Karl Fogelmark

**Tracer particle dynamics in heterogeneous many-body systems**

Master Thesis in Theoretical Physics

**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. (K. Nakazato and K. Kitahara, Prog. Theor. Phys vol 64 (6), 2261-2264,1980) 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, (MSD ∝ t

^{δ}, δ<1) and the exponent δ decreases almost linearly with increasing interaction strength and is roughly independent on the concentration of crowding particles.

LU TP 10-18