is not accurate for a tracer particle that is faster than the surrounding homogeneous crowding particles. 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 distribution. 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, and the exponent decreases almost linearly with increasing interaction strength and is roughly independent on the concentration of crowding particles. Department of Astronomy and Theoretical Physics Lund